* [misc]progress: [Phase 1 of 3] Setting up. * * * [misc]progress: [1/2] Preparing points * * * * [misc]points: Sampling 256 additional inputs, on iter 0 have 0 / 256 * * * * [misc]points: Computing exacts on every 16 of 256 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 64 * * * * [misc]points: Setting MPFR precision to 320 * * * * [misc]points: Computing exacts on every 8 of 256 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 64 * * * * [misc]points: Setting MPFR precision to 320 * * * * [misc]points: Computing exacts on every 4 of 256 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 64 * * * * [misc]points: Setting MPFR precision to 320 * * * * [misc]points: Computing exacts on every 2 of 256 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 64 * * * * [misc]points: Setting MPFR precision to 320 * * * * [misc]points: Computing exacts for 256 points * * * * [misc]points: Setting MPFR precision to 64 * * * * [misc]points: Setting MPFR precision to 320 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 128 additional inputs, on iter 1 have 128 / 256 * * * * [misc]points: Computing exacts on every 8 of 128 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 64 * * * * [misc]points: Setting MPFR precision to 320 * * * * [misc]points: Computing exacts on every 4 of 128 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 64 * * * * [misc]points: Setting MPFR precision to 320 * * * * [misc]points: Computing exacts on every 2 of 128 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 64 * * * * [misc]points: Setting MPFR precision to 320 * * * * [misc]points: Computing exacts for 128 points * * * * [misc]points: Setting MPFR precision to 64 * * * * [misc]points: Setting MPFR precision to 320 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 73 additional inputs, on iter 2 have 183 / 256 * * * * [misc]points: Computing exacts on every 4 of 73 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 64 * * * * [misc]points: Setting MPFR precision to 320 * * * * [misc]points: Computing exacts on every 2 of 73 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 64 * * * * [misc]points: Setting MPFR precision to 320 * * * * [misc]points: Computing exacts for 73 points * * * * [misc]points: Setting MPFR precision to 64 * * * * [misc]points: Setting MPFR precision to 320 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 38 additional inputs, on iter 3 have 218 / 256 * * * * [misc]points: Computing exacts on every 2 of 38 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 64 * * * * [misc]points: Setting MPFR precision to 320 * * * * [misc]points: Computing exacts for 38 points * * * * [misc]points: Setting MPFR precision to 64 * * * * [misc]points: Setting MPFR precision to 320 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 23 additional inputs, on iter 4 have 233 / 256 * * * * [misc]points: Computing exacts for 23 points * * * * [misc]points: Setting MPFR precision to 64 * * * * [misc]points: Setting MPFR precision to 320 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 9 additional inputs, on iter 5 have 247 / 256 * * * * [misc]points: Computing exacts for 9 points * * * * [misc]points: Setting MPFR precision to 64 * * * * [misc]points: Setting MPFR precision to 320 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 4 additional inputs, on iter 6 have 252 / 256 * * * * [misc]points: Computing exacts for 4 points * * * * [misc]points: Setting MPFR precision to 64 * * * * [misc]points: Setting MPFR precision to 320 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [exit]points: Sampled 256 points with exact outputs * * * [misc]progress: [2/2] Setting up program. * [misc]progress: [Phase 2 of 3] Improving. * [enter]simplify: Simplifying (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (223 enodes) * [exit]simplify: Simplified to (* (/ (- 1 (* v v)) (/ 4 (sqrt 2))) (sqrt (+ (* -3 (* v v)) 1))) * * [misc]progress: iteration 1 / 4 * * * [misc]progress: picking best candidate * * * * [misc]pick: Picked # * * * [misc]progress: localizing error * * * [misc]progress: generating rewritten candidates * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 1 2 1 2) * * * * [misc]progress: [ 2 / 4 ] rewriting at (2) * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 1) * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 1 2) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 4 ] generating series at (2 1 2 1 2) * [misc]approximate: Taking taylor expansion of (* 3 (* v v)) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 3 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 1) (* 0 0))) into 1 * [misc]backup-simplify: Simplify (+ (* 3 1) (+ (* 0 0) (* 0 0))) into 3 * [misc]backup-simplify: Simplify 3 into 3 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 1) (+ (* 0 0) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0))))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* 3 (pow v 2)) into (* 3 (pow v 2)) * [misc]approximate: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify 3 into 3 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* 3 (pow (/ 1 (/ 1 v)) 2)) into (* 3 (pow v 2)) * [misc]approximate: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify 3 into 3 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* 3 (pow (/ 1 (/ 1 (- v))) 2)) into (* 3 (pow v 2)) * * * * [misc]progress: [ 2 / 4 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* v v)))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* v v))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 3 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1))) into 0 * [misc]taylor: Taking taylor expansion of (- 1 (* v v)) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* v v)))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* v v))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 3 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1))) into 0 * [misc]taylor: Taking taylor expansion of (- 1 (* v v)) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) 1) into (* 1/4 (sqrt 2)) * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) 1) into (* 1/4 (sqrt 2)) * [misc]backup-simplify: Simplify (* 1/4 (sqrt 2)) into (* 1/4 (sqrt 2)) * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 1) (* 0 0))) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 1) (* 0 0))) into 1 * [misc]backup-simplify: Simplify (+ (* 3 1) (+ (* 0 0) (* 0 0))) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (/ (- -3 (pow 0 2) (+)) (* 2 1)) into -3/2 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -3/2) (+ (* 0 0) (* 0 1))) into (- (* 3/8 (sqrt 2))) * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -1) (+ (* 0 0) (* (- (* 3/8 (sqrt 2))) 1))) into (- (* 5/8 (sqrt 2))) * [misc]backup-simplify: Simplify (- (* 5/8 (sqrt 2))) into (- (* 5/8 (sqrt 2))) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 1) (+ (* 0 0) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 -3/2)))) (* 2 1)) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 -3/2) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 -1) (+ (* (- (* 3/8 (sqrt 2))) 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow -3/2 2) (+ (* 2 (* 0 0)))) (* 2 1)) into -9/8 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -9/8) (+ (* 0 0) (+ (* 0 -3/2) (+ (* 0 0) (* 0 1))))) into (- (* 9/32 (sqrt 2))) * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 0) (+ (* (- (* 3/8 (sqrt 2))) -1) (+ (* 0 0) (* (- (* 9/32 (sqrt 2))) 1))))) into (* 3/32 (sqrt 2)) * [misc]backup-simplify: Simplify (* 3/32 (sqrt 2)) into (* 3/32 (sqrt 2)) * [misc]backup-simplify: Simplify (+ (* (* 3/32 (sqrt 2)) (pow v 4)) (+ (* (- (* 5/8 (sqrt 2))) (pow v 2)) (* 1/4 (sqrt 2)))) into (- (+ (* 1/4 (sqrt 2)) (* 3/32 (* (sqrt 2) (pow v 4)))) (* 5/8 (* (sqrt 2) (pow v 2)))) * [misc]approximate: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- 1 (* (/ 1 v) (/ 1 v)))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- 1 (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (- 1 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- 1 (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (- 1 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) (sqrt -3)) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (* (* 1/4 (* (sqrt 2) (sqrt -3))) -1) into (* -1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* -1/4 (* (sqrt 2) (sqrt -3))) into (* -1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ (- 1 (pow 0 2) (+)) (* 2 (sqrt -3))) into (/ 1/2 (sqrt -3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))) into (* 1/8 (/ (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 1) (+ (* 0 0) (* (* 1/8 (/ (sqrt 2) (sqrt -3))) -1))) into (- (* 1/4 (* (sqrt 2) (sqrt -3))) (* 1/8 (/ (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (- (* 1/4 (* (sqrt 2) (sqrt -3))) (* 1/8 (/ (sqrt 2) (sqrt -3)))) into (- (* 1/4 (* (sqrt 2) (sqrt -3))) (* 1/8 (/ (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (/ 1/2 (sqrt -3)))))) (* 2 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 1) (+ (* (* 1/8 (/ (sqrt 2) (sqrt -3))) 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ 1/2 (sqrt -3)) 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt -3))) into (/ -1/8 (pow (sqrt -3) 3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ -1/8 (pow (sqrt -3) 3))) (+ (* 0 0) (+ (* 0 (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))))) into (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (+ (* (* 1/8 (/ (sqrt 2) (sqrt -3))) 1) (+ (* 0 0) (* (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) -1))))) into (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) * [misc]backup-simplify: Simplify (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) into (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) * [misc]backup-simplify: Simplify (+ (* (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) (/ 1 v)) (+ (* (- (* 1/4 (* (sqrt 2) (sqrt -3))) (* 1/8 (/ (sqrt 2) (sqrt -3)))) (/ 1 (/ 1 v))) (* (* -1/4 (* (sqrt 2) (sqrt -3))) (pow (/ 1 (/ 1 v)) 3)))) into (- (+ (* 1/32 (/ (sqrt 2) (* v (pow (sqrt -3) 3)))) (+ (* 1/4 (* (sqrt 2) (* v (sqrt -3)))) (* 1/8 (/ (sqrt 2) (* v (sqrt -3)))))) (+ (* 1/8 (/ (* (sqrt 2) v) (sqrt -3))) (* 1/4 (* (sqrt 2) (* (pow v 3) (sqrt -3)))))) * [misc]approximate: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- 1 (* (/ 1 (- v)) (/ 1 (- v))))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- 1 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (- 1 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- 1 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (- 1 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) (sqrt -3)) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (* (* 1/4 (* (sqrt 2) (sqrt -3))) -1) into (* -1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* -1/4 (* (sqrt 2) (sqrt -3))) into (* -1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ (- 1 (pow 0 2) (+)) (* 2 (sqrt -3))) into (/ 1/2 (sqrt -3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))) into (* 1/8 (/ (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 1) (+ (* 0 0) (* (* 1/8 (/ (sqrt 2) (sqrt -3))) -1))) into (- (* 1/4 (* (sqrt 2) (sqrt -3))) (* 1/8 (/ (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (- (* 1/4 (* (sqrt 2) (sqrt -3))) (* 1/8 (/ (sqrt 2) (sqrt -3)))) into (- (* 1/4 (* (sqrt 2) (sqrt -3))) (* 1/8 (/ (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (/ 1/2 (sqrt -3)))))) (* 2 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 1) (+ (* (* 1/8 (/ (sqrt 2) (sqrt -3))) 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ 1/2 (sqrt -3)) 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt -3))) into (/ -1/8 (pow (sqrt -3) 3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ -1/8 (pow (sqrt -3) 3))) (+ (* 0 0) (+ (* 0 (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))))) into (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (+ (* (* 1/8 (/ (sqrt 2) (sqrt -3))) 1) (+ (* 0 0) (* (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) -1))))) into (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) * [misc]backup-simplify: Simplify (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) into (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) * [misc]backup-simplify: Simplify (+ (* (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) (/ 1 (- v))) (+ (* (- (* 1/4 (* (sqrt 2) (sqrt -3))) (* 1/8 (/ (sqrt 2) (sqrt -3)))) (/ 1 (/ 1 (- v)))) (* (* -1/4 (* (sqrt 2) (sqrt -3))) (pow (/ 1 (/ 1 (- v))) 3)))) into (- (+ (* 1/8 (/ (* (sqrt 2) v) (sqrt -3))) (* 1/4 (* (sqrt 2) (* (pow v 3) (sqrt -3))))) (+ (* 1/32 (/ (sqrt 2) (* v (pow (sqrt -3) 3)))) (+ (* 1/4 (* (sqrt 2) (* v (sqrt -3)))) (* 1/8 (/ (sqrt 2) (* v (sqrt -3))))))) * * * * [misc]progress: [ 3 / 4 ] generating series at (2 1) * [misc]approximate: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* v v)))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* v v))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 3 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1))) into 0 * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* v v)))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* v v))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 3 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1))) into 0 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) 1) into (* 1/4 (sqrt 2)) * [misc]backup-simplify: Simplify (* 1/4 (sqrt 2)) into (* 1/4 (sqrt 2)) * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 1) (* 0 0))) into 1 * [misc]backup-simplify: Simplify (+ (* 3 1) (+ (* 0 0) (* 0 0))) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (/ (- -3 (pow 0 2) (+)) (* 2 1)) into -3/2 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -3/2) (+ (* 0 0) (* 0 1))) into (- (* 3/8 (sqrt 2))) * [misc]backup-simplify: Simplify (- (* 3/8 (sqrt 2))) into (- (* 3/8 (sqrt 2))) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 1) (+ (* 0 0) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 -3/2)))) (* 2 1)) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 -3/2) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow -3/2 2) (+ (* 2 (* 0 0)))) (* 2 1)) into -9/8 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -9/8) (+ (* 0 0) (+ (* 0 -3/2) (+ (* 0 0) (* 0 1))))) into (- (* 9/32 (sqrt 2))) * [misc]backup-simplify: Simplify (- (* 9/32 (sqrt 2))) into (- (* 9/32 (sqrt 2))) * [misc]backup-simplify: Simplify (+ (* (- (* 9/32 (sqrt 2))) (pow v 4)) (+ (* (- (* 3/8 (sqrt 2))) (pow v 2)) (* 1/4 (sqrt 2)))) into (- (* 1/4 (sqrt 2)) (+ (* 9/32 (* (sqrt 2) (pow v 4))) (* 3/8 (* (sqrt 2) (pow v 2))))) * [misc]approximate: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) (sqrt -3)) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* 1/4 (* (sqrt 2) (sqrt -3))) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ (- 1 (pow 0 2) (+)) (* 2 (sqrt -3))) into (/ 1/2 (sqrt -3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))) into (* 1/8 (/ (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* 1/8 (/ (sqrt 2) (sqrt -3))) into (* 1/8 (/ (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (/ 1/2 (sqrt -3)))))) (* 2 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ 1/2 (sqrt -3)) 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt -3))) into (/ -1/8 (pow (sqrt -3) 3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ -1/8 (pow (sqrt -3) 3))) (+ (* 0 0) (+ (* 0 (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))))) into (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) * [misc]backup-simplify: Simplify (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) into (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) * [misc]backup-simplify: Simplify (+ (* (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) (pow (/ 1 v) 3)) (+ (* (* 1/8 (/ (sqrt 2) (sqrt -3))) (/ 1 v)) (* (* 1/4 (* (sqrt 2) (sqrt -3))) (/ 1 (/ 1 v))))) into (- (+ (* 1/4 (* (sqrt 2) (* v (sqrt -3)))) (* 1/8 (/ (sqrt 2) (* v (sqrt -3))))) (* 1/32 (/ (sqrt 2) (* (pow v 3) (pow (sqrt -3) 3))))) * [misc]approximate: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) (sqrt -3)) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* 1/4 (* (sqrt 2) (sqrt -3))) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ (- 1 (pow 0 2) (+)) (* 2 (sqrt -3))) into (/ 1/2 (sqrt -3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))) into (* 1/8 (/ (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* 1/8 (/ (sqrt 2) (sqrt -3))) into (* 1/8 (/ (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (/ 1/2 (sqrt -3)))))) (* 2 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ 1/2 (sqrt -3)) 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt -3))) into (/ -1/8 (pow (sqrt -3) 3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ -1/8 (pow (sqrt -3) 3))) (+ (* 0 0) (+ (* 0 (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))))) into (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) * [misc]backup-simplify: Simplify (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) into (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) * [misc]backup-simplify: Simplify (+ (* (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) (pow (/ 1 (- v)) 3)) (+ (* (* 1/8 (/ (sqrt 2) (sqrt -3))) (/ 1 (- v))) (* (* 1/4 (* (sqrt 2) (sqrt -3))) (/ 1 (/ 1 (- v)))))) into (- (* 1/32 (/ (sqrt 2) (* (pow v 3) (pow (sqrt -3) 3)))) (+ (* 1/4 (* (sqrt 2) (* v (sqrt -3)))) (* 1/8 (/ (sqrt 2) (* v (sqrt -3)))))) * * * * [misc]progress: [ 4 / 4 ] generating series at (2 1 2) * [misc]approximate: Taking taylor expansion of (sqrt (- 1 (* 3 (* v v)))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* v v)))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* v v))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 3 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1))) into 0 * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* v v)))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* v v))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 3 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1))) into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 1) (* 0 0))) into 1 * [misc]backup-simplify: Simplify (+ (* 3 1) (+ (* 0 0) (* 0 0))) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (/ (- -3 (pow 0 2) (+)) (* 2 1)) into -3/2 * [misc]backup-simplify: Simplify -3/2 into -3/2 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 1) (+ (* 0 0) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 -3/2)))) (* 2 1)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow -3/2 2) (+ (* 2 (* 0 0)))) (* 2 1)) into -9/8 * [misc]backup-simplify: Simplify -9/8 into -9/8 * [misc]backup-simplify: Simplify (+ (* -9/8 (pow v 4)) (+ (* -3/2 (pow v 2)) 1)) into (- 1 (+ (* 9/8 (pow v 4)) (* 3/2 (pow v 2)))) * [misc]approximate: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v))))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ (- 1 (pow 0 2) (+)) (* 2 (sqrt -3))) into (/ 1/2 (sqrt -3)) * [misc]backup-simplify: Simplify (/ 1/2 (sqrt -3)) into (/ 1/2 (sqrt -3)) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (/ 1/2 (sqrt -3)))))) (* 2 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ 1/2 (sqrt -3)) 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt -3))) into (/ -1/8 (pow (sqrt -3) 3)) * [misc]backup-simplify: Simplify (/ -1/8 (pow (sqrt -3) 3)) into (/ -1/8 (pow (sqrt -3) 3)) * [misc]backup-simplify: Simplify (+ (* (/ -1/8 (pow (sqrt -3) 3)) (pow (/ 1 v) 3)) (+ (* (/ 1/2 (sqrt -3)) (/ 1 v)) (* (sqrt -3) (/ 1 (/ 1 v))))) into (- (+ (* 1/2 (/ 1 (* (sqrt -3) v))) (* (sqrt -3) v)) (* 1/8 (/ 1 (* (pow (sqrt -3) 3) (pow v 3))))) * [misc]approximate: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v)))))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ (- 1 (pow 0 2) (+)) (* 2 (sqrt -3))) into (/ 1/2 (sqrt -3)) * [misc]backup-simplify: Simplify (/ 1/2 (sqrt -3)) into (/ 1/2 (sqrt -3)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (/ 1/2 (sqrt -3)))))) (* 2 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ 1/2 (sqrt -3)) 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt -3))) into (/ -1/8 (pow (sqrt -3) 3)) * [misc]backup-simplify: Simplify (/ -1/8 (pow (sqrt -3) 3)) into (/ -1/8 (pow (sqrt -3) 3)) * [misc]backup-simplify: Simplify (+ (* (/ -1/8 (pow (sqrt -3) 3)) (pow (/ 1 (- v)) 3)) (+ (* (/ 1/2 (sqrt -3)) (/ 1 (- v))) (* (sqrt -3) (/ 1 (/ 1 (- v)))))) into (- (* 1/8 (/ 1 (* (pow (sqrt -3) 3) (pow v 3)))) (+ (* 1/2 (/ 1 (* (sqrt -3) v))) (* (sqrt -3) v))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 2 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 3 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 4 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 5 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 6 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 7 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 8 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 9 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 10 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (223 enodes) * [exit]simplify: Simplified to (* (/ (- 1 (* v v)) (/ 4 (sqrt 2))) (sqrt (+ (* -3 (* v v)) 1))) * [misc]simplify: Simplified (2 1) to (λ (v) (pow (* (/ (- 1 (* v v)) (/ 4 (sqrt 2))) (sqrt (+ (* -3 (* v v)) 1))) 1)) * * * * [misc]progress: [ 11 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (223 enodes) * [exit]simplify: Simplified to (* (/ (- 1 (* v v)) (/ 4 (sqrt 2))) (sqrt (+ (* -3 (* v v)) 1))) * [misc]simplify: Simplified (2 1) to (λ (v) (pow (* (/ (- 1 (* v v)) (/ 4 (sqrt 2))) (sqrt (+ (* -3 (* v v)) 1))) 1)) * * * * [misc]progress: [ 12 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 13 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (+ (log (/ (sqrt 2) 4)) (log (sqrt (- 1 (* 3 (* v v)))))) (log (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (100 enodes) * * [misc]simplify: iters left: 2 (143 enodes) * * [misc]simplify: iters left: 1 (236 enodes) * [exit]simplify: Simplified to (+ (+ (log (/ (sqrt 2) 4)) (log (- 1 (* v v)))) (log (sqrt (+ 1 (* v (* -3 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (exp (+ (+ (log (/ (sqrt 2) 4)) (log (- 1 (* v v)))) (log (sqrt (+ 1 (* v (* -3 v)))))))) * * * * [misc]progress: [ 14 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))) (log (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (128 enodes) * * [misc]simplify: iters left: 1 (183 enodes) * [exit]simplify: Simplified to (+ (log (sqrt (+ 1 (* -3 (* v v))))) (+ (log (- 1 (* v v))) (log (/ (sqrt 2) 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (exp (+ (log (sqrt (+ 1 (* -3 (* v v))))) (+ (log (- 1 (* v v))) (log (/ (sqrt 2) 4)))))) * * * * [misc]progress: [ 15 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 16 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 17 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (* (/ (sqrt 2) 4) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)) (* (* (sqrt (- 1 (* 3 (* v v)))) (sqrt (- 1 (* 3 (* v v))))) (sqrt (- 1 (* 3 (* v v)))))) (* (* (- 1 (* v v)) (- 1 (* v v))) (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (189 enodes) * [exit]simplify: Simplified to (* (* (- 1 (* v v)) (/ (* 1/2 (sqrt 2)) 16)) (* (sqrt (+ 1 (* v (* -3 v)))) (* (+ 1 (* v (* -3 v))) (* (- 1 (* v v)) (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (cbrt (* (* (- 1 (* v v)) (/ (* 1/2 (sqrt 2)) 16)) (* (sqrt (+ 1 (* v (* -3 v)))) (* (+ 1 (* v (* -3 v))) (* (- 1 (* v v)) (- 1 (* v v)))))))) * * * * [misc]progress: [ 18 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))) (* (* (- 1 (* v v)) (- 1 (* v v))) (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (152 enodes) * [exit]simplify: Simplified to (* (* (sqrt (+ (* v (* v -3)) 1)) (* (/ (sqrt 2) 4) (/ (sqrt 2) 4))) (* (+ (* v (* v -3)) 1) (* (* (/ (sqrt 2) 4) (- 1 (* v v))) (* (- 1 (* v v)) (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (cbrt (* (* (sqrt (+ (* v (* v -3)) 1)) (* (/ (sqrt 2) 4) (/ (sqrt 2) 4))) (* (+ (* v (* v -3)) 1) (* (* (/ (sqrt 2) 4) (- 1 (* v v))) (* (- 1 (* v v)) (- 1 (* v v)))))))) * * * * [misc]progress: [ 19 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 20 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 21 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 22 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (pow 1 3) (pow (* v v) 3))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (113 enodes) * * [misc]simplify: iters left: 3 (438 enodes) * [exit]simplify: Simplified to (* (* (sqrt 2) (- 1 (* v (pow v 5)))) (sqrt (- 1 (* (* v 27) (pow v 5))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (* (sqrt 2) (- 1 (* v (pow v 5)))) (sqrt (- 1 (* (* v 27) (pow v 5))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * [enter]simplify: Simplifying (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (61 enodes) * * [misc]simplify: iters left: 4 (197 enodes) * [exit]simplify: Simplified to (* (+ (* (* 4 (* v v)) (+ 1 (* v v))) 4) (sqrt (+ (* (* v v) (* (* v v) 9)) (+ 1 (* v (* 3 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (* (sqrt 2) (- 1 (* v (pow v 5)))) (sqrt (- 1 (* (* v 27) (pow v 5))))) (* (+ (* (* 4 (* v v)) (+ 1 (* v v))) 4) (sqrt (+ (* (* v v) (* (* v v) 9)) (+ 1 (* v (* 3 v)))))))) * * * * [misc]progress: [ 23 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* 1 1) (* (* v v) (* v v)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (110 enodes) * * [misc]simplify: iters left: 3 (403 enodes) * [exit]simplify: Simplified to (* (* (- 1 (pow v 4)) (sqrt 2)) (sqrt (- 1 (* (pow v 5) (* v 27))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (* (- 1 (pow v 4)) (sqrt 2)) (sqrt (- 1 (* (pow v 5) (* v 27))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (+ 1 (* v v))))) * [enter]simplify: Simplifying (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (+ 1 (* v v))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (120 enodes) * * [misc]simplify: iters left: 3 (268 enodes) * * [misc]simplify: iters left: 2 (482 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* 3 v) v) (+ (* (* v 9) (pow v 3)) 1))) (+ (* 4 (* v v)) 4)) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (* (- 1 (pow v 4)) (sqrt 2)) (sqrt (- 1 (* (pow v 5) (* v 27))))) (* (sqrt (+ (* (* 3 v) v) (+ (* (* v 9) (pow v 3)) 1))) (+ (* 4 (* v v)) 4)))) * * * * [misc]progress: [ 24 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (pow 1 3) (pow (* v v) 3))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (105 enodes) * * [misc]simplify: iters left: 3 (322 enodes) * [exit]simplify: Simplified to (* (* (sqrt 2) (- 1 (pow (* v v) 3))) (sqrt (- 1 (* (pow v 4) 9)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (* (sqrt 2) (- 1 (pow (* v v) 3))) (sqrt (- 1 (* (pow v 4) 9)))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * [enter]simplify: Simplifying (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (137 enodes) * * [misc]simplify: iters left: 3 (432 enodes) * [exit]simplify: Simplified to (* (+ 4 (* (* v (* v 4)) (+ (* v v) 1))) (sqrt (+ 1 (* v (* v 3))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (* (sqrt 2) (- 1 (pow (* v v) 3))) (sqrt (- 1 (* (pow v 4) 9)))) (* (+ 4 (* (* v (* v 4)) (+ (* v v) 1))) (sqrt (+ 1 (* v (* v 3))))))) * * * * [misc]progress: [ 25 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* 1 1) (* (* v v) (* v v)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (96 enodes) * * [misc]simplify: iters left: 3 (277 enodes) * [exit]simplify: Simplified to (* (* (- 1 (pow v 4)) (sqrt 2)) (sqrt (+ (* (pow v 4) -9) 1))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (* (- 1 (pow v 4)) (sqrt 2)) (sqrt (+ (* (pow v 4) -9) 1))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (+ 1 (* v v))))) * [enter]simplify: Simplifying (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (+ 1 (* v v))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (130 enodes) * * [misc]simplify: iters left: 2 (281 enodes) * * [misc]simplify: iters left: 1 (411 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* v (* 3 v)))) (+ (* v (* v 4)) 4)) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (* (- 1 (pow v 4)) (sqrt 2)) (sqrt (+ (* (pow v 4) -9) 1))) (* (sqrt (+ 1 (* v (* 3 v)))) (+ (* v (* v 4)) 4)))) * * * * [misc]progress: [ 26 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (pow 1 3) (pow (* v v) 3))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (127 enodes) * [exit]simplify: Simplified to (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (- 1 (pow (* v v) 3)) (/ (sqrt 2) 4))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (- 1 (pow (* v v) 3)) (/ (sqrt 2) 4))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * [enter]simplify: Simplifying (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (55 enodes) * * [misc]simplify: iters left: 4 (189 enodes) * * [misc]simplify: iters left: 3 (479 enodes) * [exit]simplify: Simplified to (* (+ (* v v) (+ 1 (pow v 4))) (sqrt (+ 1 (+ (* (* 9 v) (pow v 3)) (* (* v v) 3))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (- 1 (pow (* v v) 3)) (/ (sqrt 2) 4))) (* (+ (* v v) (+ 1 (pow v 4))) (sqrt (+ 1 (+ (* (* 9 v) (pow v 3)) (* (* v v) 3))))))) * * * * [misc]progress: [ 27 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* 1 1) (* (* v v) (* v v)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (124 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt 2) 4) (- 1 (pow v 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (* (/ (sqrt 2) 4) (- 1 (pow v 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (+ 1 (* v v))))) * [enter]simplify: Simplifying (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (+ 1 (* v v))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (109 enodes) * * [misc]simplify: iters left: 3 (256 enodes) * * [misc]simplify: iters left: 2 (413 enodes) * * [misc]simplify: iters left: 1 (477 enodes) * [exit]simplify: Simplified to (* (+ 1 (* v v)) (sqrt (+ 1 (+ (* (* v v) 3) (* 9 (pow v 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (* (/ (sqrt 2) 4) (- 1 (pow v 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (+ 1 (* v v)) (sqrt (+ 1 (+ (* (* v v) 3) (* 9 (pow v 4)))))))) * * * * [misc]progress: [ 28 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (pow 1 3) (pow (* v v) 3))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (119 enodes) * * [misc]simplify: iters left: 3 (400 enodes) * [exit]simplify: Simplified to (* (sqrt (- 1 (* (pow v 4) 9))) (* (/ (sqrt 2) 4) (- 1 (* (pow v 3) (pow v 3))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- 1 (* (pow v 4) 9))) (* (/ (sqrt 2) 4) (- 1 (* (pow v 3) (pow v 3))))) (* (sqrt (+ 1 (* 3 (* v v)))) (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * [enter]simplify: Simplifying (* (sqrt (+ 1 (* 3 (* v v)))) (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (262 enodes) * * [misc]simplify: iters left: 2 (447 enodes) * [exit]simplify: Simplified to (* (+ (+ 1 (* v v)) (pow v 4)) (sqrt (+ 1 (* (* v 3) v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- 1 (* (pow v 4) 9))) (* (/ (sqrt 2) 4) (- 1 (* (pow v 3) (pow v 3))))) (* (+ (+ 1 (* v v)) (pow v 4)) (sqrt (+ 1 (* (* v 3) v)))))) * * * * [misc]progress: [ 29 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* 1 1) (* (* v v) (* v v)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (110 enodes) * * [misc]simplify: iters left: 3 (353 enodes) * [exit]simplify: Simplified to (* (sqrt (- 1 (* 9 (pow v 4)))) (/ (- 1 (pow v 4)) (/ 4 (sqrt 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- 1 (* 9 (pow v 4)))) (/ (- 1 (pow v 4)) (/ 4 (sqrt 2)))) (* (sqrt (+ 1 (* 3 (* v v)))) (+ 1 (* v v))))) * [enter]simplify: Simplifying (* (sqrt (+ 1 (* 3 (* v v)))) (+ 1 (* v v))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (77 enodes) * * [misc]simplify: iters left: 2 (112 enodes) * * [misc]simplify: iters left: 1 (128 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* (* v v) 3))) (+ (* v v) 1)) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- 1 (* 9 (pow v 4)))) (/ (- 1 (pow v 4)) (/ 4 (sqrt 2)))) (* (sqrt (+ 1 (* (* v v) 3))) (+ (* v v) 1)))) * * * * [misc]progress: [ 30 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (pow 1 3) (pow (* v v) 3))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (237 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* -3 v) v) 1)) (* (sqrt 2) (- 1 (pow (* v v) 3)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* -3 v) v) 1)) (* (sqrt 2) (- 1 (pow (* v v) 3)))) (* 4 (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * [enter]simplify: Simplifying (* 4 (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (101 enodes) * * [misc]simplify: iters left: 3 (270 enodes) * [exit]simplify: Simplified to (+ (* (* (* v v) 4) (+ (* v v) 1)) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* -3 v) v) 1)) (* (sqrt 2) (- 1 (pow (* v v) 3)))) (+ (* (* (* v v) 4) (+ (* v v) 1)) 4))) * * * * [misc]progress: [ 31 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* 1 1) (* (* v v) (* v v)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (192 enodes) * * [misc]simplify: iters left: 2 (474 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* (* v v) -3))) (- (sqrt 2) (* (pow v 4) (sqrt 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ 1 (* (* v v) -3))) (- (sqrt 2) (* (pow v 4) (sqrt 2)))) (* 4 (+ 1 (* v v))))) * [enter]simplify: Simplifying (* 4 (+ 1 (* v v))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * [exit]simplify: Simplified to (+ (* (* v v) 4) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ 1 (* (* v v) -3))) (- (sqrt 2) (* (pow v 4) (sqrt 2)))) (+ (* (* v v) 4) 4))) * * * * [misc]progress: [ 32 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 33 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (207 enodes) * * [misc]simplify: iters left: 2 (387 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (* -3 (* v v)))) (/ (/ 4 (* v v)) (- (sqrt 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (/ (sqrt (+ 1 (* -3 (* v v)))) (/ (/ 4 (* v v)) (- (sqrt 2)))))) * * * * [misc]progress: [ 34 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (207 enodes) * * [misc]simplify: iters left: 2 (387 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (* -3 (* v v)))) (/ (/ 4 (* v v)) (- (sqrt 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (/ (sqrt (+ 1 (* -3 (* v v)))) (/ (/ 4 (* v v)) (- (sqrt 2)))))) * * * * [misc]progress: [ 35 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (* (- (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (202 enodes) * * [misc]simplify: iters left: 2 (360 enodes) * * [misc]simplify: iters left: 1 (492 enodes) * [exit]simplify: Simplified to (* (/ (* (sqrt 2) v) (/ 4 (- v))) (sqrt (- 1 (* 3 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (+ (* 1 (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))) (* (/ (* (sqrt 2) v) (/ 4 (- v))) (sqrt (- 1 (* 3 (* v v))))))) * * * * [misc]progress: [ 36 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (* (- (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (202 enodes) * * [misc]simplify: iters left: 2 (360 enodes) * * [misc]simplify: iters left: 1 (492 enodes) * [exit]simplify: Simplified to (* (/ (* (sqrt 2) v) (/ 4 (- v))) (sqrt (- 1 (* 3 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (+ (* 1 (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))) (* (/ (* (sqrt 2) v) (/ 4 (- v))) (sqrt (- 1 (* 3 (* v v))))))) * * * * [misc]progress: [ 37 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (cbrt (- 1 (* v v))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (9 enodes) * * [misc]simplify: iters left: 3 (13 enodes) * [exit]simplify: Simplified to (cbrt (- 1 (* v v))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (cbrt (- 1 (* v v))))) * * * * [misc]progress: [ 38 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (- 1 (* v v))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (9 enodes) * * [misc]simplify: iters left: 3 (13 enodes) * [exit]simplify: Simplified to (sqrt (- 1 (* v v))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (sqrt (- 1 (* v v)))) (sqrt (- 1 (* v v))))) * * * * [misc]progress: [ 39 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (- 1 (* v v)) * * [misc]simplify: iters left: 4 (4 enodes) * * [misc]simplify: iters left: 3 (8 enodes) * * [misc]simplify: iters left: 2 (12 enodes) * [exit]simplify: Simplified to (- 1 (* v v)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (- 1 (* v v)))) * * * * [misc]progress: [ 40 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt 2) 4) * * [misc]simplify: iters left: 3 (4 enodes) * [exit]simplify: Simplified to (/ (sqrt 2) 4) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt 2) 4) (* (sqrt (- 1 (* 3 (* v v)))) (- 1 (* v v))))) * * * * [misc]progress: [ 41 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (87 enodes) * * [misc]simplify: iters left: 2 (118 enodes) * * [misc]simplify: iters left: 1 (146 enodes) * [exit]simplify: Simplified to (+ 1 (+ (* v v) (pow v 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (pow 1 3) (pow (* v v) 3))) (+ 1 (+ (* v v) (pow v 4))))) * * * * [misc]progress: [ 42 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (+ 1 (* v v)) * * [misc]simplify: iters left: 4 (4 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (+ 1 (* v v)) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* 1 1) (* (* v v) (* v v)))) (+ 1 (* v v)))) * * * * [misc]progress: [ 43 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- 1 (* v v))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (99 enodes) * * [misc]simplify: iters left: 3 (366 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* v v) (* -3 v)) (* (* v v) (* 9 v))) 1)) (* (- 1 (* v v)) (sqrt 2))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (* v v) (* -3 v)) (* (* v v) (* 9 v))) 1)) (* (- 1 (* v v)) (sqrt 2))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * * * [misc]progress: [ 44 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- 1 (* v v))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (246 enodes) * [exit]simplify: Simplified to (* (* (- 1 (* v v)) (sqrt 2)) (sqrt (- 1 (* (pow v 3) (* v 9))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (* (- 1 (* v v)) (sqrt 2)) (sqrt (- 1 (* (pow v 3) (* v 9))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * * * * [misc]progress: [ 45 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- 1 (* v v))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (113 enodes) * * [misc]simplify: iters left: 3 (443 enodes) * [exit]simplify: Simplified to (* (sqrt (- 1 (* (* (* v v) (* 9 v)) (* (* v 3) (* v v))))) (* (/ (sqrt 2) 4) (- 1 (* v v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- 1 (* (* (* v v) (* 9 v)) (* (* v 3) (* v v))))) (* (/ (sqrt 2) 4) (- 1 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) * * * * [misc]progress: [ 46 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- 1 (* v v))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (98 enodes) * * [misc]simplify: iters left: 3 (323 enodes) * [exit]simplify: Simplified to (* (/ (- 1 (* v v)) (/ 4 (sqrt 2))) (sqrt (- 1 (* (* v 9) (pow v 3))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (/ (- 1 (* v v)) (/ 4 (sqrt 2))) (sqrt (- 1 (* (* v 9) (pow v 3))))) (sqrt (+ 1 (* 3 (* v v)))))) * * * * [misc]progress: [ 47 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (320 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* -3 v) v) 1)) (- (sqrt 2) (* (sqrt 2) (* v v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* -3 v) v) 1)) (- (sqrt 2) (* (sqrt 2) (* v v)))) 4)) * * * * [misc]progress: [ 48 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 49 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* v (* -3 v)))) (/ (sqrt 2) 4)) * [misc]simplify: Simplified (2 1 1) to (λ (v) (* (pow (* (sqrt (+ 1 (* v (* -3 v)))) (/ (sqrt 2) 4)) 1) (- 1 (* v v)))) * * * * [misc]progress: [ 50 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 51 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (/ (sqrt 2) 4)) (log (sqrt (- 1 (* 3 (* v v)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (72 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (+ (log (sqrt (+ 1 (* v (* -3 v))))) (log (/ (sqrt 2) 4))) * [misc]simplify: Simplified (2 1 1) to (λ (v) (* (exp (+ (log (sqrt (+ 1 (* v (* -3 v))))) (log (/ (sqrt 2) 4)))) (- 1 (* v v)))) * * * * [misc]progress: [ 52 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 53 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 54 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (/ (sqrt 2) 4) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)) (* (* (sqrt (- 1 (* 3 (* v v)))) (sqrt (- 1 (* 3 (* v v))))) (sqrt (- 1 (* 3 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (111 enodes) * * [misc]simplify: iters left: 3 (367 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* -3 (* v v)))) (* (/ (sqrt 2) 4) (+ 1/8 (* (* v v) -3/8)))) * [misc]simplify: Simplified (2 1 1) to (λ (v) (* (cbrt (* (sqrt (+ 1 (* -3 (* v v)))) (* (/ (sqrt 2) 4) (+ 1/8 (* (* v v) -3/8))))) (- 1 (* v v)))) * * * * [misc]progress: [ 55 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 56 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 57 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 58 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (253 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* v 9) (* v v)) (* (* -3 v) (* v v))) 1)) (sqrt 2)) * [misc]simplify: Simplified (2 1 1) to (λ (v) (* (/ (* (sqrt (+ (* (* (* v 9) (* v v)) (* (* -3 v) (* v v))) 1)) (sqrt 2)) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (- 1 (* v v)))) * [enter]simplify: Simplifying (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (214 enodes) * * [misc]simplify: iters left: 1 (270 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ (* (pow v 4) 9) 1) (* 3 (* v v)))) 4) * [misc]simplify: Simplified (2 1 2) to (λ (v) (* (/ (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ (* (pow v 4) 9) 1) (* 3 (* v v)))) 4)) (- 1 (* v v)))) * * * * [misc]progress: [ 59 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (134 enodes) * * [misc]simplify: iters left: 2 (254 enodes) * * [misc]simplify: iters left: 1 (289 enodes) * [exit]simplify: Simplified to (* (sqrt (- 1 (* (pow v 4) 9))) (sqrt 2)) * [misc]simplify: Simplified (2 1 1) to (λ (v) (* (/ (* (sqrt (- 1 (* (pow v 4) 9))) (sqrt 2)) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (- 1 (* v v)))) * [enter]simplify: Simplifying (* 4 (sqrt (+ 1 (* 3 (* v v))))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* v (* 3 v)))) 4) * [misc]simplify: Simplified (2 1 2) to (λ (v) (* (/ (* (sqrt (- 1 (* (pow v 4) 9))) (sqrt 2)) (* (sqrt (+ 1 (* v (* 3 v)))) 4)) (- 1 (* v v)))) * * * * [misc]progress: [ 60 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 61 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (cbrt (sqrt (- 1 (* 3 (* v v))))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (cbrt (sqrt (- 1 (* (* v v) 3)))) * [misc]simplify: Simplified (2 1 2) to (λ (v) (* (* (* (/ (sqrt 2) 4) (* (cbrt (sqrt (- 1 (* 3 (* v v))))) (cbrt (sqrt (- 1 (* 3 (* v v))))))) (cbrt (sqrt (- 1 (* (* v v) 3))))) (- 1 (* v v)))) * * * * [misc]progress: [ 62 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (cbrt (- 1 (* 3 (* v v))))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (sqrt (cbrt (- 1 (* (* v v) 3)))) * [misc]simplify: Simplified (2 1 2) to (λ (v) (* (* (* (/ (sqrt 2) 4) (sqrt (* (cbrt (- 1 (* 3 (* v v)))) (cbrt (- 1 (* 3 (* v v))))))) (sqrt (cbrt (- 1 (* (* v v) 3))))) (- 1 (* v v)))) * * * * [misc]progress: [ 63 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (sqrt (- 1 (* 3 (* v v))))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (sqrt (sqrt (- 1 (* (* v v) 3)))) * [misc]simplify: Simplified (2 1 2) to (λ (v) (* (* (* (/ (sqrt 2) 4) (sqrt (sqrt (- 1 (* 3 (* v v)))))) (sqrt (sqrt (- 1 (* (* v v) 3))))) (- 1 (* v v)))) * * * * [misc]progress: [ 64 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (- 1 (* 3 (* v v)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (sqrt (+ 1 (* (* v v) -3))) * [misc]simplify: Simplified (2 1 2) to (λ (v) (* (* (* (/ (sqrt 2) 4) (sqrt 1)) (sqrt (+ 1 (* (* v v) -3)))) (- 1 (* v v)))) * * * * [misc]progress: [ 65 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (sqrt (- 1 (* 3 (* v v))))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (sqrt (sqrt (- 1 (* (* v v) 3)))) * [misc]simplify: Simplified (2 1 2) to (λ (v) (* (* (* (/ (sqrt 2) 4) (sqrt (sqrt (- 1 (* 3 (* v v)))))) (sqrt (sqrt (- 1 (* (* v v) 3))))) (- 1 (* v v)))) * * * * [misc]progress: [ 66 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (- 1 (* 3 (* v v)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (sqrt (+ 1 (* (* v v) -3))) * [misc]simplify: Simplified (2 1 2) to (λ (v) (* (* (* (/ (sqrt 2) 4) 1) (sqrt (+ 1 (* (* v v) -3)))) (- 1 (* v v)))) * * * * [misc]progress: [ 67 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ (sqrt 2) 4)) (cbrt (/ (sqrt 2) 4))) * * [misc]simplify: iters left: 6 (6 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (sqrt 2) 4)) (cbrt (/ (sqrt 2) 4))) * [misc]simplify: Simplified (2 1 1) to (λ (v) (* (* (* (cbrt (/ (sqrt 2) 4)) (cbrt (/ (sqrt 2) 4))) (* (cbrt (/ (sqrt 2) 4)) (sqrt (- 1 (* 3 (* v v)))))) (- 1 (* v v)))) * * * * [misc]progress: [ 68 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (sqrt 2) 4)) * * [misc]simplify: iters left: 4 (5 enodes) * [exit]simplify: Simplified to (sqrt (/ (sqrt 2) 4)) * [misc]simplify: Simplified (2 1 1) to (λ (v) (* (* (sqrt (/ (sqrt 2) 4)) (* (sqrt (/ (sqrt 2) 4)) (sqrt (- 1 (* 3 (* v v)))))) (- 1 (* v v)))) * * * * [misc]progress: [ 69 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 70 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt 2) * * [misc]simplify: iters left: 1 (2 enodes) * [exit]simplify: Simplified to (sqrt 2) * [misc]simplify: Simplified (2 1 1) to (λ (v) (* (* (sqrt 2) (* (/ 1 4) (sqrt (- 1 (* 3 (* v v)))))) (- 1 (* v v)))) * * * * [misc]progress: [ 71 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (132 enodes) * * [misc]simplify: iters left: 2 (227 enodes) * * [misc]simplify: iters left: 1 (306 enodes) * [exit]simplify: Simplified to (sqrt (+ 1 (+ (* 3 (* v v)) (* (pow v 4) 9)))) * [misc]simplify: Simplified (2 1 2) to (λ (v) (* (/ (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (sqrt (+ 1 (+ (* 3 (* v v)) (* (pow v 4) 9))))) (- 1 (* v v)))) * * * * [misc]progress: [ 72 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (+ 1 (* 3 (* v v)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (sqrt (+ 1 (* (* v v) 3))) * [misc]simplify: Simplified (2 1 2) to (λ (v) (* (/ (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ 1 (* (* v v) 3)))) (- 1 (* v v)))) * * * * [misc]progress: [ 73 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* v (* v -3)) 1)) (sqrt 2)) * [misc]simplify: Simplified (2 1 1) to (λ (v) (* (/ (* (sqrt (+ (* v (* v -3)) 1)) (sqrt 2)) 4) (- 1 (* v v)))) * * * * [misc]progress: [ 74 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 75 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 76 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 77 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 78 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 79 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 80 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 81 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (cbrt (- 1 (* 3 (* v v)))) (cbrt (- 1 (* 3 (* v v)))))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (fabs (cbrt (- 1 (* (* v v) 3)))) * [misc]simplify: Simplified (2 1 2 1) to (λ (v) (* (* (/ (sqrt 2) 4) (* (fabs (cbrt (- 1 (* (* v v) 3)))) (sqrt (cbrt (- 1 (* 3 (* v v))))))) (- 1 (* v v)))) * * * * [misc]progress: [ 82 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (sqrt (- 1 (* 3 (* v v))))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (sqrt (sqrt (- 1 (* (* v v) 3)))) * [misc]simplify: Simplified (2 1 2 1) to (λ (v) (* (* (/ (sqrt 2) 4) (* (sqrt (sqrt (- 1 (* (* v v) 3)))) (sqrt (sqrt (- 1 (* 3 (* v v))))))) (- 1 (* v v)))) * * * * [misc]progress: [ 83 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt 1) * * [misc]simplify: iters left: 1 (2 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 1 2 1) to (λ (v) (* (* (/ (sqrt 2) 4) (* 1 (sqrt (- 1 (* 3 (* v v)))))) (- 1 (* v v)))) * * * * [misc]progress: [ 84 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (251 enodes) * [exit]simplify: Simplified to (sqrt (- 1 (* (* (* v v) (* 9 v)) (* (* v v) (* v 3))))) * [misc]simplify: Simplified (2 1 2 1) to (λ (v) (* (* (/ (sqrt 2) 4) (/ (sqrt (- 1 (* (* (* v v) (* 9 v)) (* (* v v) (* v 3))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (- 1 (* v v)))) * * * * [misc]progress: [ 85 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v))))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (132 enodes) * * [misc]simplify: iters left: 2 (264 enodes) * * [misc]simplify: iters left: 1 (303 enodes) * [exit]simplify: Simplified to (sqrt (+ (* -9 (pow v 4)) 1)) * [misc]simplify: Simplified (2 1 2 1) to (λ (v) (* (* (/ (sqrt 2) 4) (/ (sqrt (+ (* -9 (pow v 4)) 1)) (sqrt (+ 1 (* 3 (* v v)))))) (- 1 (* v v)))) * * * * [misc]progress: [ 86 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 87 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (- 1 (* 3 (* v v)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (sqrt (+ 1 (* (* v v) -3))) * [misc]simplify: Simplified (2 1 2 1) to (λ (v) (* (* (/ (sqrt 2) 4) (fabs (sqrt (+ 1 (* (* v v) -3))))) (- 1 (* v v)))) * * * * [misc]progress: [ 88 / 100 ] simplifiying candidate # * * * * [misc]progress: [ 89 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (* 3 (pow v 2)) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * * [misc]simplify: iters left: 1 (11 enodes) * [exit]simplify: Simplified to (* (* v v) 3) * [misc]simplify: Simplified (2 1 2 1 2) to (λ (v) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v v) 3)))) (- 1 (* v v)))) * * * * [misc]progress: [ 90 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (* 3 (pow v 2)) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * * [misc]simplify: iters left: 1 (11 enodes) * [exit]simplify: Simplified to (* (* v v) 3) * [misc]simplify: Simplified (2 1 2 1 2) to (λ (v) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v v) 3)))) (- 1 (* v v)))) * * * * [misc]progress: [ 91 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (* 3 (pow v 2)) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * * [misc]simplify: iters left: 1 (11 enodes) * [exit]simplify: Simplified to (* (* v v) 3) * [misc]simplify: Simplified (2 1 2 1 2) to (λ (v) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v v) 3)))) (- 1 (* v v)))) * * * * [misc]progress: [ 92 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 1/4 (sqrt 2)) (* 3/32 (* (sqrt 2) (pow v 4)))) (* 5/8 (* (sqrt 2) (pow v 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (133 enodes) * * [misc]simplify: iters left: 2 (232 enodes) * * [misc]simplify: iters left: 1 (314 enodes) * [exit]simplify: Simplified to (* (+ (+ 1/4 (* (pow v 4) 3/32)) (* (* -5/8 v) v)) (sqrt 2)) * [misc]simplify: Simplified (2) to (λ (v) (* (+ (+ 1/4 (* (pow v 4) 3/32)) (* (* -5/8 v) v)) (sqrt 2))) * * * * [misc]progress: [ 93 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 1/32 (/ (sqrt 2) (* v (pow (sqrt -3) 3)))) (+ (* 1/4 (* (sqrt 2) (* v (sqrt -3)))) (* 1/8 (/ (sqrt 2) (* v (sqrt -3)))))) (+ (* 1/8 (/ (* (sqrt 2) v) (sqrt -3))) (* 1/4 (* (sqrt 2) (* (pow v 3) (sqrt -3)))))) * * [misc]simplify: iters left: 6 (29 enodes) * * [misc]simplify: iters left: 5 (74 enodes) * * [misc]simplify: iters left: 4 (207 enodes) * [exit]simplify: Simplified to (- (+ (* (/ (sqrt 2) v) (+ (/ -1/96 (sqrt -3)) (/ 1/8 (sqrt -3)))) (- (* (* (* 1/4 v) (sqrt 2)) (sqrt -3)) (/ (* 1/8 (sqrt 2)) (/ (sqrt -3) v)))) (* (* (* 1/4 v) (sqrt 2)) (* (sqrt -3) (* v v)))) * [misc]simplify: Simplified (2) to (λ (v) (- (+ (* (/ (sqrt 2) v) (+ (/ -1/96 (sqrt -3)) (/ 1/8 (sqrt -3)))) (- (* (* (* 1/4 v) (sqrt 2)) (sqrt -3)) (/ (* 1/8 (sqrt 2)) (/ (sqrt -3) v)))) (* (* (* 1/4 v) (sqrt 2)) (* (sqrt -3) (* v v))))) * * * * [misc]progress: [ 94 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 1/8 (/ (* (sqrt 2) v) (sqrt -3))) (* 1/4 (* (sqrt 2) (* (pow v 3) (sqrt -3))))) (+ (* 1/32 (/ (sqrt 2) (* v (pow (sqrt -3) 3)))) (+ (* 1/4 (* (sqrt 2) (* v (sqrt -3)))) (* 1/8 (/ (sqrt 2) (* v (sqrt -3))))))) * * [misc]simplify: iters left: 6 (29 enodes) * * [misc]simplify: iters left: 5 (74 enodes) * * [misc]simplify: iters left: 4 (209 enodes) * [exit]simplify: Simplified to (- (- (+ (* (/ 1/8 (sqrt -3)) (* (sqrt 2) v)) (* (* (sqrt 2) (* 1/4 v)) (* (sqrt -3) (* v v)))) (* (/ (sqrt 2) v) (+ (/ 1/8 (sqrt -3)) (/ -1/96 (sqrt -3))))) (* (sqrt -3) (* (sqrt 2) (* 1/4 v)))) * [misc]simplify: Simplified (2) to (λ (v) (- (- (+ (* (/ 1/8 (sqrt -3)) (* (sqrt 2) v)) (* (* (sqrt 2) (* 1/4 v)) (* (sqrt -3) (* v v)))) (* (/ (sqrt 2) v) (+ (/ 1/8 (sqrt -3)) (/ -1/96 (sqrt -3))))) (* (sqrt -3) (* (sqrt 2) (* 1/4 v))))) * * * * [misc]progress: [ 95 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* 1/4 (sqrt 2)) (+ (* 9/32 (* (sqrt 2) (pow v 4))) (* 3/8 (* (sqrt 2) (pow v 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (282 enodes) * * [misc]simplify: iters left: 1 (474 enodes) * [exit]simplify: Simplified to (* (- 1/4 (- (* (pow v 4) 9/32) (* (* v v) -3/8))) (sqrt 2)) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (- 1/4 (- (* (pow v 4) 9/32) (* (* v v) -3/8))) (sqrt 2)) (- 1 (* v v)))) * * * * [misc]progress: [ 96 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 1/4 (* (sqrt 2) (* v (sqrt -3)))) (* 1/8 (/ (sqrt 2) (* v (sqrt -3))))) (* 1/32 (/ (sqrt 2) (* (pow v 3) (pow (sqrt -3) 3))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (142 enodes) * * [misc]simplify: iters left: 3 (384 enodes) * [exit]simplify: Simplified to (+ (* (* (sqrt 2) (sqrt -3)) (* v 1/4)) (* (/ (sqrt 2) (sqrt -3)) (- (/ 1/8 v) (/ -1/96 (pow v 3))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (+ (* (* (sqrt 2) (sqrt -3)) (* v 1/4)) (* (/ (sqrt 2) (sqrt -3)) (- (/ 1/8 v) (/ -1/96 (pow v 3))))) (- 1 (* v v)))) * * * * [misc]progress: [ 97 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* 1/32 (/ (sqrt 2) (* (pow v 3) (pow (sqrt -3) 3)))) (+ (* 1/4 (* (sqrt 2) (* v (sqrt -3)))) (* 1/8 (/ (sqrt 2) (* v (sqrt -3)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (133 enodes) * * [misc]simplify: iters left: 3 (402 enodes) * [exit]simplify: Simplified to (+ (* (* (sqrt -3) -1/4) (* (sqrt 2) v)) (* (/ (sqrt 2) (sqrt -3)) (- (/ -1/96 (pow v 3)) (/ 1/8 v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (+ (* (* (sqrt -3) -1/4) (* (sqrt 2) v)) (* (/ (sqrt 2) (sqrt -3)) (- (/ -1/96 (pow v 3)) (/ 1/8 v)))) (- 1 (* v v)))) * * * * [misc]progress: [ 98 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (- 1 (+ (* 9/8 (pow v 4)) (* 3/2 (pow v 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (87 enodes) * * [misc]simplify: iters left: 1 (103 enodes) * [exit]simplify: Simplified to (- (* v (* -3/2 v)) (+ (* 9/8 (pow v 4)) -1)) * [misc]simplify: Simplified (2 1 2) to (λ (v) (* (* (/ (sqrt 2) 4) (- (* v (* -3/2 v)) (+ (* 9/8 (pow v 4)) -1))) (- 1 (* v v)))) * * * * [misc]progress: [ 99 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 1/2 (/ 1 (* (sqrt -3) v))) (* (sqrt -3) v)) (* 1/8 (/ 1 (* (pow (sqrt -3) 3) (pow v 3))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (177 enodes) * * [misc]simplify: iters left: 2 (281 enodes) * [exit]simplify: Simplified to (+ (+ (* v (sqrt -3)) (/ (/ 1/2 v) (sqrt -3))) (/ (/ -1/8 (* v v)) (* (sqrt -3) (* v -3)))) * [misc]simplify: Simplified (2 1 2) to (λ (v) (* (* (/ (sqrt 2) 4) (+ (+ (* v (sqrt -3)) (/ (/ 1/2 v) (sqrt -3))) (/ (/ -1/8 (* v v)) (* (sqrt -3) (* v -3))))) (- 1 (* v v)))) * * * * [misc]progress: [ 100 / 100 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* 1/8 (/ 1 (* (pow (sqrt -3) 3) (pow v 3)))) (+ (* 1/2 (/ 1 (* (sqrt -3) v))) (* (sqrt -3) v))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (182 enodes) * * [misc]simplify: iters left: 2 (303 enodes) * [exit]simplify: Simplified to (+ (- (/ (/ -1/24 v) (* (sqrt -3) (* v v))) (* v (sqrt -3))) (/ (/ -1/2 (sqrt -3)) v)) * [misc]simplify: Simplified (2 1 2) to (λ (v) (* (* (/ (sqrt 2) 4) (+ (- (/ (/ -1/24 v) (* (sqrt -3) (* v v))) (* v (sqrt -3))) (/ (/ -1/2 (sqrt -3)) v))) (- 1 (* v v)))) * * * [misc]progress: adding candidates to table * * [misc]progress: iteration 2 / 4 * * * [misc]progress: picking best candidate * * * * [misc]pick: Picked # * * * [misc]progress: localizing error * * * [misc]progress: generating rewritten candidates * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 2) * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 2 1 2 1 2) * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 1 1 2 1 2) * * * * [misc]progress: [ 4 / 4 ] rewriting at (2) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2) * [misc]approximate: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* v v)))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* v v))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 3 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1))) into 0 * [misc]taylor: Taking taylor expansion of (- (* v v)) in v * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* v v)))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* v v))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 3 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1))) into 0 * [misc]taylor: Taking taylor expansion of (- (* v v)) in v * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) 1) into (* 1/4 (sqrt 2)) * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 1) (* 0 0))) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 1) (* 0 0))) into 1 * [misc]backup-simplify: Simplify (+ (* 3 1) (+ (* 0 0) (* 0 0))) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (/ (- -3 (pow 0 2) (+)) (* 2 1)) into -3/2 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -3/2) (+ (* 0 0) (* 0 1))) into (- (* 3/8 (sqrt 2))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -1) (+ (* 0 0) (* (- (* 3/8 (sqrt 2))) 0))) into (- (* 1/4 (sqrt 2))) * [misc]backup-simplify: Simplify (- (* 1/4 (sqrt 2))) into (- (* 1/4 (sqrt 2))) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 1) (+ (* 0 0) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 -3/2)))) (* 2 1)) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 -3/2) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 -1) (+ (* (- (* 3/8 (sqrt 2))) 0) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow -3/2 2) (+ (* 2 (* 0 0)))) (* 2 1)) into -9/8 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -9/8) (+ (* 0 0) (+ (* 0 -3/2) (+ (* 0 0) (* 0 1))))) into (- (* 9/32 (sqrt 2))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 0) (+ (* (- (* 3/8 (sqrt 2))) -1) (+ (* 0 0) (* (- (* 9/32 (sqrt 2))) 0))))) into (* 3/8 (sqrt 2)) * [misc]backup-simplify: Simplify (* 3/8 (sqrt 2)) into (* 3/8 (sqrt 2)) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0)))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 -9/8)) (* 2 (* -3/2 0)))) (* 2 1)) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 -9/8) (+ (* 0 0) (+ (* 0 -3/2) (+ (* 0 0) (* 0 1)))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 0) (+ (* (- (* 3/8 (sqrt 2))) 0) (+ (* 0 -1) (+ (* (- (* 9/32 (sqrt 2))) 0) (* 0 0)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0))))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* -3/2 -9/8)))) (* 2 1)) into -27/16 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -27/16) (+ (* 0 0) (+ (* 0 -9/8) (+ (* 0 0) (+ (* 0 -3/2) (+ (* 0 0) (* 0 1))))))) into (- (* 27/64 (sqrt 2))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 0) (+ (* (- (* 3/8 (sqrt 2))) 0) (+ (* 0 0) (+ (* (- (* 9/32 (sqrt 2))) -1) (+ (* 0 0) (* (- (* 27/64 (sqrt 2))) 0))))))) into (* 9/32 (sqrt 2)) * [misc]backup-simplify: Simplify (* 9/32 (sqrt 2)) into (* 9/32 (sqrt 2)) * [misc]backup-simplify: Simplify (+ (* (* 9/32 (sqrt 2)) (pow v 6)) (+ (* (* 3/8 (sqrt 2)) (pow v 4)) (* (- (* 1/4 (sqrt 2))) (pow v 2)))) into (- (+ (* 9/32 (* (sqrt 2) (pow v 6))) (* 3/8 (* (sqrt 2) (pow v 4)))) (* 1/4 (* (sqrt 2) (pow v 2)))) * [misc]approximate: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- (* (/ 1 v) (/ 1 v)))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (- (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (- (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) (sqrt -3)) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (* (* 1/4 (* (sqrt 2) (sqrt -3))) -1) into (* -1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* -1/4 (* (sqrt 2) (sqrt -3))) into (* -1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ (- 1 (pow 0 2) (+)) (* 2 (sqrt -3))) into (/ 1/2 (sqrt -3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))) into (* 1/8 (/ (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (* (* 1/8 (/ (sqrt 2) (sqrt -3))) -1))) into (- (* 1/8 (/ (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (- (* 1/8 (/ (sqrt 2) (sqrt -3)))) into (- (* 1/8 (/ (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (/ 1/2 (sqrt -3)))))) (* 2 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3))))) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (+ (* (* 1/8 (/ (sqrt 2) (sqrt -3))) 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ 1/2 (sqrt -3)) 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt -3))) into (/ -1/8 (pow (sqrt -3) 3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ -1/8 (pow (sqrt -3) 3))) (+ (* 0 0) (+ (* 0 (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))))) into (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (+ (* (* 1/8 (/ (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (* (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) -1))))) into (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3))) * [misc]backup-simplify: Simplify (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3))) into (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3))) * [misc]backup-simplify: Simplify (+ (* (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3))) (/ 1 v)) (+ (* (- (* 1/8 (/ (sqrt 2) (sqrt -3)))) (/ 1 (/ 1 v))) (* (* -1/4 (* (sqrt 2) (sqrt -3))) (pow (/ 1 (/ 1 v)) 3)))) into (- (* 1/32 (/ (sqrt 2) (* v (pow (sqrt -3) 3)))) (+ (* 1/4 (* (sqrt 2) (* (pow v 3) (sqrt -3)))) (* 1/8 (/ (* (sqrt 2) v) (sqrt -3))))) * [misc]approximate: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- (* (/ 1 (- v)) (/ 1 (- v))))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (- (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (- (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) (sqrt -3)) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (* (* 1/4 (* (sqrt 2) (sqrt -3))) -1) into (* -1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* -1/4 (* (sqrt 2) (sqrt -3))) into (* -1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ (- 1 (pow 0 2) (+)) (* 2 (sqrt -3))) into (/ 1/2 (sqrt -3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))) into (* 1/8 (/ (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (* (* 1/8 (/ (sqrt 2) (sqrt -3))) -1))) into (- (* 1/8 (/ (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (- (* 1/8 (/ (sqrt 2) (sqrt -3)))) into (- (* 1/8 (/ (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (/ 1/2 (sqrt -3)))))) (* 2 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3))))) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (+ (* (* 1/8 (/ (sqrt 2) (sqrt -3))) 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ 1/2 (sqrt -3)) 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt -3))) into (/ -1/8 (pow (sqrt -3) 3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ -1/8 (pow (sqrt -3) 3))) (+ (* 0 0) (+ (* 0 (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))))) into (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (+ (* (* 1/8 (/ (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (* (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) -1))))) into (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3))) * [misc]backup-simplify: Simplify (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3))) into (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3))) * [misc]backup-simplify: Simplify (+ (* (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3))) (/ 1 (- v))) (+ (* (- (* 1/8 (/ (sqrt 2) (sqrt -3)))) (/ 1 (/ 1 (- v)))) (* (* -1/4 (* (sqrt 2) (sqrt -3))) (pow (/ 1 (/ 1 (- v))) 3)))) into (- (+ (* 1/4 (* (sqrt 2) (* (pow v 3) (sqrt -3)))) (* 1/8 (/ (* (sqrt 2) v) (sqrt -3)))) (* 1/32 (/ (sqrt 2) (* v (pow (sqrt -3) 3))))) * * * * [misc]progress: [ 2 / 4 ] generating series at (2 2 1 2 1 2) * [misc]approximate: Taking taylor expansion of (* 3 (* v v)) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 3 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 1) (* 0 0))) into 1 * [misc]backup-simplify: Simplify (+ (* 3 1) (+ (* 0 0) (* 0 0))) into 3 * [misc]backup-simplify: Simplify 3 into 3 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 1) (+ (* 0 0) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0))))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* 3 (pow v 2)) into (* 3 (pow v 2)) * [misc]approximate: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify 3 into 3 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* 3 (pow (/ 1 (/ 1 v)) 2)) into (* 3 (pow v 2)) * [misc]approximate: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify 3 into 3 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* 3 (pow (/ 1 (/ 1 (- v))) 2)) into (* 3 (pow v 2)) * * * * [misc]progress: [ 3 / 4 ] generating series at (2 1 1 2 1 2) * [misc]approximate: Taking taylor expansion of (* 3 (* v v)) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 3 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 1) (* 0 0))) into 1 * [misc]backup-simplify: Simplify (+ (* 3 1) (+ (* 0 0) (* 0 0))) into 3 * [misc]backup-simplify: Simplify 3 into 3 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 1) (+ (* 0 0) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0))))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* 3 (pow v 2)) into (* 3 (pow v 2)) * [misc]approximate: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify 3 into 3 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* 3 (pow (/ 1 (/ 1 v)) 2)) into (* 3 (pow v 2)) * [misc]approximate: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify 3 into 3 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* 3 (pow (/ 1 (/ 1 (- v))) 2)) into (* 3 (pow v 2)) * * * * [misc]progress: [ 4 / 4 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) in v * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* v v)))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* v v))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 3 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1))) into 0 * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* v v)))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* v v))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 3 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1))) into 0 * [misc]taylor: Taking taylor expansion of (- (* v v)) in v * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) in v * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* v v)))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* v v))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 3 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1))) into 0 * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* v v)))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* v v))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 3 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1))) into 0 * [misc]taylor: Taking taylor expansion of (- (* v v)) in v * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) 1) into (* 1/4 (sqrt 2)) * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) 1) into (* 1/4 (sqrt 2)) * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) 1) into (* 1/4 (sqrt 2)) * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/4 (sqrt 2)) 0) into (* 1/4 (sqrt 2)) * [misc]backup-simplify: Simplify (* 1/4 (sqrt 2)) into (* 1/4 (sqrt 2)) * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 1) (* 0 0))) into 1 * [misc]backup-simplify: Simplify (+ (* 3 1) (+ (* 0 0) (* 0 0))) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (/ (- -3 (pow 0 2) (+)) (* 2 1)) into -3/2 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -3/2) (+ (* 0 0) (* 0 1))) into (- (* 3/8 (sqrt 2))) * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 0) (* (- (* 3/8 (sqrt 2))) 1))) into (- (* 3/8 (sqrt 2))) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 1) (* 0 0))) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 1) (* 0 0))) into 1 * [misc]backup-simplify: Simplify (+ (* 3 1) (+ (* 0 0) (* 0 0))) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (/ (- -3 (pow 0 2) (+)) (* 2 1)) into -3/2 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -3/2) (+ (* 0 0) (* 0 1))) into (- (* 3/8 (sqrt 2))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -1) (+ (* 0 0) (* (- (* 3/8 (sqrt 2))) 0))) into (- (* 1/4 (sqrt 2))) * [misc]backup-simplify: Simplify (+ (- (* 3/8 (sqrt 2))) (- (* 1/4 (sqrt 2)))) into (- (* 5/8 (sqrt 2))) * [misc]backup-simplify: Simplify (- (* 5/8 (sqrt 2))) into (- (* 5/8 (sqrt 2))) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 1) (+ (* 0 0) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 -3/2)))) (* 2 1)) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 -3/2) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 0) (+ (* (- (* 3/8 (sqrt 2))) 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 1) (+ (* 0 0) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 -3/2)))) (* 2 1)) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 -3/2) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 -1) (+ (* (- (* 3/8 (sqrt 2))) 0) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow -3/2 2) (+ (* 2 (* 0 0)))) (* 2 1)) into -9/8 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -9/8) (+ (* 0 0) (+ (* 0 -3/2) (+ (* 0 0) (* 0 1))))) into (- (* 9/32 (sqrt 2))) * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 0) (+ (* (- (* 3/8 (sqrt 2))) 0) (+ (* 0 0) (* (- (* 9/32 (sqrt 2))) 1))))) into (- (* 9/32 (sqrt 2))) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow -3/2 2) (+ (* 2 (* 0 0)))) (* 2 1)) into -9/8 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -9/8) (+ (* 0 0) (+ (* 0 -3/2) (+ (* 0 0) (* 0 1))))) into (- (* 9/32 (sqrt 2))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 0) (+ (* (- (* 3/8 (sqrt 2))) -1) (+ (* 0 0) (* (- (* 9/32 (sqrt 2))) 0))))) into (* 3/8 (sqrt 2)) * [misc]backup-simplify: Simplify (+ (- (* 9/32 (sqrt 2))) (* 3/8 (sqrt 2))) into (* 3/32 (sqrt 2)) * [misc]backup-simplify: Simplify (* 3/32 (sqrt 2)) into (* 3/32 (sqrt 2)) * [misc]backup-simplify: Simplify (+ (* (* 3/32 (sqrt 2)) (pow v 4)) (+ (* (- (* 5/8 (sqrt 2))) (pow v 2)) (* 1/4 (sqrt 2)))) into (- (+ (* 1/4 (sqrt 2)) (* 3/32 (* (sqrt 2) (pow v 4)))) (* 5/8 (* (sqrt 2) (pow v 2)))) * [misc]approximate: Taking taylor expansion of (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- (* (/ 1 v) (/ 1 v))))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) 1) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (- (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) 1) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (- (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) (sqrt -3)) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (* (* 1/4 (* (sqrt 2) (sqrt -3))) -1) into (* -1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (+ 0 (* -1/4 (* (sqrt 2) (sqrt -3)))) into (- (* 1/4 (* (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (- (* 1/4 (* (sqrt 2) (sqrt -3)))) into (- (* 1/4 (* (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) (sqrt -3)) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* (* 1/4 (* (sqrt 2) (sqrt -3))) 1) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ (- 1 (pow 0 2) (+)) (* 2 (sqrt -3))) into (/ 1/2 (sqrt -3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))) into (* 1/8 (/ (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (* (* 1/8 (/ (sqrt 2) (sqrt -3))) -1))) into (- (* 1/8 (/ (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (+ (* 1/4 (* (sqrt 2) (sqrt -3))) (- (* 1/8 (/ (sqrt 2) (sqrt -3))))) into (- (* 1/4 (* (sqrt 2) (sqrt -3))) (* 1/8 (/ (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (- (* 1/4 (* (sqrt 2) (sqrt -3))) (* 1/8 (/ (sqrt 2) (sqrt -3)))) into (- (* 1/4 (* (sqrt 2) (sqrt -3))) (* 1/8 (/ (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (/ 1/2 (sqrt -3)))))) (* 2 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3))))) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (+ (* (* 1/8 (/ (sqrt 2) (sqrt -3))) 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ (- 1 (pow 0 2) (+)) (* 2 (sqrt -3))) into (/ 1/2 (sqrt -3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))) into (* 1/8 (/ (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (* (* 1/8 (/ (sqrt 2) (sqrt -3))) 1))) into (* 1/8 (/ (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ 1/2 (sqrt -3)) 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt -3))) into (/ -1/8 (pow (sqrt -3) 3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ -1/8 (pow (sqrt -3) 3))) (+ (* 0 0) (+ (* 0 (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))))) into (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (+ (* (* 1/8 (/ (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (* (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) -1))))) into (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3))) * [misc]backup-simplify: Simplify (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) into (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) * [misc]backup-simplify: Simplify (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) into (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) * [misc]backup-simplify: Simplify (+ (* (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) (/ 1 v)) (+ (* (- (* 1/4 (* (sqrt 2) (sqrt -3))) (* 1/8 (/ (sqrt 2) (sqrt -3)))) (/ 1 (/ 1 v))) (* (- (* 1/4 (* (sqrt 2) (sqrt -3)))) (pow (/ 1 (/ 1 v)) 3)))) into (- (+ (* 1/32 (/ (sqrt 2) (* v (pow (sqrt -3) 3)))) (+ (* 1/4 (* (sqrt 2) (* v (sqrt -3)))) (* 1/8 (/ (sqrt 2) (* v (sqrt -3)))))) (+ (* 1/8 (/ (* (sqrt 2) v) (sqrt -3))) (* 1/4 (* (sqrt 2) (* (pow v 3) (sqrt -3)))))) * [misc]approximate: Taking taylor expansion of (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- (* (/ 1 (- v)) (/ 1 (- v)))))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) 1) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (- (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) 1) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (- (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) (sqrt -3)) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (* (* 1/4 (* (sqrt 2) (sqrt -3))) -1) into (* -1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (+ 0 (* -1/4 (* (sqrt 2) (sqrt -3)))) into (- (* 1/4 (* (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (- (* 1/4 (* (sqrt 2) (sqrt -3)))) into (- (* 1/4 (* (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) (sqrt -3)) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* (* 1/4 (* (sqrt 2) (sqrt -3))) 1) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ (- 1 (pow 0 2) (+)) (* 2 (sqrt -3))) into (/ 1/2 (sqrt -3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))) into (* 1/8 (/ (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (* (* 1/8 (/ (sqrt 2) (sqrt -3))) -1))) into (- (* 1/8 (/ (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (+ (* 1/4 (* (sqrt 2) (sqrt -3))) (- (* 1/8 (/ (sqrt 2) (sqrt -3))))) into (- (* 1/4 (* (sqrt 2) (sqrt -3))) (* 1/8 (/ (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (- (* 1/4 (* (sqrt 2) (sqrt -3))) (* 1/8 (/ (sqrt 2) (sqrt -3)))) into (- (* 1/4 (* (sqrt 2) (sqrt -3))) (* 1/8 (/ (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (/ 1/2 (sqrt -3)))))) (* 2 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3))))) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (+ (* (* 1/8 (/ (sqrt 2) (sqrt -3))) 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ (- 1 (pow 0 2) (+)) (* 2 (sqrt -3))) into (/ 1/2 (sqrt -3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))) into (* 1/8 (/ (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (* (* 1/8 (/ (sqrt 2) (sqrt -3))) 1))) into (* 1/8 (/ (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ 1/2 (sqrt -3)) 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt -3))) into (/ -1/8 (pow (sqrt -3) 3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ -1/8 (pow (sqrt -3) 3))) (+ (* 0 0) (+ (* 0 (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))))) into (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (+ (* (* 1/8 (/ (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (* (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) -1))))) into (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3))) * [misc]backup-simplify: Simplify (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) into (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) * [misc]backup-simplify: Simplify (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) into (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) * [misc]backup-simplify: Simplify (+ (* (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) (/ 1 (- v))) (+ (* (- (* 1/4 (* (sqrt 2) (sqrt -3))) (* 1/8 (/ (sqrt 2) (sqrt -3)))) (/ 1 (/ 1 (- v)))) (* (- (* 1/4 (* (sqrt 2) (sqrt -3)))) (pow (/ 1 (/ 1 (- v))) 3)))) into (- (+ (* 1/8 (/ (* (sqrt 2) v) (sqrt -3))) (* 1/4 (* (sqrt 2) (* (pow v 3) (sqrt -3))))) (+ (* 1/32 (/ (sqrt 2) (* v (pow (sqrt -3) 3)))) (+ (* 1/4 (* (sqrt 2) (* v (sqrt -3)))) (* 1/8 (/ (sqrt 2) (* v (sqrt -3))))))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (207 enodes) * * [misc]simplify: iters left: 2 (387 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (* -3 (* v v)))) (/ (/ 4 (* v v)) (- (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (pow (/ (sqrt (+ 1 (* -3 (* v v)))) (/ (/ 4 (* v v)) (- (sqrt 2)))) 1))) * * * * [misc]progress: [ 2 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (207 enodes) * * [misc]simplify: iters left: 2 (387 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (* -3 (* v v)))) (/ (/ 4 (* v v)) (- (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (pow (/ (sqrt (+ 1 (* -3 (* v v)))) (/ (/ 4 (* v v)) (- (sqrt 2)))) 1))) * * * * [misc]progress: [ 3 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 4 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (+ (log (/ (sqrt 2) 4)) (log (sqrt (- 1 (* 3 (* v v)))))) (log (- (* v v)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (125 enodes) * * [misc]simplify: iters left: 2 (274 enodes) * [exit]simplify: Simplified to (+ (log (sqrt (+ 1 (* -3 (* v v))))) (+ (log (/ (sqrt 2) 4)) (log (* (- v) v)))) * [misc]simplify: Simplified (2 2 1) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (exp (+ (log (sqrt (+ 1 (* -3 (* v v))))) (+ (log (/ (sqrt 2) 4)) (log (* (- v) v))))))) * * * * [misc]progress: [ 5 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))) (log (- (* v v)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (102 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (391 enodes) * [exit]simplify: Simplified to (+ (log (sqrt (+ 1 (* v (* v -3))))) (+ (log (/ (sqrt 2) 4)) (log (* v (- v))))) * [misc]simplify: Simplified (2 2 1) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (exp (+ (log (sqrt (+ 1 (* v (* v -3))))) (+ (log (/ (sqrt 2) 4)) (log (* v (- v)))))))) * * * * [misc]progress: [ 6 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 7 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 8 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (* (/ (sqrt 2) 4) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)) (* (* (sqrt (- 1 (* 3 (* v v)))) (sqrt (- 1 (* 3 (* v v))))) (sqrt (- 1 (* 3 (* v v)))))) (* (* (- (* v v)) (- (* v v))) (- (* v v)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (56 enodes) * * [misc]simplify: iters left: 4 (234 enodes) * [exit]simplify: Simplified to (* (* (* (/ (* (sqrt 2) 1/2) 16) (* (- (* v v)) (* (* v v) (* v v)))) (+ (* v (* -3 v)) 1)) (sqrt (+ (* v (* -3 v)) 1))) * [misc]simplify: Simplified (2 2 1) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (cbrt (* (* (* (/ (* (sqrt 2) 1/2) 16) (* (- (* v v)) (* (* v v) (* v v)))) (+ (* v (* -3 v)) 1)) (sqrt (+ (* v (* -3 v)) 1)))))) * * * * [misc]progress: [ 9 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))) (* (* (- (* v v)) (- (* v v))) (- (* v v)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (200 enodes) * [exit]simplify: Simplified to (* (* (sqrt (+ (* -3 (* v v)) 1)) (* (/ (sqrt 2) 4) (* v (- v)))) (* (* (/ (sqrt 2) 4) (+ (* -3 (* v v)) 1)) (* (/ (sqrt 2) 4) (* (* v v) (* v v))))) * [misc]simplify: Simplified (2 2 1) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (cbrt (* (* (sqrt (+ (* -3 (* v v)) 1)) (* (/ (sqrt 2) 4) (* v (- v)))) (* (* (/ (sqrt 2) 4) (+ (* -3 (* v v)) 1)) (* (/ (sqrt 2) 4) (* (* v v) (* v v)))))))) * * * * [misc]progress: [ 10 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 11 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 12 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 13 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 14 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 15 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (cbrt (- (* v v))) * * [misc]simplify: iters left: 5 (4 enodes) * * [misc]simplify: iters left: 4 (7 enodes) * [exit]simplify: Simplified to (cbrt (* (- v) v)) * [misc]simplify: Simplified (2 2 2) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* (cbrt (- (* v v))) (cbrt (- (* v v))))) (cbrt (* (- v) v))))) * * * * [misc]progress: [ 16 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (- (* v v))) * * [misc]simplify: iters left: 5 (4 enodes) * * [misc]simplify: iters left: 4 (7 enodes) * [exit]simplify: Simplified to (sqrt (* (- v) v)) * [misc]simplify: Simplified (2 2 2) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (sqrt (- (* v v)))) (sqrt (* (- v) v))))) * * * * [misc]progress: [ 17 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* v v)) * * [misc]simplify: iters left: 4 (3 enodes) * * [misc]simplify: iters left: 3 (6 enodes) * [exit]simplify: Simplified to (* (- v) v) * [misc]simplify: Simplified (2 2 2) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (- v) v)))) * * * * [misc]progress: [ 18 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (* v v) * * [misc]simplify: iters left: 2 (2 enodes) * [exit]simplify: Simplified to (* v v) * [misc]simplify: Simplified (2 2 2) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) -1) (* v v)))) * * * * [misc]progress: [ 19 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 20 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (- v) * * [misc]simplify: iters left: 2 (2 enodes) * [exit]simplify: Simplified to (- v) * [misc]simplify: Simplified (2 2 2) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) v) (- v)))) * * * * [misc]progress: [ 21 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt 2) 4) * * [misc]simplify: iters left: 3 (4 enodes) * [exit]simplify: Simplified to (/ (sqrt 2) 4) * [misc]simplify: Simplified (2 2 1) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (/ (sqrt 2) 4) (* (sqrt (- 1 (* 3 (* v v)))) (- (* v v)))))) * * * * [misc]progress: [ 22 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (108 enodes) * * [misc]simplify: iters left: 3 (353 enodes) * [exit]simplify: Simplified to (* (- (* (* v v) (sqrt 2))) (sqrt (+ 1 (* (* (* v v) (* -3 v)) (* (* v v) (* 9 v)))))) * [misc]simplify: Simplified (2 2 1) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (/ (* (- (* (* v v) (sqrt 2))) (sqrt (+ 1 (* (* (* v v) (* -3 v)) (* (* v v) (* 9 v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * * * [misc]progress: [ 23 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (229 enodes) * * [misc]simplify: iters left: 2 (392 enodes) * * [misc]simplify: iters left: 1 (447 enodes) * [exit]simplify: Simplified to (* (* (- v) (* v (sqrt 2))) (sqrt (+ (* -9 (pow v 4)) 1))) * [misc]simplify: Simplified (2 2 1) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (/ (* (* (- v) (* v (sqrt 2))) (sqrt (+ (* -9 (pow v 4)) 1))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * * * [misc]progress: [ 24 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (124 enodes) * * [misc]simplify: iters left: 3 (427 enodes) * [exit]simplify: Simplified to (* (sqrt (- 1 (* (* (* v v) (* v 3)) (* (* 9 v) (* v v))))) (* (* (- v) v) (/ (sqrt 2) 4))) * [misc]simplify: Simplified (2 2 1) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (/ (* (sqrt (- 1 (* (* (* v v) (* v 3)) (* (* 9 v) (* v v))))) (* (* (- v) v) (/ (sqrt 2) 4))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * * * [misc]progress: [ 25 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (109 enodes) * * [misc]simplify: iters left: 3 (305 enodes) * [exit]simplify: Simplified to (* (* (* v (- v)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (pow v 3) (* 9 v))))) * [misc]simplify: Simplified (2 2 1) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (/ (* (* (* v (- v)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (pow v 3) (* 9 v))))) (sqrt (+ 1 (* 3 (* v v))))))) * * * * [misc]progress: [ 26 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (128 enodes) * * [misc]simplify: iters left: 2 (177 enodes) * * [misc]simplify: iters left: 1 (188 enodes) * [exit]simplify: Simplified to (* (* (* (sqrt 2) (- v)) v) (sqrt (+ (* v (* -3 v)) 1))) * [misc]simplify: Simplified (2 2 1) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (/ (* (* (* (sqrt 2) (- v)) v) (sqrt (+ (* v (* -3 v)) 1))) 4))) * * * * [misc]progress: [ 27 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 28 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 29 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 30 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 31 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 32 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 33 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 34 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 35 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 36 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 37 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 38 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 39 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 40 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 41 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 42 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 43 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 44 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 45 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 46 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (* (exp (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (exp (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (125 enodes) * * [misc]simplify: iters left: 3 (369 enodes) * [exit]simplify: Simplified to (pow (exp (* (- 1 (* v v)) (/ (sqrt 2) 4))) (sqrt (+ (* (* -3 v) v) 1))) * [misc]simplify: Simplified (2 1) to (λ (v) (log (pow (exp (* (- 1 (* v v)) (/ (sqrt 2) 4))) (sqrt (+ (* (* -3 v) v) 1))))) * * * * [misc]progress: [ 47 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 48 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 49 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 50 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 51 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 52 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 53 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (77 enodes) * * [misc]simplify: iters left: 4 (245 enodes) * [exit]simplify: Simplified to (* (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (+ (sqrt 2) (* v (* (- v) (sqrt 2))))) (* 4 (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ (* v (* 3 v)) 1))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (+ (sqrt 2) (* v (* (- v) (sqrt 2))))) (* 4 (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ (* v (* 3 v)) 1))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (148 enodes) * * [misc]simplify: iters left: 2 (259 enodes) * [exit]simplify: Simplified to (+ 16 (* 16 (+ (* (pow v 3) (* v 9)) (* 3 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (+ (sqrt 2) (* v (* (- v) (sqrt 2))))) (* 4 (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ (* v (* 3 v)) 1))))) (+ 16 (* 16 (+ (* (pow v 3) (* v 9)) (* 3 (* v v))))))) * * * * [misc]progress: [ 54 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (89 enodes) * * [misc]simplify: iters left: 4 (275 enodes) * [exit]simplify: Simplified to (- (* (sqrt 2) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (sqrt (+ (* 3 (* v v)) 1))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (* (sqrt 2) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (sqrt (+ (* 3 (* v v)) 1))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * [enter]simplify: Simplifying (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (102 enodes) * * [misc]simplify: iters left: 3 (197 enodes) * * [misc]simplify: iters left: 2 (330 enodes) * * [misc]simplify: iters left: 1 (391 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* 9 (pow v 4)))) (* 16 (sqrt (+ 1 (* (* 3 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (* (sqrt 2) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (sqrt (+ (* 3 (* v v)) 1))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4))) (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* 9 (pow v 4)))) (* 16 (sqrt (+ 1 (* (* 3 v) v))))))) * * * * [misc]progress: [ 55 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))) * * [misc]simplify: iters left: 6 (28 enodes) * * [misc]simplify: iters left: 5 (80 enodes) * * [misc]simplify: iters left: 4 (273 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (163 enodes) * * [misc]simplify: iters left: 2 (322 enodes) * [exit]simplify: Simplified to (+ (+ (* (* 12 v) v) 4) (* (* (* v 4) (* v v)) (* 9 v))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)))) (+ (+ (* (* 12 v) v) 4) (* (* (* v 4) (* v v)) (* 9 v))))) * * * * [misc]progress: [ 56 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (88 enodes) * * [misc]simplify: iters left: 4 (272 enodes) * [exit]simplify: Simplified to (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))) * [enter]simplify: Simplifying (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (85 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (228 enodes) * * [misc]simplify: iters left: 1 (280 enodes) * [exit]simplify: Simplified to (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (+ (+ (* (pow v 4) 9) 1) (* (* v v) 3)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)))) (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (+ (+ (* (pow v 4) 9) 1) (* (* v v) 3)))))) * * * * [misc]progress: [ 57 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) * * [misc]simplify: iters left: 6 (29 enodes) * * [misc]simplify: iters left: 5 (82 enodes) * * [misc]simplify: iters left: 4 (260 enodes) * [exit]simplify: Simplified to (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* 4 (* (- v) (* v (sqrt 2)))) (sqrt (- 1 (* (* 3 v) v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* 4 (* (- v) (* v (sqrt 2)))) (sqrt (- 1 (* (* 3 v) v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))) * [enter]simplify: Simplifying (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (136 enodes) * * [misc]simplify: iters left: 2 (222 enodes) * * [misc]simplify: iters left: 1 (273 enodes) * [exit]simplify: Simplified to (* 16 (sqrt (+ (+ (* (pow v 4) 9) (* 3 (* v v))) 1))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* 4 (* (- v) (* v (sqrt 2)))) (sqrt (- 1 (* (* 3 v) v)))))) (* 16 (sqrt (+ (+ (* (pow v 4) 9) (* 3 (* v v))) 1))))) * * * * [misc]progress: [ 58 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (89 enodes) * * [misc]simplify: iters left: 4 (276 enodes) * [exit]simplify: Simplified to (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (sqrt 2))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* v v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (sqrt 2))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* v v)))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (101 enodes) * * [misc]simplify: iters left: 3 (178 enodes) * * [misc]simplify: iters left: 2 (291 enodes) * * [misc]simplify: iters left: 1 (314 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* 16 (sqrt (+ (* v (* 3 v)) 1)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (sqrt 2))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* v v)))) (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* 16 (sqrt (+ (* v (* 3 v)) 1)))))) * * * * [misc]progress: [ 59 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (57 enodes) * * [misc]simplify: iters left: 4 (173 enodes) * [exit]simplify: Simplified to (* (* (sqrt (+ (* (* (* v v) -9) (* v v)) 1)) (+ (sqrt 2) (* (- (* v v)) (sqrt 2)))) (* (sqrt (+ (* (* v v) 3) 1)) 4)) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (* (sqrt (+ (* (* (* v v) -9) (* v v)) 1)) (+ (sqrt 2) (* (- (* v v)) (sqrt 2)))) (* (sqrt (+ (* (* v v) 3) 1)) 4)) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * [enter]simplify: Simplifying (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * * [misc]simplify: iters left: 2 (45 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (+ (* (* v v) 48) 16) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (* (sqrt (+ (* (* (* v v) -9) (* v v)) 1)) (+ (sqrt 2) (* (- (* v v)) (sqrt 2)))) (* (sqrt (+ (* (* v v) 3) 1)) 4)) (+ (* (* v v) 48) 16))) * * * * [misc]progress: [ 60 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (88 enodes) * * [misc]simplify: iters left: 4 (274 enodes) * [exit]simplify: Simplified to (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (/ (sqrt 2) 4))) (* (* v v) (sqrt (- 1 (pow (* (* v v) 3) 3)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (/ (sqrt 2) 4))) (* (* v v) (sqrt (- 1 (pow (* (* v v) 3) 3)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (85 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (247 enodes) * * [misc]simplify: iters left: 1 (328 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ (* (* 3 v) v) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* (* 3 v) v) 1)) 4)) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (/ (sqrt 2) 4))) (* (* v v) (sqrt (- 1 (pow (* (* v v) 3) 3)))))) (* (sqrt (+ (+ (* (* 3 v) v) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* (* 3 v) v) 1)) 4)))) * * * * [misc]progress: [ 61 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (60 enodes) * * [misc]simplify: iters left: 4 (199 enodes) * [exit]simplify: Simplified to (- (* (* (sqrt (+ (* (* v v) 3) 1)) (sqrt 2)) (sqrt (+ 1 (* (* v v) (* (* v v) -9))))) (* (* (sqrt (+ 1 (* (* v v) (* (* v v) -9)))) (* (/ (sqrt 2) 4) (* v v))) (* 4 (sqrt (+ (* (* v v) 3) 1))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (* (* (sqrt (+ (* (* v v) 3) 1)) (sqrt 2)) (sqrt (+ 1 (* (* v v) (* (* v v) -9))))) (* (* (sqrt (+ 1 (* (* v v) (* (* v v) -9)))) (* (/ (sqrt 2) 4) (* v v))) (* 4 (sqrt (+ (* (* v v) 3) 1))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))) * [enter]simplify: Simplifying (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * * [misc]simplify: iters left: 2 (49 enodes) * * [misc]simplify: iters left: 1 (59 enodes) * [exit]simplify: Simplified to (+ (* (* v v) 12) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (* (* (sqrt (+ (* (* v v) 3) 1)) (sqrt 2)) (sqrt (+ 1 (* (* v v) (* (* v v) -9))))) (* (* (sqrt (+ 1 (* (* v v) (* (* v v) -9)))) (* (/ (sqrt 2) 4) (* v v))) (* 4 (sqrt (+ (* (* v v) 3) 1))))) (+ (* (* v v) 12) 4))) * * * * [misc]progress: [ 62 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (62 enodes) * * [misc]simplify: iters left: 4 (181 enodes) * [exit]simplify: Simplified to (- (* (* (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 9) (* v v))))) (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* (sqrt (+ 1 (* (* v v) -3))) (* (sqrt 2) (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (* (* (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 9) (* v v))))) (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* (sqrt (+ 1 (* (* v v) -3))) (* (sqrt 2) (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))) * [enter]simplify: Simplifying (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (* 16 (sqrt (+ 1 (* (* v v) 3)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (* (* (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 9) (* v v))))) (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* (sqrt (+ 1 (* (* v v) -3))) (* (sqrt 2) (* v v))))) (* 16 (sqrt (+ 1 (* (* v v) 3)))))) * * * * [misc]progress: [ 63 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))) * * [misc]simplify: iters left: 6 (28 enodes) * * [misc]simplify: iters left: 5 (80 enodes) * * [misc]simplify: iters left: 4 (271 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (170 enodes) * * [misc]simplify: iters left: 2 (318 enodes) * [exit]simplify: Simplified to (+ (* (pow v 4) 36) (+ (* (* v v) 12) 4)) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))))) (+ (* (pow v 4) 36) (+ (* (* v v) 12) 4)))) * * * * [misc]progress: [ 64 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (88 enodes) * * [misc]simplify: iters left: 4 (273 enodes) * [exit]simplify: Simplified to (- (/ (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (sqrt 2)) (/ 4 (sqrt (- 1 (pow (* (* v v) 3) 3))))) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* v v) (sqrt 2))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (/ (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (sqrt 2)) (/ 4 (sqrt (- 1 (pow (* (* v v) 3) 3))))) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* v v) (sqrt 2))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * [enter]simplify: Simplifying (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (250 enodes) * * [misc]simplify: iters left: 1 (334 enodes) * [exit]simplify: Simplified to (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (/ (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (sqrt 2)) (/ 4 (sqrt (- 1 (pow (* (* v v) 3) 3))))) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* v v) (sqrt 2))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))))) (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9))))))) * * * * [misc]progress: [ 65 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (74 enodes) * * [misc]simplify: iters left: 4 (233 enodes) * [exit]simplify: Simplified to (- (/ (* (sqrt 2) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (/ 4 (sqrt (- 1 (pow (* (* v v) 3) 3))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (/ (* (sqrt 2) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (/ 4 (sqrt (- 1 (pow (* (* v v) 3) 3))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (74 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * * [misc]simplify: iters left: 2 (265 enodes) * * [misc]simplify: iters left: 1 (350 enodes) * [exit]simplify: Simplified to (+ 1 (+ (* (* v v) 3) (* 9 (pow v 4)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (/ (* (sqrt 2) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (/ 4 (sqrt (- 1 (pow (* (* v v) 3) 3))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))))) (+ 1 (+ (* (* v v) 3) (* 9 (pow v 4)))))) * * * * [misc]progress: [ 66 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))) * * [misc]simplify: iters left: 6 (31 enodes) * * [misc]simplify: iters left: 5 (86 enodes) * * [misc]simplify: iters left: 4 (263 enodes) * [exit]simplify: Simplified to (- (* (* (sqrt (+ (* (* v 3) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (* (* (sqrt (+ (* (* v 3) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))) * [enter]simplify: Simplifying (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (74 enodes) * * [misc]simplify: iters left: 3 (161 enodes) * * [misc]simplify: iters left: 2 (296 enodes) * * [misc]simplify: iters left: 1 (363 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (+ (* 3 (* v v)) (* 9 (pow v 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (* (* (sqrt (+ (* (* v 3) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (+ (* 3 (* v v)) (* 9 (pow v 4)))))))) * * * * [misc]progress: [ 67 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) * * [misc]simplify: iters left: 6 (29 enodes) * * [misc]simplify: iters left: 5 (81 enodes) * * [misc]simplify: iters left: 4 (256 enodes) * [exit]simplify: Simplified to (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (- 1 (* (* v v) 3))) (* (* v v) (sqrt 2))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (- 1 (* (* v v) 3))) (* (* v v) (sqrt 2))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))) * [enter]simplify: Simplifying (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (214 enodes) * * [misc]simplify: iters left: 1 (266 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9)))) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (- 1 (* (* v v) 3))) (* (* v v) (sqrt 2))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))))) (* (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9)))) 4))) * * * * [misc]progress: [ 68 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (88 enodes) * * [misc]simplify: iters left: 4 (262 enodes) * [exit]simplify: Simplified to (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (85 enodes) * * [misc]simplify: iters left: 3 (138 enodes) * * [misc]simplify: iters left: 2 (227 enodes) * * [misc]simplify: iters left: 1 (276 enodes) * [exit]simplify: Simplified to (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (+ 1 (* (pow v 4) 9)) (* 3 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (+ 1 (* (pow v 4) 9)) (* 3 (* v v))))))) * * * * [misc]progress: [ 69 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (60 enodes) * * [misc]simplify: iters left: 4 (192 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* (* v 3) v))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* v v) (sqrt 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ 1 (* (* v 3) v))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* v v) (sqrt 2))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * [enter]simplify: Simplifying (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * * [misc]simplify: iters left: 2 (32 enodes) * * [misc]simplify: iters left: 1 (49 enodes) * [exit]simplify: Simplified to (+ 4 (* (* v v) 12)) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ 1 (* (* v 3) v))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* v v) (sqrt 2))))) (+ 4 (* (* v v) 12)))) * * * * [misc]progress: [ 70 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))) * * [misc]simplify: iters left: 6 (31 enodes) * * [misc]simplify: iters left: 5 (86 enodes) * * [misc]simplify: iters left: 4 (253 enodes) * [exit]simplify: Simplified to (+ (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))) (* (* (sqrt (+ 1 (* (* v 3) v))) (* (/ (sqrt 2) 4) (* (- v) v))) (sqrt (- 1 (pow (* (* v 3) v) 3))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (+ (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))) (* (* (sqrt (+ 1 (* (* v 3) v))) (* (/ (sqrt 2) 4) (* (- v) v))) (sqrt (- 1 (pow (* (* v 3) v) 3))))) (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (156 enodes) * * [misc]simplify: iters left: 2 (270 enodes) * * [misc]simplify: iters left: 1 (290 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ 1 (* v (* v 3))) (* 9 (pow v 4)))) (sqrt (+ 1 (* v (* v 3))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (+ (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))) (* (* (sqrt (+ 1 (* (* v 3) v))) (* (/ (sqrt 2) 4) (* (- v) v))) (sqrt (- 1 (pow (* (* v 3) v) 3))))) (* (sqrt (+ (+ 1 (* v (* v 3))) (* 9 (pow v 4)))) (sqrt (+ 1 (* v (* v 3))))))) * * * * [misc]progress: [ 71 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (54 enodes) * * [misc]simplify: iters left: 4 (157 enodes) * [exit]simplify: Simplified to (- (* (* (sqrt (+ 1 (* v (* v 3)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (* (* (sqrt (+ 1 (* v (* v 3)))) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (* (* (sqrt (+ 1 (* v (* v 3)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (* (* (sqrt (+ 1 (* v (* v 3)))) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))) * [enter]simplify: Simplifying (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * [exit]simplify: Simplified to (+ 1 (* (* v v) 3)) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (* (* (sqrt (+ 1 (* v (* v 3)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (* (* (sqrt (+ 1 (* v (* v 3)))) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))))) (+ 1 (* (* v v) 3)))) * * * * [misc]progress: [ 72 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (61 enodes) * * [misc]simplify: iters left: 4 (174 enodes) * * [misc]simplify: iters left: 3 (433 enodes) * [exit]simplify: Simplified to (- (* (/ (* (sqrt 2) 4) 4) (sqrt (- 1 (* (pow v 3) (* 9 v))))) (* (* (sqrt (+ 1 (* (* v 3) v))) (sqrt 2)) (* (* v v) (sqrt (+ 1 (* (* v -3) v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (* (/ (* (sqrt 2) 4) 4) (sqrt (- 1 (* (pow v 3) (* 9 v))))) (* (* (sqrt (+ 1 (* (* v 3) v))) (sqrt 2)) (* (* v v) (sqrt (+ 1 (* (* v -3) v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) 4))) * [enter]simplify: Simplifying (* (sqrt (+ 1 (* 3 (* v v)))) 4) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * [exit]simplify: Simplified to (* 4 (sqrt (+ 1 (* (* v 3) v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (* (/ (* (sqrt 2) 4) 4) (sqrt (- 1 (* (pow v 3) (* 9 v))))) (* (* (sqrt (+ 1 (* (* v 3) v))) (sqrt 2)) (* (* v v) (sqrt (+ 1 (* (* v -3) v)))))) (* 4 (sqrt (+ 1 (* (* v 3) v)))))) * * * * [misc]progress: [ 73 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))) * * [misc]simplify: iters left: 6 (29 enodes) * * [misc]simplify: iters left: 5 (82 enodes) * * [misc]simplify: iters left: 4 (257 enodes) * [exit]simplify: Simplified to (- (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* v (* -3 v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* v (* -3 v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4))) (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (138 enodes) * * [misc]simplify: iters left: 2 (221 enodes) * * [misc]simplify: iters left: 1 (274 enodes) * [exit]simplify: Simplified to (* 16 (sqrt (+ (+ (* (pow v 4) 9) (* (* v v) 3)) 1))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* v (* -3 v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4))) (* 16 (sqrt (+ (+ (* (pow v 4) 9) (* (* v v) 3)) 1))))) * * * * [misc]progress: [ 74 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (62 enodes) * * [misc]simplify: iters left: 4 (176 enodes) * * [misc]simplify: iters left: 3 (476 enodes) * [exit]simplify: Simplified to (- (* (* (sqrt 2) (sqrt (+ 1 (* (* -3 v) v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* (* (* v v) 4) (sqrt 2)) (sqrt (- 1 (* (pow v 3) (* v 9)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (* (* (sqrt 2) (sqrt (+ 1 (* (* -3 v) v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* (* (* v v) 4) (sqrt 2)) (sqrt (- 1 (* (pow v 3) (* v 9)))))) (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * [enter]simplify: Simplifying (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * [exit]simplify: Simplified to (* 16 (sqrt (+ 1 (* (* v v) 3)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (* (* (sqrt 2) (sqrt (+ 1 (* (* -3 v) v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* (* (* v v) 4) (sqrt 2)) (sqrt (- 1 (* (pow v 3) (* v 9)))))) (* 16 (sqrt (+ 1 (* (* v v) 3)))))) * * * * [misc]progress: [ 75 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))) * * [misc]simplify: iters left: 6 (29 enodes) * * [misc]simplify: iters left: 5 (81 enodes) * * [misc]simplify: iters left: 4 (255 enodes) * [exit]simplify: Simplified to (- (* (* (sqrt (- 1 (* (* v v) 3))) (sqrt 2)) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (* (* (sqrt (- 1 (* (* v v) 3))) (sqrt 2)) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (214 enodes) * * [misc]simplify: iters left: 1 (270 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ (* (pow v 4) 9) 1) (* 3 (* v v)))) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (* (* (sqrt (- 1 (* (* v v) 3))) (sqrt 2)) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4))) (* (sqrt (+ (+ (* (pow v 4) 9) 1) (* 3 (* v v)))) 4))) * * * * [misc]progress: [ 76 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (61 enodes) * * [misc]simplify: iters left: 4 (174 enodes) * [exit]simplify: Simplified to (- (* (sqrt (+ 1 (* 3 (* v v)))) (* (sqrt (+ 1 (* (* v -3) v))) (sqrt 2))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (* v v)) 4))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (* (sqrt (+ 1 (* 3 (* v v)))) (* (sqrt (+ 1 (* (* v -3) v))) (sqrt 2))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (* v v)) 4))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * [enter]simplify: Simplifying (* 4 (sqrt (+ 1 (* 3 (* v v))))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* v (* 3 v)))) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (* (sqrt (+ 1 (* 3 (* v v)))) (* (sqrt (+ 1 (* (* v -3) v))) (sqrt 2))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (* v v)) 4))) (* (sqrt (+ 1 (* v (* 3 v)))) 4))) * * * * [misc]progress: [ 77 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (115 enodes) * * [misc]simplify: iters left: 3 (294 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* v v) -3) 1)) (* (sqrt 2) (- 4 (* 4 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* v v) -3) 1)) (* (sqrt 2) (- 4 (* 4 (* v v))))) (* 4 4))) * [enter]simplify: Simplifying (* 4 4) * * [misc]simplify: iters left: 2 (2 enodes) * * [misc]simplify: iters left: 1 (3 enodes) * [exit]simplify: Simplified to 16 * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* v v) -3) 1)) (* (sqrt 2) (- 4 (* 4 (* v v))))) 16)) * * * * [misc]progress: [ 78 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 79 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* v v)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (118 enodes) * * [misc]simplify: iters left: 2 (155 enodes) * * [misc]simplify: iters left: 1 (186 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (* (* -3 v) v))) (/ (/ 4 v) (* v (sqrt 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (/ (sqrt (+ 1 (* (* -3 v) v))) (/ (/ 4 v) (* v (sqrt 2)))))) * * * * [misc]progress: [ 80 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 81 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 82 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* v (* -3 v)))) (/ (sqrt 2) 4)) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (sqrt (+ 1 (* v (* -3 v)))) (/ (sqrt 2) 4)) (+ 1 (- (* v v))))) * [enter]simplify: Simplifying (+ 1 (- (* v v))) * * [misc]simplify: iters left: 6 (5 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * [exit]simplify: Simplified to (- 1 (* v v)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v)))) * * * * [misc]progress: [ 83 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* v v)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (118 enodes) * * [misc]simplify: iters left: 2 (155 enodes) * * [misc]simplify: iters left: 1 (186 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (* (* -3 v) v))) (/ (/ 4 v) (* v (sqrt 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (/ (sqrt (+ 1 (* (* -3 v) v))) (/ (/ 4 v) (* v (sqrt 2)))))) * * * * [misc]progress: [ 84 / 96 ] simplifiying candidate # * * * * [misc]progress: [ 85 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 9/32 (* (sqrt 2) (pow v 6))) (* 3/8 (* (sqrt 2) (pow v 4)))) (* 1/4 (* (sqrt 2) (pow v 2)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (245 enodes) * * [misc]simplify: iters left: 1 (365 enodes) * [exit]simplify: Simplified to (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)) * [misc]simplify: Simplified (2 2) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)))) * * * * [misc]progress: [ 86 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* 1/32 (/ (sqrt 2) (* v (pow (sqrt -3) 3)))) (+ (* 1/4 (* (sqrt 2) (* (pow v 3) (sqrt -3)))) (* 1/8 (/ (* (sqrt 2) v) (sqrt -3))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (129 enodes) * * [misc]simplify: iters left: 3 (360 enodes) * [exit]simplify: Simplified to (- (* (/ (sqrt 2) (sqrt -3)) (- (/ -1/96 v) (* v 1/8))) (* (* (* v v) (sqrt -3)) (* (sqrt 2) (* v 1/4)))) * [misc]simplify: Simplified (2 2) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (- (* (/ (sqrt 2) (sqrt -3)) (- (/ -1/96 v) (* v 1/8))) (* (* (* v v) (sqrt -3)) (* (sqrt 2) (* v 1/4)))))) * * * * [misc]progress: [ 87 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 1/4 (* (sqrt 2) (* (pow v 3) (sqrt -3)))) (* 1/8 (/ (* (sqrt 2) v) (sqrt -3)))) (* 1/32 (/ (sqrt 2) (* v (pow (sqrt -3) 3))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (138 enodes) * * [misc]simplify: iters left: 3 (344 enodes) * [exit]simplify: Simplified to (+ (* (* (* v 1/4) (sqrt 2)) (* (* v v) (sqrt -3))) (* (/ (sqrt 2) (sqrt -3)) (- (* v 1/8) (/ -1/96 v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (+ (* (* (* v 1/4) (sqrt 2)) (* (* v v) (sqrt -3))) (* (/ (sqrt 2) (sqrt -3)) (- (* v 1/8) (/ -1/96 v)))))) * * * * [misc]progress: [ 88 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (* 3 (pow v 2)) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * * [misc]simplify: iters left: 1 (11 enodes) * [exit]simplify: Simplified to (* (* v v) 3) * [misc]simplify: Simplified (2 2 1 2 1 2) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v v) 3)))) (- (* v v))))) * * * * [misc]progress: [ 89 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (* 3 (pow v 2)) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * * [misc]simplify: iters left: 1 (11 enodes) * [exit]simplify: Simplified to (* (* v v) 3) * [misc]simplify: Simplified (2 2 1 2 1 2) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v v) 3)))) (- (* v v))))) * * * * [misc]progress: [ 90 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (* 3 (pow v 2)) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * * [misc]simplify: iters left: 1 (11 enodes) * [exit]simplify: Simplified to (* (* v v) 3) * [misc]simplify: Simplified (2 2 1 2 1 2) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v v) 3)))) (- (* v v))))) * * * * [misc]progress: [ 91 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (* 3 (pow v 2)) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * * [misc]simplify: iters left: 1 (11 enodes) * [exit]simplify: Simplified to (* (* v v) 3) * [misc]simplify: Simplified (2 1 1 2 1 2) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v v) 3)))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) * * * * [misc]progress: [ 92 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (* 3 (pow v 2)) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * * [misc]simplify: iters left: 1 (11 enodes) * [exit]simplify: Simplified to (* (* v v) 3) * [misc]simplify: Simplified (2 1 1 2 1 2) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v v) 3)))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) * * * * [misc]progress: [ 93 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (* 3 (pow v 2)) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * * [misc]simplify: iters left: 1 (11 enodes) * [exit]simplify: Simplified to (* (* v v) 3) * [misc]simplify: Simplified (2 1 1 2 1 2) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v v) 3)))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) * * * * [misc]progress: [ 94 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 1/4 (sqrt 2)) (* 3/32 (* (sqrt 2) (pow v 4)))) (* 5/8 (* (sqrt 2) (pow v 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (133 enodes) * * [misc]simplify: iters left: 2 (232 enodes) * * [misc]simplify: iters left: 1 (314 enodes) * [exit]simplify: Simplified to (* (+ (+ 1/4 (* (pow v 4) 3/32)) (* (* -5/8 v) v)) (sqrt 2)) * [misc]simplify: Simplified (2) to (λ (v) (* (+ (+ 1/4 (* (pow v 4) 3/32)) (* (* -5/8 v) v)) (sqrt 2))) * * * * [misc]progress: [ 95 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 1/32 (/ (sqrt 2) (* v (pow (sqrt -3) 3)))) (+ (* 1/4 (* (sqrt 2) (* v (sqrt -3)))) (* 1/8 (/ (sqrt 2) (* v (sqrt -3)))))) (+ (* 1/8 (/ (* (sqrt 2) v) (sqrt -3))) (* 1/4 (* (sqrt 2) (* (pow v 3) (sqrt -3)))))) * * [misc]simplify: iters left: 6 (29 enodes) * * [misc]simplify: iters left: 5 (74 enodes) * * [misc]simplify: iters left: 4 (207 enodes) * [exit]simplify: Simplified to (- (+ (* (/ (sqrt 2) v) (+ (/ -1/96 (sqrt -3)) (/ 1/8 (sqrt -3)))) (- (* (* (* 1/4 v) (sqrt 2)) (sqrt -3)) (/ (* 1/8 (sqrt 2)) (/ (sqrt -3) v)))) (* (* (* 1/4 v) (sqrt 2)) (* (sqrt -3) (* v v)))) * [misc]simplify: Simplified (2) to (λ (v) (- (+ (* (/ (sqrt 2) v) (+ (/ -1/96 (sqrt -3)) (/ 1/8 (sqrt -3)))) (- (* (* (* 1/4 v) (sqrt 2)) (sqrt -3)) (/ (* 1/8 (sqrt 2)) (/ (sqrt -3) v)))) (* (* (* 1/4 v) (sqrt 2)) (* (sqrt -3) (* v v))))) * * * * [misc]progress: [ 96 / 96 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 1/8 (/ (* (sqrt 2) v) (sqrt -3))) (* 1/4 (* (sqrt 2) (* (pow v 3) (sqrt -3))))) (+ (* 1/32 (/ (sqrt 2) (* v (pow (sqrt -3) 3)))) (+ (* 1/4 (* (sqrt 2) (* v (sqrt -3)))) (* 1/8 (/ (sqrt 2) (* v (sqrt -3))))))) * * [misc]simplify: iters left: 6 (29 enodes) * * [misc]simplify: iters left: 5 (74 enodes) * * [misc]simplify: iters left: 4 (209 enodes) * [exit]simplify: Simplified to (- (- (+ (* (/ 1/8 (sqrt -3)) (* (sqrt 2) v)) (* (* (sqrt 2) (* 1/4 v)) (* (sqrt -3) (* v v)))) (* (/ (sqrt 2) v) (+ (/ 1/8 (sqrt -3)) (/ -1/96 (sqrt -3))))) (* (sqrt -3) (* (sqrt 2) (* 1/4 v)))) * [misc]simplify: Simplified (2) to (λ (v) (- (- (+ (* (/ 1/8 (sqrt -3)) (* (sqrt 2) v)) (* (* (sqrt 2) (* 1/4 v)) (* (sqrt -3) (* v v)))) (* (/ (sqrt 2) v) (+ (/ 1/8 (sqrt -3)) (/ -1/96 (sqrt -3))))) (* (sqrt -3) (* (sqrt 2) (* 1/4 v))))) * * * [misc]progress: adding candidates to table * * [misc]progress: iteration 3 / 4 * * * [misc]progress: picking best candidate * * * * [misc]pick: Picked # * * * [misc]progress: localizing error * * * [misc]progress: generating rewritten candidates * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 2) * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 1 1 2 1 2) * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 2 1 2) * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 1 1) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2) * [misc]approximate: Taking taylor expansion of (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)) in v * [misc]taylor: Taking taylor expansion of (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) in v * [misc]taylor: Taking taylor expansion of (- (* (pow v 6) 9/32) (* (* v v) 1/4)) in v * [misc]taylor: Taking taylor expansion of (* (pow v 6) 9/32) in v * [misc]taylor: Taking taylor expansion of (pow v 6) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 9/32 in v * [misc]backup-simplify: Simplify 9/32 into 9/32 * [misc]taylor: Taking taylor expansion of (* (* v v) 1/4) in v * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 1/4 in v * [misc]backup-simplify: Simplify 1/4 into 1/4 * [misc]taylor: Taking taylor expansion of (* 3/8 (pow v 4)) in v * [misc]taylor: Taking taylor expansion of 3/8 in v * [misc]backup-simplify: Simplify 3/8 into 3/8 * [misc]taylor: Taking taylor expansion of (pow v 4) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)) in v * [misc]taylor: Taking taylor expansion of (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) in v * [misc]taylor: Taking taylor expansion of (- (* (pow v 6) 9/32) (* (* v v) 1/4)) in v * [misc]taylor: Taking taylor expansion of (* (pow v 6) 9/32) in v * [misc]taylor: Taking taylor expansion of (pow v 6) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 9/32 in v * [misc]backup-simplify: Simplify 9/32 into 9/32 * [misc]taylor: Taking taylor expansion of (* (* v v) 1/4) in v * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 1/4 in v * [misc]backup-simplify: Simplify 1/4 into 1/4 * [misc]taylor: Taking taylor expansion of (* 3/8 (pow v 4)) in v * [misc]taylor: Taking taylor expansion of 3/8 in v * [misc]backup-simplify: Simplify 3/8 into 3/8 * [misc]taylor: Taking taylor expansion of (pow v 4) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 0 1/4) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (* 0 (sqrt 2)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 0 1/4)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 0 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 1) (* 0 0))) into 1 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 0 0) (* 1 1/4))) into 1/4 * [misc]backup-simplify: Simplify (- 1/4) into -1/4 * [misc]backup-simplify: Simplify (+ 0 -1/4) into -1/4 * [misc]backup-simplify: Simplify (+ -1/4 0) into -1/4 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 0 0) (* -1/4 (sqrt 2)))) into (- (* 1/4 (sqrt 2))) * [misc]backup-simplify: Simplify (- (* 1/4 (sqrt 2))) into (- (* 1/4 (sqrt 2))) * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 0 0) (+ (* 1 0) (* 0 1/4)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 0 0) (+ (* -1/4 0) (* 0 (sqrt 2))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 1/4))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3/8 1) into 3/8 * [misc]backup-simplify: Simplify (+ 0 3/8) into 3/8 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 0 0) (+ (* -1/4 0) (+ (* 0 0) (* 3/8 (sqrt 2)))))) into (* 3/8 (sqrt 2)) * [misc]backup-simplify: Simplify (* 3/8 (sqrt 2)) into (* 3/8 (sqrt 2)) * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 1/4)))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3/8 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 0 0) (+ (* -1/4 0) (+ (* 0 0) (+ (* 3/8 0) (* 0 (sqrt 2))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 9/32) into 9/32 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1/4))))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 9/32 0) into 9/32 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3/8 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (+ 9/32 0) into 9/32 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 0 0) (+ (* -1/4 0) (+ (* 0 0) (+ (* 3/8 0) (+ (* 0 0) (* 9/32 (sqrt 2)))))))) into (* 9/32 (sqrt 2)) * [misc]backup-simplify: Simplify (* 9/32 (sqrt 2)) into (* 9/32 (sqrt 2)) * [misc]backup-simplify: Simplify (+ (* (* 9/32 (sqrt 2)) (pow v 6)) (+ (* (* 3/8 (sqrt 2)) (pow v 4)) (* (- (* 1/4 (sqrt 2))) (pow v 2)))) into (- (+ (* 9/32 (* (sqrt 2) (pow v 6))) (* 3/8 (* (sqrt 2) (pow v 4)))) (* 1/4 (* (sqrt 2) (pow v 2)))) * [misc]approximate: Taking taylor expansion of (* (+ (- (* (pow (/ 1 v) 6) 9/32) (* (* (/ 1 v) (/ 1 v)) 1/4)) (* 3/8 (pow (/ 1 v) 4))) (sqrt 2)) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (+ (- (* (pow (/ 1 v) 6) 9/32) (* (* (/ 1 v) (/ 1 v)) 1/4)) (* 3/8 (pow (/ 1 v) 4))) (sqrt 2)) in v * [misc]taylor: Taking taylor expansion of (+ (- (* (pow (/ 1 v) 6) 9/32) (* (* (/ 1 v) (/ 1 v)) 1/4)) (* 3/8 (pow (/ 1 v) 4))) in v * [misc]taylor: Taking taylor expansion of (- (* (pow (/ 1 v) 6) 9/32) (* (* (/ 1 v) (/ 1 v)) 1/4)) in v * [misc]taylor: Taking taylor expansion of (* (pow (/ 1 v) 6) 9/32) in v * [misc]taylor: Taking taylor expansion of (pow (/ 1 v) 6) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 9/32 in v * [misc]backup-simplify: Simplify 9/32 into 9/32 * [misc]taylor: Taking taylor expansion of (* (* (/ 1 v) (/ 1 v)) 1/4) in v * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 1/4 in v * [misc]backup-simplify: Simplify 1/4 into 1/4 * [misc]taylor: Taking taylor expansion of (* 3/8 (pow (/ 1 v) 4)) in v * [misc]taylor: Taking taylor expansion of 3/8 in v * [misc]backup-simplify: Simplify 3/8 into 3/8 * [misc]taylor: Taking taylor expansion of (pow (/ 1 v) 4) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of (* (+ (- (* (pow (/ 1 v) 6) 9/32) (* (* (/ 1 v) (/ 1 v)) 1/4)) (* 3/8 (pow (/ 1 v) 4))) (sqrt 2)) in v * [misc]taylor: Taking taylor expansion of (+ (- (* (pow (/ 1 v) 6) 9/32) (* (* (/ 1 v) (/ 1 v)) 1/4)) (* 3/8 (pow (/ 1 v) 4))) in v * [misc]taylor: Taking taylor expansion of (- (* (pow (/ 1 v) 6) 9/32) (* (* (/ 1 v) (/ 1 v)) 1/4)) in v * [misc]taylor: Taking taylor expansion of (* (pow (/ 1 v) 6) 9/32) in v * [misc]taylor: Taking taylor expansion of (pow (/ 1 v) 6) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 9/32 in v * [misc]backup-simplify: Simplify 9/32 into 9/32 * [misc]taylor: Taking taylor expansion of (* (* (/ 1 v) (/ 1 v)) 1/4) in v * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 1/4 in v * [misc]backup-simplify: Simplify 1/4 into 1/4 * [misc]taylor: Taking taylor expansion of (* 3/8 (pow (/ 1 v) 4)) in v * [misc]taylor: Taking taylor expansion of 3/8 in v * [misc]backup-simplify: Simplify 3/8 into 3/8 * [misc]taylor: Taking taylor expansion of (pow (/ 1 v) 4) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 9/32) into 9/32 * [misc]backup-simplify: Simplify (+ 9/32 0) into 9/32 * [misc]backup-simplify: Simplify (+ 9/32 0) into 9/32 * [misc]backup-simplify: Simplify (* 9/32 (sqrt 2)) into (* 9/32 (sqrt 2)) * [misc]backup-simplify: Simplify (* 9/32 (sqrt 2)) into (* 9/32 (sqrt 2)) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 9/32)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 9/32 0) (* 0 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 9/32))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3/8 1) into 3/8 * [misc]backup-simplify: Simplify (+ 0 3/8) into 3/8 * [misc]backup-simplify: Simplify (+ (* 9/32 0) (+ (* 0 0) (* 3/8 (sqrt 2)))) into (* 3/8 (sqrt 2)) * [misc]backup-simplify: Simplify (* 3/8 (sqrt 2)) into (* 3/8 (sqrt 2)) * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 9/32)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3/8 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 9/32 0) (+ (* 0 0) (+ (* 3/8 0) (* 0 (sqrt 2))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 9/32))))) into 0 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1/4) into 1/4 * [misc]backup-simplify: Simplify (- 1/4) into -1/4 * [misc]backup-simplify: Simplify (+ 0 -1/4) into -1/4 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3/8 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (+ -1/4 0) into -1/4 * [misc]backup-simplify: Simplify (+ (* 9/32 0) (+ (* 0 0) (+ (* 3/8 0) (+ (* 0 0) (* -1/4 (sqrt 2)))))) into (- (* 1/4 (sqrt 2))) * [misc]backup-simplify: Simplify (- (* 1/4 (sqrt 2))) into (- (* 1/4 (sqrt 2))) * [misc]backup-simplify: Simplify (+ (* (- (* 1/4 (sqrt 2))) (pow (/ 1 (/ 1 v)) 2)) (+ (* (* 3/8 (sqrt 2)) (pow (/ 1 (/ 1 v)) 4)) (* (* 9/32 (sqrt 2)) (pow (/ 1 (/ 1 v)) 6)))) into (- (+ (* 9/32 (* (sqrt 2) (pow v 6))) (* 3/8 (* (sqrt 2) (pow v 4)))) (* 1/4 (* (sqrt 2) (pow v 2)))) * [misc]approximate: Taking taylor expansion of (* (+ (- (* (pow (/ 1 (- v)) 6) 9/32) (* (* (/ 1 (- v)) (/ 1 (- v))) 1/4)) (* 3/8 (pow (/ 1 (- v)) 4))) (sqrt 2)) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (+ (- (* (pow (/ 1 (- v)) 6) 9/32) (* (* (/ 1 (- v)) (/ 1 (- v))) 1/4)) (* 3/8 (pow (/ 1 (- v)) 4))) (sqrt 2)) in v * [misc]taylor: Taking taylor expansion of (+ (- (* (pow (/ 1 (- v)) 6) 9/32) (* (* (/ 1 (- v)) (/ 1 (- v))) 1/4)) (* 3/8 (pow (/ 1 (- v)) 4))) in v * [misc]taylor: Taking taylor expansion of (- (* (pow (/ 1 (- v)) 6) 9/32) (* (* (/ 1 (- v)) (/ 1 (- v))) 1/4)) in v * [misc]taylor: Taking taylor expansion of (* (pow (/ 1 (- v)) 6) 9/32) in v * [misc]taylor: Taking taylor expansion of (pow (/ 1 (- v)) 6) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 9/32 in v * [misc]backup-simplify: Simplify 9/32 into 9/32 * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- v)) (/ 1 (- v))) 1/4) in v * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 1/4 in v * [misc]backup-simplify: Simplify 1/4 into 1/4 * [misc]taylor: Taking taylor expansion of (* 3/8 (pow (/ 1 (- v)) 4)) in v * [misc]taylor: Taking taylor expansion of 3/8 in v * [misc]backup-simplify: Simplify 3/8 into 3/8 * [misc]taylor: Taking taylor expansion of (pow (/ 1 (- v)) 4) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of (* (+ (- (* (pow (/ 1 (- v)) 6) 9/32) (* (* (/ 1 (- v)) (/ 1 (- v))) 1/4)) (* 3/8 (pow (/ 1 (- v)) 4))) (sqrt 2)) in v * [misc]taylor: Taking taylor expansion of (+ (- (* (pow (/ 1 (- v)) 6) 9/32) (* (* (/ 1 (- v)) (/ 1 (- v))) 1/4)) (* 3/8 (pow (/ 1 (- v)) 4))) in v * [misc]taylor: Taking taylor expansion of (- (* (pow (/ 1 (- v)) 6) 9/32) (* (* (/ 1 (- v)) (/ 1 (- v))) 1/4)) in v * [misc]taylor: Taking taylor expansion of (* (pow (/ 1 (- v)) 6) 9/32) in v * [misc]taylor: Taking taylor expansion of (pow (/ 1 (- v)) 6) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 9/32 in v * [misc]backup-simplify: Simplify 9/32 into 9/32 * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- v)) (/ 1 (- v))) 1/4) in v * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 1/4 in v * [misc]backup-simplify: Simplify 1/4 into 1/4 * [misc]taylor: Taking taylor expansion of (* 3/8 (pow (/ 1 (- v)) 4)) in v * [misc]taylor: Taking taylor expansion of 3/8 in v * [misc]backup-simplify: Simplify 3/8 into 3/8 * [misc]taylor: Taking taylor expansion of (pow (/ 1 (- v)) 4) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* -1 1) into -1 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 1 9/32) into 9/32 * [misc]backup-simplify: Simplify (+ 9/32 0) into 9/32 * [misc]backup-simplify: Simplify (+ 9/32 0) into 9/32 * [misc]backup-simplify: Simplify (* 9/32 (sqrt 2)) into (* 9/32 (sqrt 2)) * [misc]backup-simplify: Simplify (* 9/32 (sqrt 2)) into (* 9/32 (sqrt 2)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 9/32)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 9/32 0) (* 0 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 9/32))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3/8 1) into 3/8 * [misc]backup-simplify: Simplify (+ 0 3/8) into 3/8 * [misc]backup-simplify: Simplify (+ (* 9/32 0) (+ (* 0 0) (* 3/8 (sqrt 2)))) into (* 3/8 (sqrt 2)) * [misc]backup-simplify: Simplify (* 3/8 (sqrt 2)) into (* 3/8 (sqrt 2)) * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 9/32)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3/8 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 9/32 0) (+ (* 0 0) (+ (* 3/8 0) (* 0 (sqrt 2))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 9/32))))) into 0 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 1 1/4) into 1/4 * [misc]backup-simplify: Simplify (- 1/4) into -1/4 * [misc]backup-simplify: Simplify (+ 0 -1/4) into -1/4 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3/8 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (+ -1/4 0) into -1/4 * [misc]backup-simplify: Simplify (+ (* 9/32 0) (+ (* 0 0) (+ (* 3/8 0) (+ (* 0 0) (* -1/4 (sqrt 2)))))) into (- (* 1/4 (sqrt 2))) * [misc]backup-simplify: Simplify (- (* 1/4 (sqrt 2))) into (- (* 1/4 (sqrt 2))) * [misc]backup-simplify: Simplify (+ (* (- (* 1/4 (sqrt 2))) (pow (/ 1 (/ 1 (- v))) 2)) (+ (* (* 3/8 (sqrt 2)) (pow (/ 1 (/ 1 (- v))) 4)) (* (* 9/32 (sqrt 2)) (pow (/ 1 (/ 1 (- v))) 6)))) into (- (+ (* 9/32 (* (sqrt 2) (pow v 6))) (* 3/8 (* (sqrt 2) (pow v 4)))) (* 1/4 (* (sqrt 2) (pow v 2)))) * * * * [misc]progress: [ 2 / 4 ] generating series at (2 1 1 2 1 2) * [misc]approximate: Taking taylor expansion of (* 3 (* v v)) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 3 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 1) (* 0 0))) into 1 * [misc]backup-simplify: Simplify (+ (* 3 1) (+ (* 0 0) (* 0 0))) into 3 * [misc]backup-simplify: Simplify 3 into 3 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 1) (+ (* 0 0) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0))))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* 3 (pow v 2)) into (* 3 (pow v 2)) * [misc]approximate: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify 3 into 3 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* 3 (pow (/ 1 (/ 1 v)) 2)) into (* 3 (pow v 2)) * [misc]approximate: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify 3 into 3 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* 3 (pow (/ 1 (/ 1 (- v))) 2)) into (* 3 (pow v 2)) * * * * [misc]progress: [ 3 / 4 ] generating series at (2 2 1 2) * [misc]approximate: Taking taylor expansion of (* 3/8 (pow v 4)) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* 3/8 (pow v 4)) in v * [misc]taylor: Taking taylor expansion of 3/8 in v * [misc]backup-simplify: Simplify 3/8 into 3/8 * [misc]taylor: Taking taylor expansion of (pow v 4) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3/8 (pow v 4)) in v * [misc]taylor: Taking taylor expansion of 3/8 in v * [misc]backup-simplify: Simplify 3/8 into 3/8 * [misc]taylor: Taking taylor expansion of (pow v 4) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3/8 1) into 3/8 * [misc]backup-simplify: Simplify 3/8 into 3/8 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3/8 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3/8 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3/8 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3/8 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3/8 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3/8 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* 3/8 (pow v 4)) into (* 3/8 (pow v 4)) * [misc]approximate: Taking taylor expansion of (* 3/8 (pow (/ 1 v) 4)) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* 3/8 (pow (/ 1 v) 4)) in v * [misc]taylor: Taking taylor expansion of 3/8 in v * [misc]backup-simplify: Simplify 3/8 into 3/8 * [misc]taylor: Taking taylor expansion of (pow (/ 1 v) 4) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (* 3/8 (pow (/ 1 v) 4)) in v * [misc]taylor: Taking taylor expansion of 3/8 in v * [misc]backup-simplify: Simplify 3/8 into 3/8 * [misc]taylor: Taking taylor expansion of (pow (/ 1 v) 4) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3/8 1) into 3/8 * [misc]backup-simplify: Simplify 3/8 into 3/8 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3/8 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3/8 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3/8 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3/8 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3/8 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3/8 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* 3/8 (pow (/ 1 (/ 1 v)) 4)) into (* 3/8 (pow v 4)) * [misc]approximate: Taking taylor expansion of (* 3/8 (pow (/ 1 (- v)) 4)) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* 3/8 (pow (/ 1 (- v)) 4)) in v * [misc]taylor: Taking taylor expansion of 3/8 in v * [misc]backup-simplify: Simplify 3/8 into 3/8 * [misc]taylor: Taking taylor expansion of (pow (/ 1 (- v)) 4) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (* 3/8 (pow (/ 1 (- v)) 4)) in v * [misc]taylor: Taking taylor expansion of 3/8 in v * [misc]backup-simplify: Simplify 3/8 into 3/8 * [misc]taylor: Taking taylor expansion of (pow (/ 1 (- v)) 4) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3/8 1) into 3/8 * [misc]backup-simplify: Simplify 3/8 into 3/8 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3/8 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3/8 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3/8 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3/8 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3/8 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3/8 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* 3/8 (pow (/ 1 (/ 1 (- v))) 4)) into (* 3/8 (pow v 4)) * * * * [misc]progress: [ 4 / 4 ] generating series at (2 1 1) * [misc]approximate: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* v v)))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* v v))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 3 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1))) into 0 * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* v v)))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* v v))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 3 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1))) into 0 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) 1) into (* 1/4 (sqrt 2)) * [misc]backup-simplify: Simplify (* 1/4 (sqrt 2)) into (* 1/4 (sqrt 2)) * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 1) (* 0 0))) into 1 * [misc]backup-simplify: Simplify (+ (* 3 1) (+ (* 0 0) (* 0 0))) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (/ (- -3 (pow 0 2) (+)) (* 2 1)) into -3/2 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -3/2) (+ (* 0 0) (* 0 1))) into (- (* 3/8 (sqrt 2))) * [misc]backup-simplify: Simplify (- (* 3/8 (sqrt 2))) into (- (* 3/8 (sqrt 2))) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 1) (+ (* 0 0) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 -3/2)))) (* 2 1)) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 -3/2) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow -3/2 2) (+ (* 2 (* 0 0)))) (* 2 1)) into -9/8 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -9/8) (+ (* 0 0) (+ (* 0 -3/2) (+ (* 0 0) (* 0 1))))) into (- (* 9/32 (sqrt 2))) * [misc]backup-simplify: Simplify (- (* 9/32 (sqrt 2))) into (- (* 9/32 (sqrt 2))) * [misc]backup-simplify: Simplify (+ (* (- (* 9/32 (sqrt 2))) (pow v 4)) (+ (* (- (* 3/8 (sqrt 2))) (pow v 2)) (* 1/4 (sqrt 2)))) into (- (* 1/4 (sqrt 2)) (+ (* 9/32 (* (sqrt 2) (pow v 4))) (* 3/8 (* (sqrt 2) (pow v 2))))) * [misc]approximate: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) (sqrt -3)) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* 1/4 (* (sqrt 2) (sqrt -3))) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ (- 1 (pow 0 2) (+)) (* 2 (sqrt -3))) into (/ 1/2 (sqrt -3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))) into (* 1/8 (/ (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* 1/8 (/ (sqrt 2) (sqrt -3))) into (* 1/8 (/ (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (/ 1/2 (sqrt -3)))))) (* 2 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ 1/2 (sqrt -3)) 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt -3))) into (/ -1/8 (pow (sqrt -3) 3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ -1/8 (pow (sqrt -3) 3))) (+ (* 0 0) (+ (* 0 (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))))) into (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) * [misc]backup-simplify: Simplify (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) into (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) * [misc]backup-simplify: Simplify (+ (* (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) (pow (/ 1 v) 3)) (+ (* (* 1/8 (/ (sqrt 2) (sqrt -3))) (/ 1 v)) (* (* 1/4 (* (sqrt 2) (sqrt -3))) (/ 1 (/ 1 v))))) into (- (+ (* 1/4 (* (sqrt 2) (* v (sqrt -3)))) (* 1/8 (/ (sqrt 2) (* v (sqrt -3))))) (* 1/32 (/ (sqrt 2) (* (pow v 3) (pow (sqrt -3) 3))))) * [misc]approximate: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) (sqrt -3)) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* 1/4 (* (sqrt 2) (sqrt -3))) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ (- 1 (pow 0 2) (+)) (* 2 (sqrt -3))) into (/ 1/2 (sqrt -3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))) into (* 1/8 (/ (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* 1/8 (/ (sqrt 2) (sqrt -3))) into (* 1/8 (/ (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (/ 1/2 (sqrt -3)))))) (* 2 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ 1/2 (sqrt -3)) 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt -3))) into (/ -1/8 (pow (sqrt -3) 3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ -1/8 (pow (sqrt -3) 3))) (+ (* 0 0) (+ (* 0 (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))))) into (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) * [misc]backup-simplify: Simplify (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) into (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) * [misc]backup-simplify: Simplify (+ (* (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) (pow (/ 1 (- v)) 3)) (+ (* (* 1/8 (/ (sqrt 2) (sqrt -3))) (/ 1 (- v))) (* (* 1/4 (* (sqrt 2) (sqrt -3))) (/ 1 (/ 1 (- v)))))) into (- (* 1/32 (/ (sqrt 2) (* (pow v 3) (pow (sqrt -3) 3)))) (+ (* 1/4 (* (sqrt 2) (* v (sqrt -3)))) (* 1/8 (/ (sqrt 2) (* v (sqrt -3)))))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (189 enodes) * * [misc]simplify: iters left: 1 (271 enodes) * [exit]simplify: Simplified to (* (+ (- (* (pow v 6) 9/32) (* -3/8 (pow v 4))) (* -1/4 (* v v))) (sqrt 2)) * [misc]simplify: Simplified (2 2 1) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (pow (* (+ (- (* (pow v 6) 9/32) (* -3/8 (pow v 4))) (* -1/4 (* v v))) (sqrt 2)) 1))) * * * * [misc]progress: [ 2 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 3 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4)))) (log (sqrt 2))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (81 enodes) * * [misc]simplify: iters left: 2 (93 enodes) * * [misc]simplify: iters left: 1 (101 enodes) * [exit]simplify: Simplified to (+ (log (- (* (pow v 4) 3/8) (- (* (* v 1/4) v) (* (pow v 6) 9/32)))) (log (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (exp (+ (log (- (* (pow v 4) 3/8) (- (* (* v 1/4) v) (* (pow v 6) 9/32)))) (log (sqrt 2)))))) * * * * [misc]progress: [ 4 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 5 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 6 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4)))) (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4)))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (190 enodes) * [exit]simplify: Simplified to (* (* (+ (+ (* (pow v 4) 3/8) (* (pow v 6) 9/32)) (* v (* -1/4 v))) (+ (+ (* (pow v 4) 3/8) (* (pow v 6) 9/32)) (* v (* -1/4 v)))) (* (+ (+ (* (pow v 4) 3/8) (* (pow v 6) 9/32)) (* v (* -1/4 v))) (* 2 (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (cbrt (* (* (+ (+ (* (pow v 4) 3/8) (* (pow v 6) 9/32)) (* v (* -1/4 v))) (+ (+ (* (pow v 4) 3/8) (* (pow v 6) 9/32)) (* v (* -1/4 v)))) (* (+ (+ (* (pow v 4) 3/8) (* (pow v 6) 9/32)) (* v (* -1/4 v))) (* 2 (sqrt 2))))))) * * * * [misc]progress: [ 7 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 8 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 9 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 10 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 11 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (cbrt (sqrt 2)) * * [misc]simplify: iters left: 2 (3 enodes) * [exit]simplify: Simplified to (cbrt (sqrt 2)) * [misc]simplify: Simplified (2 2 2) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2))))) * * * * [misc]progress: [ 12 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (sqrt 2)) * * [misc]simplify: iters left: 2 (3 enodes) * [exit]simplify: Simplified to (sqrt (sqrt 2)) * [misc]simplify: Simplified (2 2 2) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt (sqrt 2))) (sqrt (sqrt 2))))) * * * * [misc]progress: [ 13 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt 2) * * [misc]simplify: iters left: 1 (2 enodes) * [exit]simplify: Simplified to (sqrt 2) * [misc]simplify: Simplified (2 2 2) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) 1) (sqrt 2)))) * * * * [misc]progress: [ 14 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4)))) (cbrt (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (76 enodes) * * [misc]simplify: iters left: 2 (90 enodes) * * [misc]simplify: iters left: 1 (98 enodes) * [exit]simplify: Simplified to (* (cbrt (+ (+ (* 3/8 (pow v 4)) (* (pow v 6) 9/32)) (* -1/4 (* v v)))) (cbrt (+ (+ (* 3/8 (pow v 4)) (* (pow v 6) 9/32)) (* -1/4 (* v v))))) * [misc]simplify: Simplified (2 2 1) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (cbrt (+ (+ (* 3/8 (pow v 4)) (* (pow v 6) 9/32)) (* -1/4 (* v v)))) (cbrt (+ (+ (* 3/8 (pow v 4)) (* (pow v 6) 9/32)) (* -1/4 (* v v))))) (* (cbrt (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4)))) (sqrt 2))))) * * * * [misc]progress: [ 15 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (75 enodes) * * [misc]simplify: iters left: 2 (89 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (sqrt (+ (* 3/8 (pow v 4)) (+ (* (* v v) -1/4) (* (pow v 6) 9/32)))) * [misc]simplify: Simplified (2 2 1) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (sqrt (+ (* 3/8 (pow v 4)) (+ (* (* v v) -1/4) (* (pow v 6) 9/32)))) (* (sqrt (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4)))) (sqrt 2))))) * * * * [misc]progress: [ 16 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 17 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (* (+ (pow (- (* (pow v 6) 9/32) (* (* v v) 1/4)) 3) (pow (* 3/8 (pow v 4)) 3)) (sqrt 2)) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (298 enodes) * [exit]simplify: Simplified to (* (+ (* (* 27/512 (pow v 4)) (* (pow v 4) (pow v 4))) (pow (- (* (pow v 6) 9/32) (* (* v v) 1/4)) 3)) (sqrt 2)) * [misc]simplify: Simplified (2 2 1) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (/ (* (+ (* (* 27/512 (pow v 4)) (* (pow v 4) (pow v 4))) (pow (- (* (pow v 6) 9/32) (* (* v v) 1/4)) 3)) (sqrt 2)) (+ (* (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (- (* (pow v 6) 9/32) (* (* v v) 1/4))) (- (* (* 3/8 (pow v 4)) (* 3/8 (pow v 4))) (* (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4)))))))) * * * * [misc]progress: [ 18 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (* (- (* (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (- (* (pow v 6) 9/32) (* (* v v) 1/4))) (* (* 3/8 (pow v 4)) (* 3/8 (pow v 4)))) (sqrt 2)) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (98 enodes) * * [misc]simplify: iters left: 3 (307 enodes) * [exit]simplify: Simplified to (* (+ (* (pow v 4) (* (pow v 4) -9/64)) (* (+ (* (pow v 6) 9/32) (* -1/4 (* v v))) (+ (* (pow v 6) 9/32) (* -1/4 (* v v))))) (sqrt 2)) * [misc]simplify: Simplified (2 2 1) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (/ (* (+ (* (pow v 4) (* (pow v 4) -9/64)) (* (+ (* (pow v 6) 9/32) (* -1/4 (* v v))) (+ (* (pow v 6) 9/32) (* -1/4 (* v v))))) (sqrt 2)) (- (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4)))))) * * * * [misc]progress: [ 19 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 20 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 21 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 22 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 23 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 24 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 25 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 26 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 27 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 28 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 29 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 30 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 31 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 32 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 33 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 34 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 35 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 36 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (cbrt (pow v 4)) * * [misc]simplify: iters left: 2 (4 enodes) * [exit]simplify: Simplified to (cbrt (pow v 4)) * [misc]simplify: Simplified (2 2 1 2 2) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* (* 3/8 (* (cbrt (pow v 4)) (cbrt (pow v 4)))) (cbrt (pow v 4)))) (sqrt 2)))) * * * * [misc]progress: [ 37 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (pow v 4)) * * [misc]simplify: iters left: 2 (4 enodes) * [exit]simplify: Simplified to (sqrt (pow v 4)) * [misc]simplify: Simplified (2 2 1 2 2) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* (* 3/8 (sqrt (pow v 4))) (sqrt (pow v 4)))) (sqrt 2)))) * * * * [misc]progress: [ 38 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (pow v 4) * * [misc]simplify: iters left: 1 (3 enodes) * [exit]simplify: Simplified to (pow v 4) * [misc]simplify: Simplified (2 2 1 2 2) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* (* 3/8 1) (pow v 4))) (sqrt 2)))) * * * * [misc]progress: [ 39 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 40 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* v (* -3 v)))) (/ (sqrt 2) 4)) * [misc]simplify: Simplified (2 1 1 1) to (λ (v) (+ (* (pow (* (sqrt (+ 1 (* v (* -3 v)))) (/ (sqrt 2) 4)) 1) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)))) * * * * [misc]progress: [ 41 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 42 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (/ (sqrt 2) 4)) (log (sqrt (- 1 (* 3 (* v v)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (72 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (+ (log (sqrt (+ 1 (* v (* -3 v))))) (log (/ (sqrt 2) 4))) * [misc]simplify: Simplified (2 1 1 1) to (λ (v) (+ (* (exp (+ (log (sqrt (+ 1 (* v (* -3 v))))) (log (/ (sqrt 2) 4)))) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)))) * * * * [misc]progress: [ 43 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 44 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 45 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (/ (sqrt 2) 4) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)) (* (* (sqrt (- 1 (* 3 (* v v)))) (sqrt (- 1 (* 3 (* v v))))) (sqrt (- 1 (* 3 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (111 enodes) * * [misc]simplify: iters left: 3 (367 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* -3 (* v v)))) (* (/ (sqrt 2) 4) (+ 1/8 (* (* v v) -3/8)))) * [misc]simplify: Simplified (2 1 1 1) to (λ (v) (+ (* (cbrt (* (sqrt (+ 1 (* -3 (* v v)))) (* (/ (sqrt 2) 4) (+ 1/8 (* (* v v) -3/8))))) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)))) * * * * [misc]progress: [ 46 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 47 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 48 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 49 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (253 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* v 9) (* v v)) (* (* -3 v) (* v v))) 1)) (sqrt 2)) * [misc]simplify: Simplified (2 1 1 1) to (λ (v) (+ (* (/ (* (sqrt (+ (* (* (* v 9) (* v v)) (* (* -3 v) (* v v))) 1)) (sqrt 2)) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)))) * [enter]simplify: Simplifying (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (214 enodes) * * [misc]simplify: iters left: 1 (270 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ (* (pow v 4) 9) 1) (* 3 (* v v)))) 4) * [misc]simplify: Simplified (2 1 1 2) to (λ (v) (+ (* (/ (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ (* (pow v 4) 9) 1) (* 3 (* v v)))) 4)) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)))) * * * * [misc]progress: [ 50 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (134 enodes) * * [misc]simplify: iters left: 2 (254 enodes) * * [misc]simplify: iters left: 1 (289 enodes) * [exit]simplify: Simplified to (* (sqrt (- 1 (* (pow v 4) 9))) (sqrt 2)) * [misc]simplify: Simplified (2 1 1 1) to (λ (v) (+ (* (/ (* (sqrt (- 1 (* (pow v 4) 9))) (sqrt 2)) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)))) * [enter]simplify: Simplifying (* 4 (sqrt (+ 1 (* 3 (* v v))))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* v (* 3 v)))) 4) * [misc]simplify: Simplified (2 1 1 2) to (λ (v) (+ (* (/ (* (sqrt (- 1 (* (pow v 4) 9))) (sqrt 2)) (* (sqrt (+ 1 (* v (* 3 v)))) 4)) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)))) * * * * [misc]progress: [ 51 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 52 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (cbrt (sqrt (- 1 (* 3 (* v v))))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (cbrt (sqrt (- 1 (* (* v v) 3)))) * [misc]simplify: Simplified (2 1 1 2) to (λ (v) (+ (* (* (* (/ (sqrt 2) 4) (* (cbrt (sqrt (- 1 (* 3 (* v v))))) (cbrt (sqrt (- 1 (* 3 (* v v))))))) (cbrt (sqrt (- 1 (* (* v v) 3))))) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)))) * * * * [misc]progress: [ 53 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (cbrt (- 1 (* 3 (* v v))))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (sqrt (cbrt (- 1 (* (* v v) 3)))) * [misc]simplify: Simplified (2 1 1 2) to (λ (v) (+ (* (* (* (/ (sqrt 2) 4) (sqrt (* (cbrt (- 1 (* 3 (* v v)))) (cbrt (- 1 (* 3 (* v v))))))) (sqrt (cbrt (- 1 (* (* v v) 3))))) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)))) * * * * [misc]progress: [ 54 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (sqrt (- 1 (* 3 (* v v))))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (sqrt (sqrt (- 1 (* (* v v) 3)))) * [misc]simplify: Simplified (2 1 1 2) to (λ (v) (+ (* (* (* (/ (sqrt 2) 4) (sqrt (sqrt (- 1 (* 3 (* v v)))))) (sqrt (sqrt (- 1 (* (* v v) 3))))) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)))) * * * * [misc]progress: [ 55 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (- 1 (* 3 (* v v)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (sqrt (+ 1 (* (* v v) -3))) * [misc]simplify: Simplified (2 1 1 2) to (λ (v) (+ (* (* (* (/ (sqrt 2) 4) (sqrt 1)) (sqrt (+ 1 (* (* v v) -3)))) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)))) * * * * [misc]progress: [ 56 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (sqrt (- 1 (* 3 (* v v))))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (sqrt (sqrt (- 1 (* (* v v) 3)))) * [misc]simplify: Simplified (2 1 1 2) to (λ (v) (+ (* (* (* (/ (sqrt 2) 4) (sqrt (sqrt (- 1 (* 3 (* v v)))))) (sqrt (sqrt (- 1 (* (* v v) 3))))) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)))) * * * * [misc]progress: [ 57 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (- 1 (* 3 (* v v)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (sqrt (+ 1 (* (* v v) -3))) * [misc]simplify: Simplified (2 1 1 2) to (λ (v) (+ (* (* (* (/ (sqrt 2) 4) 1) (sqrt (+ 1 (* (* v v) -3)))) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)))) * * * * [misc]progress: [ 58 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ (sqrt 2) 4)) (cbrt (/ (sqrt 2) 4))) * * [misc]simplify: iters left: 6 (6 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (sqrt 2) 4)) (cbrt (/ (sqrt 2) 4))) * [misc]simplify: Simplified (2 1 1 1) to (λ (v) (+ (* (* (* (cbrt (/ (sqrt 2) 4)) (cbrt (/ (sqrt 2) 4))) (* (cbrt (/ (sqrt 2) 4)) (sqrt (- 1 (* 3 (* v v)))))) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)))) * * * * [misc]progress: [ 59 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (sqrt 2) 4)) * * [misc]simplify: iters left: 4 (5 enodes) * [exit]simplify: Simplified to (sqrt (/ (sqrt 2) 4)) * [misc]simplify: Simplified (2 1 1 1) to (λ (v) (+ (* (* (sqrt (/ (sqrt 2) 4)) (* (sqrt (/ (sqrt 2) 4)) (sqrt (- 1 (* 3 (* v v)))))) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)))) * * * * [misc]progress: [ 60 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 61 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt 2) * * [misc]simplify: iters left: 1 (2 enodes) * [exit]simplify: Simplified to (sqrt 2) * [misc]simplify: Simplified (2 1 1 1) to (λ (v) (+ (* (* (sqrt 2) (* (/ 1 4) (sqrt (- 1 (* 3 (* v v)))))) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)))) * * * * [misc]progress: [ 62 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (132 enodes) * * [misc]simplify: iters left: 2 (227 enodes) * * [misc]simplify: iters left: 1 (306 enodes) * [exit]simplify: Simplified to (sqrt (+ 1 (+ (* 3 (* v v)) (* (pow v 4) 9)))) * [misc]simplify: Simplified (2 1 1 2) to (λ (v) (+ (* (/ (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (sqrt (+ 1 (+ (* 3 (* v v)) (* (pow v 4) 9))))) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)))) * * * * [misc]progress: [ 63 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (+ 1 (* 3 (* v v)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (sqrt (+ 1 (* (* v v) 3))) * [misc]simplify: Simplified (2 1 1 2) to (λ (v) (+ (* (/ (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ 1 (* (* v v) 3)))) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)))) * * * * [misc]progress: [ 64 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* v (* v -3)) 1)) (sqrt 2)) * [misc]simplify: Simplified (2 1 1 1) to (λ (v) (+ (* (/ (* (sqrt (+ (* v (* v -3)) 1)) (sqrt 2)) 4) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)))) * * * * [misc]progress: [ 65 / 77 ] simplifiying candidate # * * * * [misc]progress: [ 66 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 9/32 (* (sqrt 2) (pow v 6))) (* 3/8 (* (sqrt 2) (pow v 4)))) (* 1/4 (* (sqrt 2) (pow v 2)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (245 enodes) * * [misc]simplify: iters left: 1 (365 enodes) * [exit]simplify: Simplified to (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)) * [misc]simplify: Simplified (2 2) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)))) * * * * [misc]progress: [ 67 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 9/32 (* (sqrt 2) (pow v 6))) (* 3/8 (* (sqrt 2) (pow v 4)))) (* 1/4 (* (sqrt 2) (pow v 2)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (245 enodes) * * [misc]simplify: iters left: 1 (365 enodes) * [exit]simplify: Simplified to (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)) * [misc]simplify: Simplified (2 2) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)))) * * * * [misc]progress: [ 68 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 9/32 (* (sqrt 2) (pow v 6))) (* 3/8 (* (sqrt 2) (pow v 4)))) (* 1/4 (* (sqrt 2) (pow v 2)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (245 enodes) * * [misc]simplify: iters left: 1 (365 enodes) * [exit]simplify: Simplified to (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)) * [misc]simplify: Simplified (2 2) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)))) * * * * [misc]progress: [ 69 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (* 3 (pow v 2)) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * * [misc]simplify: iters left: 1 (11 enodes) * [exit]simplify: Simplified to (* (* v v) 3) * [misc]simplify: Simplified (2 1 1 2 1 2) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v v) 3)))) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)))) * * * * [misc]progress: [ 70 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (* 3 (pow v 2)) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * * [misc]simplify: iters left: 1 (11 enodes) * [exit]simplify: Simplified to (* (* v v) 3) * [misc]simplify: Simplified (2 1 1 2 1 2) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v v) 3)))) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)))) * * * * [misc]progress: [ 71 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (* 3 (pow v 2)) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * * [misc]simplify: iters left: 1 (11 enodes) * [exit]simplify: Simplified to (* (* v v) 3) * [misc]simplify: Simplified (2 1 1 2 1 2) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v v) 3)))) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)))) * * * * [misc]progress: [ 72 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (* 3/8 (pow v 4)) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (6 enodes) * [exit]simplify: Simplified to (* (pow v 4) 3/8) * [misc]simplify: Simplified (2 2 1 2) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* (pow v 4) 3/8)) (sqrt 2)))) * * * * [misc]progress: [ 73 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (* 3/8 (pow v 4)) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (6 enodes) * [exit]simplify: Simplified to (* (pow v 4) 3/8) * [misc]simplify: Simplified (2 2 1 2) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* (pow v 4) 3/8)) (sqrt 2)))) * * * * [misc]progress: [ 74 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (* 3/8 (pow v 4)) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (6 enodes) * [exit]simplify: Simplified to (* (pow v 4) 3/8) * [misc]simplify: Simplified (2 2 1 2) to (λ (v) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* (pow v 4) 3/8)) (sqrt 2)))) * * * * [misc]progress: [ 75 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* 1/4 (sqrt 2)) (+ (* 9/32 (* (sqrt 2) (pow v 4))) (* 3/8 (* (sqrt 2) (pow v 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (282 enodes) * * [misc]simplify: iters left: 1 (474 enodes) * [exit]simplify: Simplified to (* (- 1/4 (- (* (pow v 4) 9/32) (* (* v v) -3/8))) (sqrt 2)) * [misc]simplify: Simplified (2 1 1) to (λ (v) (+ (* (* (- 1/4 (- (* (pow v 4) 9/32) (* (* v v) -3/8))) (sqrt 2)) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)))) * * * * [misc]progress: [ 76 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 1/4 (* (sqrt 2) (* v (sqrt -3)))) (* 1/8 (/ (sqrt 2) (* v (sqrt -3))))) (* 1/32 (/ (sqrt 2) (* (pow v 3) (pow (sqrt -3) 3))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (142 enodes) * * [misc]simplify: iters left: 3 (384 enodes) * [exit]simplify: Simplified to (+ (* (* (sqrt 2) (sqrt -3)) (* v 1/4)) (* (/ (sqrt 2) (sqrt -3)) (- (/ 1/8 v) (/ -1/96 (pow v 3))))) * [misc]simplify: Simplified (2 1 1) to (λ (v) (+ (* (+ (* (* (sqrt 2) (sqrt -3)) (* v 1/4)) (* (/ (sqrt 2) (sqrt -3)) (- (/ 1/8 v) (/ -1/96 (pow v 3))))) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)))) * * * * [misc]progress: [ 77 / 77 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* 1/32 (/ (sqrt 2) (* (pow v 3) (pow (sqrt -3) 3)))) (+ (* 1/4 (* (sqrt 2) (* v (sqrt -3)))) (* 1/8 (/ (sqrt 2) (* v (sqrt -3)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (133 enodes) * * [misc]simplify: iters left: 3 (402 enodes) * [exit]simplify: Simplified to (+ (* (* (sqrt -3) -1/4) (* (sqrt 2) v)) (* (/ (sqrt 2) (sqrt -3)) (- (/ -1/96 (pow v 3)) (/ 1/8 v)))) * [misc]simplify: Simplified (2 1 1) to (λ (v) (+ (* (+ (* (* (sqrt -3) -1/4) (* (sqrt 2) v)) (* (/ (sqrt 2) (sqrt -3)) (- (/ -1/96 (pow v 3)) (/ 1/8 v)))) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)))) * * * [misc]progress: adding candidates to table * * [misc]progress: iteration 4 / 4 * * * [misc]progress: picking best candidate * * * * [misc]pick: Picked # * * * [misc]progress: localizing error * * * [misc]progress: generating rewritten candidates * * * * [misc]progress: [ 1 / 4 ] rewriting at (2) * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 2 1 2) * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 1 1 2) * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 2 1 2 1 2 1 2) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 4 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) in v * [misc]taylor: Taking taylor expansion of (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) in v * [misc]taylor: Taking taylor expansion of (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) in v * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* v v)))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* v v))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 3 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1))) into 0 * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* v v)))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* v v))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 3 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1))) into 0 * [misc]taylor: Taking taylor expansion of (- (* v v)) in v * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) 1) into (* 1/4 (sqrt 2)) * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) 1) into (* 1/4 (sqrt 2)) * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) 1) into (* 1/4 (sqrt 2)) * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/4 (sqrt 2)) 0) into (* 1/4 (sqrt 2)) * [misc]backup-simplify: Simplify (sqrt (* 1/4 (sqrt 2))) into (* 1/2 (sqrt (sqrt 2))) * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* 1/4 (sqrt 2))))) into 0 * [misc]taylor: Taking taylor expansion of (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) in v * [misc]taylor: Taking taylor expansion of (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) in v * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* v v)))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* v v))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 3 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1))) into 0 * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* v v)))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* v v))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 3 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1))) into 0 * [misc]taylor: Taking taylor expansion of (- (* v v)) in v * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) 1) into (* 1/4 (sqrt 2)) * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) 1) into (* 1/4 (sqrt 2)) * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) 1) into (* 1/4 (sqrt 2)) * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/4 (sqrt 2)) 0) into (* 1/4 (sqrt 2)) * [misc]backup-simplify: Simplify (sqrt (* 1/4 (sqrt 2))) into (* 1/2 (sqrt (sqrt 2))) * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* 1/4 (sqrt 2))))) into 0 * [misc]taylor: Taking taylor expansion of (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) in v * [misc]taylor: Taking taylor expansion of (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) in v * [misc]taylor: Taking taylor expansion of (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) in v * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* v v)))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* v v))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 3 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1))) into 0 * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* v v)))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* v v))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 3 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1))) into 0 * [misc]taylor: Taking taylor expansion of (- (* v v)) in v * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) 1) into (* 1/4 (sqrt 2)) * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) 1) into (* 1/4 (sqrt 2)) * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) 1) into (* 1/4 (sqrt 2)) * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/4 (sqrt 2)) 0) into (* 1/4 (sqrt 2)) * [misc]backup-simplify: Simplify (sqrt (* 1/4 (sqrt 2))) into (* 1/2 (sqrt (sqrt 2))) * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* 1/4 (sqrt 2))))) into 0 * [misc]taylor: Taking taylor expansion of (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) in v * [misc]taylor: Taking taylor expansion of (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) in v * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* v v)))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* v v))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 3 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1))) into 0 * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* v v)))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* v v))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 3 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1))) into 0 * [misc]taylor: Taking taylor expansion of (- (* v v)) in v * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) 1) into (* 1/4 (sqrt 2)) * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) 1) into (* 1/4 (sqrt 2)) * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) 1) into (* 1/4 (sqrt 2)) * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/4 (sqrt 2)) 0) into (* 1/4 (sqrt 2)) * [misc]backup-simplify: Simplify (sqrt (* 1/4 (sqrt 2))) into (* 1/2 (sqrt (sqrt 2))) * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* 1/4 (sqrt 2))))) into 0 * [misc]backup-simplify: Simplify (* (* 1/2 (sqrt (sqrt 2))) (* 1/2 (sqrt (sqrt 2)))) into (* 1/4 (sqrt 2)) * [misc]backup-simplify: Simplify (* 1/4 (sqrt 2)) into (* 1/4 (sqrt 2)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (sqrt (sqrt 2))) 0) (* 0 (* 1/2 (sqrt (sqrt 2))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 1) (* 0 0))) into 1 * [misc]backup-simplify: Simplify (+ (* 3 1) (+ (* 0 0) (* 0 0))) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (/ (- -3 (pow 0 2) (+)) (* 2 1)) into -3/2 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -3/2) (+ (* 0 0) (* 0 1))) into (- (* 3/8 (sqrt 2))) * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 0) (* (- (* 3/8 (sqrt 2))) 1))) into (- (* 3/8 (sqrt 2))) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 1) (* 0 0))) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 1) (* 0 0))) into 1 * [misc]backup-simplify: Simplify (+ (* 3 1) (+ (* 0 0) (* 0 0))) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (/ (- -3 (pow 0 2) (+)) (* 2 1)) into -3/2 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -3/2) (+ (* 0 0) (* 0 1))) into (- (* 3/8 (sqrt 2))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -1) (+ (* 0 0) (* (- (* 3/8 (sqrt 2))) 0))) into (- (* 1/4 (sqrt 2))) * [misc]backup-simplify: Simplify (+ (- (* 3/8 (sqrt 2))) (- (* 1/4 (sqrt 2)))) into (- (* 5/8 (sqrt 2))) * [misc]backup-simplify: Simplify (/ (- (- (* 5/8 (sqrt 2))) (pow 0 2) (+)) (* 2 (* 1/2 (sqrt (sqrt 2))))) into (* -5/8 (sqrt (sqrt 2))) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 1) (* 0 0))) into 1 * [misc]backup-simplify: Simplify (+ (* 3 1) (+ (* 0 0) (* 0 0))) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (/ (- -3 (pow 0 2) (+)) (* 2 1)) into -3/2 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -3/2) (+ (* 0 0) (* 0 1))) into (- (* 3/8 (sqrt 2))) * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 0) (* (- (* 3/8 (sqrt 2))) 1))) into (- (* 3/8 (sqrt 2))) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 1) (* 0 0))) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 1) (* 0 0))) into 1 * [misc]backup-simplify: Simplify (+ (* 3 1) (+ (* 0 0) (* 0 0))) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (/ (- -3 (pow 0 2) (+)) (* 2 1)) into -3/2 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -3/2) (+ (* 0 0) (* 0 1))) into (- (* 3/8 (sqrt 2))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -1) (+ (* 0 0) (* (- (* 3/8 (sqrt 2))) 0))) into (- (* 1/4 (sqrt 2))) * [misc]backup-simplify: Simplify (+ (- (* 3/8 (sqrt 2))) (- (* 1/4 (sqrt 2)))) into (- (* 5/8 (sqrt 2))) * [misc]backup-simplify: Simplify (/ (- (- (* 5/8 (sqrt 2))) (pow 0 2) (+)) (* 2 (* 1/2 (sqrt (sqrt 2))))) into (* -5/8 (sqrt (sqrt 2))) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (sqrt (sqrt 2))) (* -5/8 (sqrt (sqrt 2)))) (+ (* 0 0) (* (* -5/8 (sqrt (sqrt 2))) (* 1/2 (sqrt (sqrt 2)))))) into (- (* 5/8 (sqrt 2))) * [misc]backup-simplify: Simplify (- (* 5/8 (sqrt 2))) into (- (* 5/8 (sqrt 2))) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 1) (+ (* 0 0) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 -3/2)))) (* 2 1)) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 -3/2) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 0) (+ (* (- (* 3/8 (sqrt 2))) 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 1) (+ (* 0 0) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 -3/2)))) (* 2 1)) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 -3/2) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 -1) (+ (* (- (* 3/8 (sqrt 2))) 0) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (* -5/8 (sqrt (sqrt 2))))))) (* 2 (* 1/2 (sqrt (sqrt 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 1) (+ (* 0 0) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 -3/2)))) (* 2 1)) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 -3/2) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 0) (+ (* (- (* 3/8 (sqrt 2))) 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 1) (+ (* 0 0) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 -3/2)))) (* 2 1)) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 -3/2) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 -1) (+ (* (- (* 3/8 (sqrt 2))) 0) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (* -5/8 (sqrt (sqrt 2))))))) (* 2 (* 1/2 (sqrt (sqrt 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (sqrt (sqrt 2))) 0) (+ (* 0 (* -5/8 (sqrt (sqrt 2)))) (+ (* (* -5/8 (sqrt (sqrt 2))) 0) (* 0 (* 1/2 (sqrt (sqrt 2))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow -3/2 2) (+ (* 2 (* 0 0)))) (* 2 1)) into -9/8 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -9/8) (+ (* 0 0) (+ (* 0 -3/2) (+ (* 0 0) (* 0 1))))) into (- (* 9/32 (sqrt 2))) * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 0) (+ (* (- (* 3/8 (sqrt 2))) 0) (+ (* 0 0) (* (- (* 9/32 (sqrt 2))) 1))))) into (- (* 9/32 (sqrt 2))) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow -3/2 2) (+ (* 2 (* 0 0)))) (* 2 1)) into -9/8 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -9/8) (+ (* 0 0) (+ (* 0 -3/2) (+ (* 0 0) (* 0 1))))) into (- (* 9/32 (sqrt 2))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 0) (+ (* (- (* 3/8 (sqrt 2))) -1) (+ (* 0 0) (* (- (* 9/32 (sqrt 2))) 0))))) into (* 3/8 (sqrt 2)) * [misc]backup-simplify: Simplify (+ (- (* 9/32 (sqrt 2))) (* 3/8 (sqrt 2))) into (* 3/32 (sqrt 2)) * [misc]backup-simplify: Simplify (/ (- (* 3/32 (sqrt 2)) (pow (* -5/8 (sqrt (sqrt 2))) 2) (+ (* 2 (* 0 0)))) (* 2 (* 1/2 (sqrt (sqrt 2))))) into (* -19/64 (sqrt (sqrt 2))) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow -3/2 2) (+ (* 2 (* 0 0)))) (* 2 1)) into -9/8 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -9/8) (+ (* 0 0) (+ (* 0 -3/2) (+ (* 0 0) (* 0 1))))) into (- (* 9/32 (sqrt 2))) * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 0) (+ (* (- (* 3/8 (sqrt 2))) 0) (+ (* 0 0) (* (- (* 9/32 (sqrt 2))) 1))))) into (- (* 9/32 (sqrt 2))) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow -3/2 2) (+ (* 2 (* 0 0)))) (* 2 1)) into -9/8 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -9/8) (+ (* 0 0) (+ (* 0 -3/2) (+ (* 0 0) (* 0 1))))) into (- (* 9/32 (sqrt 2))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 0) (+ (* (- (* 3/8 (sqrt 2))) -1) (+ (* 0 0) (* (- (* 9/32 (sqrt 2))) 0))))) into (* 3/8 (sqrt 2)) * [misc]backup-simplify: Simplify (+ (- (* 9/32 (sqrt 2))) (* 3/8 (sqrt 2))) into (* 3/32 (sqrt 2)) * [misc]backup-simplify: Simplify (/ (- (* 3/32 (sqrt 2)) (pow (* -5/8 (sqrt (sqrt 2))) 2) (+ (* 2 (* 0 0)))) (* 2 (* 1/2 (sqrt (sqrt 2))))) into (* -19/64 (sqrt (sqrt 2))) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (sqrt (sqrt 2))) (* -19/64 (sqrt (sqrt 2)))) (+ (* 0 0) (+ (* (* -5/8 (sqrt (sqrt 2))) (* -5/8 (sqrt (sqrt 2)))) (+ (* 0 0) (* (* -19/64 (sqrt (sqrt 2))) (* 1/2 (sqrt (sqrt 2)))))))) into (* 3/32 (sqrt 2)) * [misc]backup-simplify: Simplify (* 3/32 (sqrt 2)) into (* 3/32 (sqrt 2)) * [misc]backup-simplify: Simplify (+ (* (* 3/32 (sqrt 2)) (pow v 4)) (+ (* (- (* 5/8 (sqrt 2))) (pow v 2)) (* 1/4 (sqrt 2)))) into (- (+ (* 1/4 (sqrt 2)) (* 3/32 (* (sqrt 2) (pow v 4)))) (* 5/8 (* (sqrt 2) (pow v 2)))) * [misc]approximate: Taking taylor expansion of (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- (* (/ 1 v) (/ 1 v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- (* (/ 1 v) (/ 1 v))))))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- (* (/ 1 v) (/ 1 v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- (* (/ 1 v) (/ 1 v))))))) in v * [misc]taylor: Taking taylor expansion of (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- (* (/ 1 v) (/ 1 v)))))) in v * [misc]taylor: Taking taylor expansion of (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) 1) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (- (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) (sqrt -3)) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (* (* 1/4 (* (sqrt 2) (sqrt -3))) -1) into (* -1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (+ 0 (* -1/4 (* (sqrt 2) (sqrt -3)))) into (- (* 1/4 (* (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ (- (* 1/4 (* (sqrt 2) (sqrt -3)))) (* 2 (sqrt 0))) into (* +nan.0 (* (sqrt 2) (sqrt -3))) * [misc]taylor: Taking taylor expansion of (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- (* (/ 1 v) (/ 1 v)))))) in v * [misc]taylor: Taking taylor expansion of (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) 1) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (- (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) (sqrt -3)) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (* (* 1/4 (* (sqrt 2) (sqrt -3))) -1) into (* -1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (+ 0 (* -1/4 (* (sqrt 2) (sqrt -3)))) into (- (* 1/4 (* (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ (- (* 1/4 (* (sqrt 2) (sqrt -3)))) (* 2 (sqrt 0))) into (* +nan.0 (* (sqrt 2) (sqrt -3))) * [misc]taylor: Taking taylor expansion of (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- (* (/ 1 v) (/ 1 v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- (* (/ 1 v) (/ 1 v))))))) in v * [misc]taylor: Taking taylor expansion of (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- (* (/ 1 v) (/ 1 v)))))) in v * [misc]taylor: Taking taylor expansion of (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) 1) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (- (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) (sqrt -3)) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (* (* 1/4 (* (sqrt 2) (sqrt -3))) -1) into (* -1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (+ 0 (* -1/4 (* (sqrt 2) (sqrt -3)))) into (- (* 1/4 (* (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ (- (* 1/4 (* (sqrt 2) (sqrt -3)))) (* 2 (sqrt 0))) into (* +nan.0 (* (sqrt 2) (sqrt -3))) * [misc]taylor: Taking taylor expansion of (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- (* (/ 1 v) (/ 1 v)))))) in v * [misc]taylor: Taking taylor expansion of (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) 1) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (- (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) (sqrt -3)) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (* (* 1/4 (* (sqrt 2) (sqrt -3))) -1) into (* -1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (+ 0 (* -1/4 (* (sqrt 2) (sqrt -3)))) into (- (* 1/4 (* (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ (- (* 1/4 (* (sqrt 2) (sqrt -3)))) (* 2 (sqrt 0))) into (* +nan.0 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 (* +nan.0 (* (sqrt 2) (sqrt -3)))) (* (* +nan.0 (* (sqrt 2) (sqrt -3))) 0)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (* (sqrt 2) (sqrt -3))) 2) (+)) (* 2 0)) into (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (* (sqrt 2) (sqrt -3))) 2) (+)) (* 2 0)) into (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2))) * [misc]backup-simplify: Simplify (+ (* 0 (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2)))) (+ (* (* +nan.0 (* (sqrt 2) (sqrt -3))) (* +nan.0 (* (sqrt 2) (sqrt -3)))) (* (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2))) 0))) into (- (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2)))) into (- (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2)))) * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) (sqrt -3)) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* (* 1/4 (* (sqrt 2) (sqrt -3))) 1) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ (- 1 (pow 0 2) (+)) (* 2 (sqrt -3))) into (/ 1/2 (sqrt -3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))) into (* 1/8 (/ (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (* (* 1/8 (/ (sqrt 2) (sqrt -3))) -1))) into (- (* 1/8 (/ (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (+ (* 1/4 (* (sqrt 2) (sqrt -3))) (- (* 1/8 (/ (sqrt 2) (sqrt -3))))) into (- (* 1/4 (* (sqrt 2) (sqrt -3))) (* 1/8 (/ (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (/ (- (- (* 1/4 (* (sqrt 2) (sqrt -3))) (* 1/8 (/ (sqrt 2) (sqrt -3)))) (+ (* 2 (* (* +nan.0 (* (sqrt 2) (sqrt -3))) (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2))))))) (* 2 0)) into (* +nan.0 (- (* 1/4 (* (sqrt 2) (sqrt -3))) (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (- (* +nan.0 (* (pow (sqrt 2) 3) (pow (sqrt -3) 3))))))) * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) (sqrt -3)) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* (* 1/4 (* (sqrt 2) (sqrt -3))) 1) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ (- 1 (pow 0 2) (+)) (* 2 (sqrt -3))) into (/ 1/2 (sqrt -3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))) into (* 1/8 (/ (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (* (* 1/8 (/ (sqrt 2) (sqrt -3))) -1))) into (- (* 1/8 (/ (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (+ (* 1/4 (* (sqrt 2) (sqrt -3))) (- (* 1/8 (/ (sqrt 2) (sqrt -3))))) into (- (* 1/4 (* (sqrt 2) (sqrt -3))) (* 1/8 (/ (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (/ (- (- (* 1/4 (* (sqrt 2) (sqrt -3))) (* 1/8 (/ (sqrt 2) (sqrt -3)))) (+ (* 2 (* (* +nan.0 (* (sqrt 2) (sqrt -3))) (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2))))))) (* 2 0)) into (* +nan.0 (- (* 1/4 (* (sqrt 2) (sqrt -3))) (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (- (* +nan.0 (* (pow (sqrt 2) 3) (pow (sqrt -3) 3))))))) * [misc]backup-simplify: Simplify (+ (* 0 (* +nan.0 (- (* 1/4 (* (sqrt 2) (sqrt -3))) (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (- (* +nan.0 (* (pow (sqrt 2) 3) (pow (sqrt -3) 3)))))))) (+ (* (* +nan.0 (* (sqrt 2) (sqrt -3))) (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2)))) (+ (* (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2))) (* +nan.0 (* (sqrt 2) (sqrt -3)))) (* (* +nan.0 (- (* 1/4 (* (sqrt 2) (sqrt -3))) (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (- (* +nan.0 (* (pow (sqrt 2) 3) (pow (sqrt -3) 3))))))) 0)))) into (- (* +nan.0 (* (pow (sqrt 2) 3) (pow (sqrt -3) 3)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (pow (sqrt 2) 3) (pow (sqrt -3) 3)))) into (- (* +nan.0 (* (pow (sqrt 2) 3) (pow (sqrt -3) 3)))) * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (/ 1/2 (sqrt -3)))))) (* 2 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3))))) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (+ (* (* 1/8 (/ (sqrt 2) (sqrt -3))) 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2))) 2) (+ (* 2 (* (* +nan.0 (* (sqrt 2) (sqrt -3))) (* +nan.0 (- (* 1/4 (* (sqrt 2) (sqrt -3))) (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (- (* +nan.0 (* (pow (sqrt 2) 3) (pow (sqrt -3) 3))))))))))) (* 2 0)) into (* +nan.0 (+ (* +nan.0 (pow (sqrt 2) 2)) (- (+ (* +nan.0 (* (pow (sqrt 2) 4) (pow (sqrt -3) 4))) (- (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2)))))))) * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (/ 1/2 (sqrt -3)))))) (* 2 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3))))) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (+ (* (* 1/8 (/ (sqrt 2) (sqrt -3))) 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2))) 2) (+ (* 2 (* (* +nan.0 (* (sqrt 2) (sqrt -3))) (* +nan.0 (- (* 1/4 (* (sqrt 2) (sqrt -3))) (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (- (* +nan.0 (* (pow (sqrt 2) 3) (pow (sqrt -3) 3))))))))))) (* 2 0)) into (* +nan.0 (+ (* +nan.0 (pow (sqrt 2) 2)) (- (+ (* +nan.0 (* (pow (sqrt 2) 4) (pow (sqrt -3) 4))) (- (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2)))))))) * [misc]backup-simplify: Simplify (+ (* 0 (* +nan.0 (+ (* +nan.0 (pow (sqrt 2) 2)) (- (+ (* +nan.0 (* (pow (sqrt 2) 4) (pow (sqrt -3) 4))) (- (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2))))))))) (+ (* (* +nan.0 (* (sqrt 2) (sqrt -3))) (* +nan.0 (- (* 1/4 (* (sqrt 2) (sqrt -3))) (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (- (* +nan.0 (* (pow (sqrt 2) 3) (pow (sqrt -3) 3)))))))) (+ (* (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2))) (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2)))) (+ (* (* +nan.0 (- (* 1/4 (* (sqrt 2) (sqrt -3))) (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (- (* +nan.0 (* (pow (sqrt 2) 3) (pow (sqrt -3) 3))))))) (* +nan.0 (* (sqrt 2) (sqrt -3)))) (* (* +nan.0 (+ (* +nan.0 (pow (sqrt 2) 2)) (- (+ (* +nan.0 (* (pow (sqrt 2) 4) (pow (sqrt -3) 4))) (- (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2)))))))) 0))))) into (- (+ (* +nan.0 (pow (sqrt 2) 2)) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2))) (- (* +nan.0 (* (pow (sqrt 2) 4) (pow (sqrt -3) 4)))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (pow (sqrt 2) 2)) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2))) (- (* +nan.0 (* (pow (sqrt 2) 4) (pow (sqrt -3) 4)))))))) into (- (+ (* +nan.0 (pow (sqrt 2) 2)) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2))) (- (* +nan.0 (* (pow (sqrt 2) 4) (pow (sqrt -3) 4)))))))) * [misc]backup-simplify: Simplify (+ (- (+ (* +nan.0 (pow (sqrt 2) 2)) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2))) (- (* +nan.0 (* (pow (sqrt 2) 4) (pow (sqrt -3) 4)))))))) (+ (* (- (* +nan.0 (* (pow (sqrt 2) 3) (pow (sqrt -3) 3)))) (/ 1 (/ 1 v))) (* (- (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2)))) (pow (/ 1 (/ 1 v)) 2)))) into (- (+ (* +nan.0 (pow (sqrt 2) 2)) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2))) (- (+ (* +nan.0 (* (pow (sqrt 2) 3) (* v (pow (sqrt -3) 3)))) (- (+ (* +nan.0 (* (pow (sqrt 2) 4) (pow (sqrt -3) 4))) (- (* +nan.0 (* (pow (sqrt 2) 2) (* (pow v 2) (pow (sqrt -3) 2))))))))))))) * [misc]approximate: Taking taylor expansion of (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- (* (/ 1 (- v)) (/ 1 (- v))))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- (* (/ 1 (- v)) (/ 1 (- v)))))))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- (* (/ 1 (- v)) (/ 1 (- v))))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- (* (/ 1 (- v)) (/ 1 (- v)))))))) in v * [misc]taylor: Taking taylor expansion of (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- (* (/ 1 (- v)) (/ 1 (- v))))))) in v * [misc]taylor: Taking taylor expansion of (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) 1) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (- (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) (sqrt -3)) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (* (* 1/4 (* (sqrt 2) (sqrt -3))) -1) into (* -1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (+ 0 (* -1/4 (* (sqrt 2) (sqrt -3)))) into (- (* 1/4 (* (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ (- (* 1/4 (* (sqrt 2) (sqrt -3)))) (* 2 (sqrt 0))) into (* +nan.0 (* (sqrt 2) (sqrt -3))) * [misc]taylor: Taking taylor expansion of (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- (* (/ 1 (- v)) (/ 1 (- v))))))) in v * [misc]taylor: Taking taylor expansion of (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) 1) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (- (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) (sqrt -3)) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (* (* 1/4 (* (sqrt 2) (sqrt -3))) -1) into (* -1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (+ 0 (* -1/4 (* (sqrt 2) (sqrt -3)))) into (- (* 1/4 (* (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ (- (* 1/4 (* (sqrt 2) (sqrt -3)))) (* 2 (sqrt 0))) into (* +nan.0 (* (sqrt 2) (sqrt -3))) * [misc]taylor: Taking taylor expansion of (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- (* (/ 1 (- v)) (/ 1 (- v))))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- (* (/ 1 (- v)) (/ 1 (- v)))))))) in v * [misc]taylor: Taking taylor expansion of (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- (* (/ 1 (- v)) (/ 1 (- v))))))) in v * [misc]taylor: Taking taylor expansion of (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) 1) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (- (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) (sqrt -3)) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (* (* 1/4 (* (sqrt 2) (sqrt -3))) -1) into (* -1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (+ 0 (* -1/4 (* (sqrt 2) (sqrt -3)))) into (- (* 1/4 (* (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ (- (* 1/4 (* (sqrt 2) (sqrt -3)))) (* 2 (sqrt 0))) into (* +nan.0 (* (sqrt 2) (sqrt -3))) * [misc]taylor: Taking taylor expansion of (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- (* (/ 1 (- v)) (/ 1 (- v))))))) in v * [misc]taylor: Taking taylor expansion of (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) 1) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (- (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) (sqrt -3)) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (* (* 1/4 (* (sqrt 2) (sqrt -3))) -1) into (* -1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (+ 0 (* -1/4 (* (sqrt 2) (sqrt -3)))) into (- (* 1/4 (* (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ (- (* 1/4 (* (sqrt 2) (sqrt -3)))) (* 2 (sqrt 0))) into (* +nan.0 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 (* +nan.0 (* (sqrt 2) (sqrt -3)))) (* (* +nan.0 (* (sqrt 2) (sqrt -3))) 0)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (* (sqrt 2) (sqrt -3))) 2) (+)) (* 2 0)) into (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (* (sqrt 2) (sqrt -3))) 2) (+)) (* 2 0)) into (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2))) * [misc]backup-simplify: Simplify (+ (* 0 (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2)))) (+ (* (* +nan.0 (* (sqrt 2) (sqrt -3))) (* +nan.0 (* (sqrt 2) (sqrt -3)))) (* (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2))) 0))) into (- (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2)))) into (- (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2)))) * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) (sqrt -3)) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* (* 1/4 (* (sqrt 2) (sqrt -3))) 1) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ (- 1 (pow 0 2) (+)) (* 2 (sqrt -3))) into (/ 1/2 (sqrt -3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))) into (* 1/8 (/ (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (* (* 1/8 (/ (sqrt 2) (sqrt -3))) -1))) into (- (* 1/8 (/ (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (+ (* 1/4 (* (sqrt 2) (sqrt -3))) (- (* 1/8 (/ (sqrt 2) (sqrt -3))))) into (- (* 1/4 (* (sqrt 2) (sqrt -3))) (* 1/8 (/ (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (/ (- (- (* 1/4 (* (sqrt 2) (sqrt -3))) (* 1/8 (/ (sqrt 2) (sqrt -3)))) (+ (* 2 (* (* +nan.0 (* (sqrt 2) (sqrt -3))) (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2))))))) (* 2 0)) into (* +nan.0 (- (* 1/4 (* (sqrt 2) (sqrt -3))) (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (- (* +nan.0 (* (pow (sqrt 2) 3) (pow (sqrt -3) 3))))))) * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) (sqrt -3)) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* (* 1/4 (* (sqrt 2) (sqrt -3))) 1) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ (- 1 (pow 0 2) (+)) (* 2 (sqrt -3))) into (/ 1/2 (sqrt -3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))) into (* 1/8 (/ (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (* (* 1/8 (/ (sqrt 2) (sqrt -3))) -1))) into (- (* 1/8 (/ (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (+ (* 1/4 (* (sqrt 2) (sqrt -3))) (- (* 1/8 (/ (sqrt 2) (sqrt -3))))) into (- (* 1/4 (* (sqrt 2) (sqrt -3))) (* 1/8 (/ (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (/ (- (- (* 1/4 (* (sqrt 2) (sqrt -3))) (* 1/8 (/ (sqrt 2) (sqrt -3)))) (+ (* 2 (* (* +nan.0 (* (sqrt 2) (sqrt -3))) (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2))))))) (* 2 0)) into (* +nan.0 (- (* 1/4 (* (sqrt 2) (sqrt -3))) (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (- (* +nan.0 (* (pow (sqrt 2) 3) (pow (sqrt -3) 3))))))) * [misc]backup-simplify: Simplify (+ (* 0 (* +nan.0 (- (* 1/4 (* (sqrt 2) (sqrt -3))) (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (- (* +nan.0 (* (pow (sqrt 2) 3) (pow (sqrt -3) 3)))))))) (+ (* (* +nan.0 (* (sqrt 2) (sqrt -3))) (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2)))) (+ (* (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2))) (* +nan.0 (* (sqrt 2) (sqrt -3)))) (* (* +nan.0 (- (* 1/4 (* (sqrt 2) (sqrt -3))) (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (- (* +nan.0 (* (pow (sqrt 2) 3) (pow (sqrt -3) 3))))))) 0)))) into (- (* +nan.0 (* (pow (sqrt 2) 3) (pow (sqrt -3) 3)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (pow (sqrt 2) 3) (pow (sqrt -3) 3)))) into (- (* +nan.0 (* (pow (sqrt 2) 3) (pow (sqrt -3) 3)))) * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (/ 1/2 (sqrt -3)))))) (* 2 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3))))) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (+ (* (* 1/8 (/ (sqrt 2) (sqrt -3))) 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2))) 2) (+ (* 2 (* (* +nan.0 (* (sqrt 2) (sqrt -3))) (* +nan.0 (- (* 1/4 (* (sqrt 2) (sqrt -3))) (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (- (* +nan.0 (* (pow (sqrt 2) 3) (pow (sqrt -3) 3))))))))))) (* 2 0)) into (* +nan.0 (+ (* +nan.0 (pow (sqrt 2) 2)) (- (+ (* +nan.0 (* (pow (sqrt 2) 4) (pow (sqrt -3) 4))) (- (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2)))))))) * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (/ 1/2 (sqrt -3)))))) (* 2 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3))))) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (+ (* (* 1/8 (/ (sqrt 2) (sqrt -3))) 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2))) 2) (+ (* 2 (* (* +nan.0 (* (sqrt 2) (sqrt -3))) (* +nan.0 (- (* 1/4 (* (sqrt 2) (sqrt -3))) (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (- (* +nan.0 (* (pow (sqrt 2) 3) (pow (sqrt -3) 3))))))))))) (* 2 0)) into (* +nan.0 (+ (* +nan.0 (pow (sqrt 2) 2)) (- (+ (* +nan.0 (* (pow (sqrt 2) 4) (pow (sqrt -3) 4))) (- (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2)))))))) * [misc]backup-simplify: Simplify (+ (* 0 (* +nan.0 (+ (* +nan.0 (pow (sqrt 2) 2)) (- (+ (* +nan.0 (* (pow (sqrt 2) 4) (pow (sqrt -3) 4))) (- (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2))))))))) (+ (* (* +nan.0 (* (sqrt 2) (sqrt -3))) (* +nan.0 (- (* 1/4 (* (sqrt 2) (sqrt -3))) (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (- (* +nan.0 (* (pow (sqrt 2) 3) (pow (sqrt -3) 3)))))))) (+ (* (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2))) (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2)))) (+ (* (* +nan.0 (- (* 1/4 (* (sqrt 2) (sqrt -3))) (+ (* 1/8 (/ (sqrt 2) (sqrt -3))) (- (* +nan.0 (* (pow (sqrt 2) 3) (pow (sqrt -3) 3))))))) (* +nan.0 (* (sqrt 2) (sqrt -3)))) (* (* +nan.0 (+ (* +nan.0 (pow (sqrt 2) 2)) (- (+ (* +nan.0 (* (pow (sqrt 2) 4) (pow (sqrt -3) 4))) (- (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2)))))))) 0))))) into (- (+ (* +nan.0 (pow (sqrt 2) 2)) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2))) (- (* +nan.0 (* (pow (sqrt 2) 4) (pow (sqrt -3) 4)))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (pow (sqrt 2) 2)) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2))) (- (* +nan.0 (* (pow (sqrt 2) 4) (pow (sqrt -3) 4)))))))) into (- (+ (* +nan.0 (pow (sqrt 2) 2)) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2))) (- (* +nan.0 (* (pow (sqrt 2) 4) (pow (sqrt -3) 4)))))))) * [misc]backup-simplify: Simplify (+ (- (+ (* +nan.0 (pow (sqrt 2) 2)) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2))) (- (* +nan.0 (* (pow (sqrt 2) 4) (pow (sqrt -3) 4)))))))) (+ (* (- (* +nan.0 (* (pow (sqrt 2) 3) (pow (sqrt -3) 3)))) (/ 1 (/ 1 (- v)))) (* (- (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2)))) (pow (/ 1 (/ 1 (- v))) 2)))) into (- (+ (* +nan.0 (pow (sqrt 2) 2)) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2))) (- (+ (* +nan.0 (* (pow (sqrt 2) 3) (* v (pow (sqrt -3) 3)))) (- (+ (* +nan.0 (* (pow (sqrt 2) 4) (pow (sqrt -3) 4))) (- (* +nan.0 (* (pow (sqrt 2) 2) (* (pow v 2) (pow (sqrt -3) 2))))))))))))) * * * * [misc]progress: [ 2 / 4 ] generating series at (2 2 1 2) * [misc]approximate: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* v v)))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* v v))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 3 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1))) into 0 * [misc]taylor: Taking taylor expansion of (- (* v v)) in v * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* v v)))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* v v))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 3 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1))) into 0 * [misc]taylor: Taking taylor expansion of (- (* v v)) in v * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) 1) into (* 1/4 (sqrt 2)) * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 1) (* 0 0))) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 1) (* 0 0))) into 1 * [misc]backup-simplify: Simplify (+ (* 3 1) (+ (* 0 0) (* 0 0))) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (/ (- -3 (pow 0 2) (+)) (* 2 1)) into -3/2 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -3/2) (+ (* 0 0) (* 0 1))) into (- (* 3/8 (sqrt 2))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -1) (+ (* 0 0) (* (- (* 3/8 (sqrt 2))) 0))) into (- (* 1/4 (sqrt 2))) * [misc]backup-simplify: Simplify (- (* 1/4 (sqrt 2))) into (- (* 1/4 (sqrt 2))) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 1) (+ (* 0 0) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 -3/2)))) (* 2 1)) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 -3/2) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 -1) (+ (* (- (* 3/8 (sqrt 2))) 0) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow -3/2 2) (+ (* 2 (* 0 0)))) (* 2 1)) into -9/8 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -9/8) (+ (* 0 0) (+ (* 0 -3/2) (+ (* 0 0) (* 0 1))))) into (- (* 9/32 (sqrt 2))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 0) (+ (* (- (* 3/8 (sqrt 2))) -1) (+ (* 0 0) (* (- (* 9/32 (sqrt 2))) 0))))) into (* 3/8 (sqrt 2)) * [misc]backup-simplify: Simplify (* 3/8 (sqrt 2)) into (* 3/8 (sqrt 2)) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0)))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 -9/8)) (* 2 (* -3/2 0)))) (* 2 1)) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 -9/8) (+ (* 0 0) (+ (* 0 -3/2) (+ (* 0 0) (* 0 1)))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 0) (+ (* (- (* 3/8 (sqrt 2))) 0) (+ (* 0 -1) (+ (* (- (* 9/32 (sqrt 2))) 0) (* 0 0)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0))))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* -3/2 -9/8)))) (* 2 1)) into -27/16 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -27/16) (+ (* 0 0) (+ (* 0 -9/8) (+ (* 0 0) (+ (* 0 -3/2) (+ (* 0 0) (* 0 1))))))) into (- (* 27/64 (sqrt 2))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 0) (+ (* (- (* 3/8 (sqrt 2))) 0) (+ (* 0 0) (+ (* (- (* 9/32 (sqrt 2))) -1) (+ (* 0 0) (* (- (* 27/64 (sqrt 2))) 0))))))) into (* 9/32 (sqrt 2)) * [misc]backup-simplify: Simplify (* 9/32 (sqrt 2)) into (* 9/32 (sqrt 2)) * [misc]backup-simplify: Simplify (+ (* (* 9/32 (sqrt 2)) (pow v 6)) (+ (* (* 3/8 (sqrt 2)) (pow v 4)) (* (- (* 1/4 (sqrt 2))) (pow v 2)))) into (- (+ (* 9/32 (* (sqrt 2) (pow v 6))) (* 3/8 (* (sqrt 2) (pow v 4)))) (* 1/4 (* (sqrt 2) (pow v 2)))) * [misc]approximate: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- (* (/ 1 v) (/ 1 v)))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (- (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (- (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) (sqrt -3)) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (* (* 1/4 (* (sqrt 2) (sqrt -3))) -1) into (* -1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* -1/4 (* (sqrt 2) (sqrt -3))) into (* -1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ (- 1 (pow 0 2) (+)) (* 2 (sqrt -3))) into (/ 1/2 (sqrt -3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))) into (* 1/8 (/ (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (* (* 1/8 (/ (sqrt 2) (sqrt -3))) -1))) into (- (* 1/8 (/ (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (- (* 1/8 (/ (sqrt 2) (sqrt -3)))) into (- (* 1/8 (/ (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (/ 1/2 (sqrt -3)))))) (* 2 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3))))) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (+ (* (* 1/8 (/ (sqrt 2) (sqrt -3))) 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ 1/2 (sqrt -3)) 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt -3))) into (/ -1/8 (pow (sqrt -3) 3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ -1/8 (pow (sqrt -3) 3))) (+ (* 0 0) (+ (* 0 (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))))) into (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (+ (* (* 1/8 (/ (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (* (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) -1))))) into (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3))) * [misc]backup-simplify: Simplify (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3))) into (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3))) * [misc]backup-simplify: Simplify (+ (* (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3))) (/ 1 v)) (+ (* (- (* 1/8 (/ (sqrt 2) (sqrt -3)))) (/ 1 (/ 1 v))) (* (* -1/4 (* (sqrt 2) (sqrt -3))) (pow (/ 1 (/ 1 v)) 3)))) into (- (* 1/32 (/ (sqrt 2) (* v (pow (sqrt -3) 3)))) (+ (* 1/4 (* (sqrt 2) (* (pow v 3) (sqrt -3)))) (* 1/8 (/ (* (sqrt 2) v) (sqrt -3))))) * [misc]approximate: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- (* (/ 1 (- v)) (/ 1 (- v))))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (- (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (- (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) (sqrt -3)) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (* (* 1/4 (* (sqrt 2) (sqrt -3))) -1) into (* -1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* -1/4 (* (sqrt 2) (sqrt -3))) into (* -1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ (- 1 (pow 0 2) (+)) (* 2 (sqrt -3))) into (/ 1/2 (sqrt -3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))) into (* 1/8 (/ (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (* (* 1/8 (/ (sqrt 2) (sqrt -3))) -1))) into (- (* 1/8 (/ (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (- (* 1/8 (/ (sqrt 2) (sqrt -3)))) into (- (* 1/8 (/ (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (/ 1/2 (sqrt -3)))))) (* 2 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3))))) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (+ (* (* 1/8 (/ (sqrt 2) (sqrt -3))) 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ 1/2 (sqrt -3)) 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt -3))) into (/ -1/8 (pow (sqrt -3) 3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ -1/8 (pow (sqrt -3) 3))) (+ (* 0 0) (+ (* 0 (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))))) into (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (+ (* (* 1/8 (/ (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (* (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) -1))))) into (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3))) * [misc]backup-simplify: Simplify (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3))) into (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3))) * [misc]backup-simplify: Simplify (+ (* (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3))) (/ 1 (- v))) (+ (* (- (* 1/8 (/ (sqrt 2) (sqrt -3)))) (/ 1 (/ 1 (- v)))) (* (* -1/4 (* (sqrt 2) (sqrt -3))) (pow (/ 1 (/ 1 (- v))) 3)))) into (- (+ (* 1/4 (* (sqrt 2) (* (pow v 3) (sqrt -3)))) (* 1/8 (/ (* (sqrt 2) v) (sqrt -3)))) (* 1/32 (/ (sqrt 2) (* v (pow (sqrt -3) 3))))) * * * * [misc]progress: [ 3 / 4 ] generating series at (2 1 1 2) * [misc]approximate: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* v v)))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* v v))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 3 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1))) into 0 * [misc]taylor: Taking taylor expansion of (- (* v v)) in v * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* v v)))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* v v))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 3 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1))) into 0 * [misc]taylor: Taking taylor expansion of (- (* v v)) in v * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) 1) into (* 1/4 (sqrt 2)) * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 1) (* 0 0))) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 1) (* 0 0))) into 1 * [misc]backup-simplify: Simplify (+ (* 3 1) (+ (* 0 0) (* 0 0))) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (/ (- -3 (pow 0 2) (+)) (* 2 1)) into -3/2 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -3/2) (+ (* 0 0) (* 0 1))) into (- (* 3/8 (sqrt 2))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -1) (+ (* 0 0) (* (- (* 3/8 (sqrt 2))) 0))) into (- (* 1/4 (sqrt 2))) * [misc]backup-simplify: Simplify (- (* 1/4 (sqrt 2))) into (- (* 1/4 (sqrt 2))) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 1) (+ (* 0 0) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 -3/2)))) (* 2 1)) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 -3/2) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 -1) (+ (* (- (* 3/8 (sqrt 2))) 0) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow -3/2 2) (+ (* 2 (* 0 0)))) (* 2 1)) into -9/8 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -9/8) (+ (* 0 0) (+ (* 0 -3/2) (+ (* 0 0) (* 0 1))))) into (- (* 9/32 (sqrt 2))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 0) (+ (* (- (* 3/8 (sqrt 2))) -1) (+ (* 0 0) (* (- (* 9/32 (sqrt 2))) 0))))) into (* 3/8 (sqrt 2)) * [misc]backup-simplify: Simplify (* 3/8 (sqrt 2)) into (* 3/8 (sqrt 2)) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0)))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 -9/8)) (* 2 (* -3/2 0)))) (* 2 1)) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 -9/8) (+ (* 0 0) (+ (* 0 -3/2) (+ (* 0 0) (* 0 1)))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 0) (+ (* (- (* 3/8 (sqrt 2))) 0) (+ (* 0 -1) (+ (* (- (* 9/32 (sqrt 2))) 0) (* 0 0)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0))))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* -3/2 -9/8)))) (* 2 1)) into -27/16 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) -27/16) (+ (* 0 0) (+ (* 0 -9/8) (+ (* 0 0) (+ (* 0 -3/2) (+ (* 0 0) (* 0 1))))))) into (- (* 27/64 (sqrt 2))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 0) (+ (* (- (* 3/8 (sqrt 2))) 0) (+ (* 0 0) (+ (* (- (* 9/32 (sqrt 2))) -1) (+ (* 0 0) (* (- (* 27/64 (sqrt 2))) 0))))))) into (* 9/32 (sqrt 2)) * [misc]backup-simplify: Simplify (* 9/32 (sqrt 2)) into (* 9/32 (sqrt 2)) * [misc]backup-simplify: Simplify (+ (* (* 9/32 (sqrt 2)) (pow v 6)) (+ (* (* 3/8 (sqrt 2)) (pow v 4)) (* (- (* 1/4 (sqrt 2))) (pow v 2)))) into (- (+ (* 9/32 (* (sqrt 2) (pow v 6))) (* 3/8 (* (sqrt 2) (pow v 4)))) (* 1/4 (* (sqrt 2) (pow v 2)))) * [misc]approximate: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- (* (/ 1 v) (/ 1 v)))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (- (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) (- (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v)))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (- (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) (sqrt -3)) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (* (* 1/4 (* (sqrt 2) (sqrt -3))) -1) into (* -1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* -1/4 (* (sqrt 2) (sqrt -3))) into (* -1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ (- 1 (pow 0 2) (+)) (* 2 (sqrt -3))) into (/ 1/2 (sqrt -3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))) into (* 1/8 (/ (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (* (* 1/8 (/ (sqrt 2) (sqrt -3))) -1))) into (- (* 1/8 (/ (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (- (* 1/8 (/ (sqrt 2) (sqrt -3)))) into (- (* 1/8 (/ (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (/ 1/2 (sqrt -3)))))) (* 2 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3))))) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (+ (* (* 1/8 (/ (sqrt 2) (sqrt -3))) 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ 1/2 (sqrt -3)) 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt -3))) into (/ -1/8 (pow (sqrt -3) 3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ -1/8 (pow (sqrt -3) 3))) (+ (* 0 0) (+ (* 0 (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))))) into (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (+ (* (* 1/8 (/ (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (* (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) -1))))) into (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3))) * [misc]backup-simplify: Simplify (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3))) into (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3))) * [misc]backup-simplify: Simplify (+ (* (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3))) (/ 1 v)) (+ (* (- (* 1/8 (/ (sqrt 2) (sqrt -3)))) (/ 1 (/ 1 v))) (* (* -1/4 (* (sqrt 2) (sqrt -3))) (pow (/ 1 (/ 1 v)) 3)))) into (- (* 1/32 (/ (sqrt 2) (* v (pow (sqrt -3) 3)))) (+ (* 1/4 (* (sqrt 2) (* (pow v 3) (sqrt -3)))) (* 1/8 (/ (* (sqrt 2) v) (sqrt -3))))) * [misc]approximate: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- (* (/ 1 (- v)) (/ 1 (- v))))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (- (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) (- (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))))) in v * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) 4) in v * [misc]taylor: Taking taylor expansion of (sqrt 2) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of 4 in v * [misc]backup-simplify: Simplify 4 into 4 * [misc]backup-simplify: Simplify (/ (sqrt 2) 4) into (* 1/4 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (- 1 (* 3 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of 1 in v * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify (- 3) into -3 * [misc]backup-simplify: Simplify (+ 0 -3) into -3 * [misc]backup-simplify: Simplify (sqrt -3) into (sqrt -3) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -3))) into 0 * [misc]taylor: Taking taylor expansion of (- (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* (* 1/4 (sqrt 2)) (sqrt -3)) into (* 1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (* (* 1/4 (* (sqrt 2) (sqrt -3))) -1) into (* -1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (* -1/4 (* (sqrt 2) (sqrt -3))) into (* -1/4 (* (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (* 0 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ (- 1 (pow 0 2) (+)) (* 2 (sqrt -3))) into (/ 1/2 (sqrt -3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))) into (* 1/8 (/ (sqrt 2) (sqrt -3))) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (* (* 1/8 (/ (sqrt 2) (sqrt -3))) -1))) into (- (* 1/8 (/ (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (- (* 1/8 (/ (sqrt 2) (sqrt -3)))) into (- (* 1/8 (/ (sqrt 2) (sqrt -3)))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (/ 1/2 (sqrt -3)))))) (* 2 (sqrt -3))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) 0) (+ (* 0 (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3))))) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (+ (* (* 1/8 (/ (sqrt 2) (sqrt -3))) 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ 1/2 (sqrt -3)) 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt -3))) into (/ -1/8 (pow (sqrt -3) 3)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 4) (+ (* (* 1/4 (sqrt 2)) (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)) (* 0 (/ 0 4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (sqrt 2)) (/ -1/8 (pow (sqrt -3) 3))) (+ (* 0 0) (+ (* 0 (/ 1/2 (sqrt -3))) (+ (* 0 0) (* 0 (sqrt -3)))))) into (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ (* (* 1/4 (* (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (+ (* (* 1/8 (/ (sqrt 2) (sqrt -3))) 0) (+ (* 0 0) (* (- (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3)))) -1))))) into (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3))) * [misc]backup-simplify: Simplify (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3))) into (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3))) * [misc]backup-simplify: Simplify (+ (* (* 1/32 (/ (sqrt 2) (pow (sqrt -3) 3))) (/ 1 (- v))) (+ (* (- (* 1/8 (/ (sqrt 2) (sqrt -3)))) (/ 1 (/ 1 (- v)))) (* (* -1/4 (* (sqrt 2) (sqrt -3))) (pow (/ 1 (/ 1 (- v))) 3)))) into (- (+ (* 1/4 (* (sqrt 2) (* (pow v 3) (sqrt -3)))) (* 1/8 (/ (* (sqrt 2) v) (sqrt -3)))) (* 1/32 (/ (sqrt 2) (* v (pow (sqrt -3) 3))))) * * * * [misc]progress: [ 4 / 4 ] generating series at (2 2 1 2 1 2 1 2) * [misc]approximate: Taking taylor expansion of (* 3 (* v v)) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* v v)) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* v v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 3 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 0)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 1) (* 0 0))) into 1 * [misc]backup-simplify: Simplify (+ (* 3 1) (+ (* 0 0) (* 0 0))) into 3 * [misc]backup-simplify: Simplify 3 into 3 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 1) (+ (* 0 0) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (+ (* 0 0) (* 0 0))))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* 3 (pow v 2)) into (* 3 (pow v 2)) * [misc]approximate: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 v) (/ 1 v))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 v) (/ 1 v)) in v * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify 3 into 3 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* 3 (pow (/ 1 (/ 1 v)) 2)) into (* 3 (pow v 2)) * [misc]approximate: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (* 3 (* (/ 1 (- v)) (/ 1 (- v)))) in v * [misc]taylor: Taking taylor expansion of 3 in v * [misc]backup-simplify: Simplify 3 into 3 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- v)) (/ 1 (- v))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- v)) in v * [misc]taylor: Taking taylor expansion of (- v) in v * [misc]taylor: Taking taylor expansion of v in v * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 3 1) into 3 * [misc]backup-simplify: Simplify 3 into 3 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* 3 (pow (/ 1 (/ 1 (- v))) 2)) into (* 3 (pow v 2)) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (114 enodes) * * [misc]simplify: iters left: 3 (329 enodes) * [exit]simplify: Simplified to (* (/ (* (- 1 (* v v)) (sqrt 2)) 4) (sqrt (+ 1 (* (* v -3) v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (pow (* (/ (* (- 1 (* v v)) (sqrt 2)) 4) (sqrt (+ 1 (* (* v -3) v)))) (+ 1/2 1/2))) * [enter]simplify: Simplifying (+ 1/2 1/2) * * [misc]simplify: iters left: 2 (2 enodes) * * [misc]simplify: iters left: 1 (3 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 2) to (λ (v) (pow (* (/ (* (- 1 (* v v)) (sqrt 2)) 4) (sqrt (+ 1 (* (* v -3) v)))) 1)) * * * * [misc]progress: [ 2 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (115 enodes) * * [misc]simplify: iters left: 3 (327 enodes) * [exit]simplify: Simplified to (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1)))) * [misc]simplify: Simplified (2 1) to (λ (v) (pow (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1)))) (+ 1 1))) * [enter]simplify: Simplifying (+ 1 1) * * [misc]simplify: iters left: 2 (2 enodes) * * [misc]simplify: iters left: 1 (5 enodes) * [exit]simplify: Simplified to 2 * [misc]simplify: Simplified (2 2) to (λ (v) (pow (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1)))) 2)) * * * * [misc]progress: [ 3 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (166 enodes) * [exit]simplify: Simplified to (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1)))) * [misc]simplify: Simplified (2 1) to (λ (v) (pow (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1)))) 1/2)) * * * * [misc]progress: [ 4 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (117 enodes) * * [misc]simplify: iters left: 3 (337 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (* v (* -3 v)))) (/ 4 (* (sqrt 2) (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (pow (/ (sqrt (+ 1 (* v (* -3 v)))) (/ 4 (* (sqrt 2) (- 1 (* v v))))) 1)) * * * * [misc]progress: [ 5 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 6 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (115 enodes) * * [misc]simplify: iters left: 3 (327 enodes) * [exit]simplify: Simplified to (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1)))) * [misc]simplify: Simplified (2 1) to (λ (v) (pow (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1)))) (+ 1 1))) * * * * [misc]progress: [ 7 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 8 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (log (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (117 enodes) * * [misc]simplify: iters left: 3 (335 enodes) * [exit]simplify: Simplified to (+ (log (sqrt (* (/ (* (- 1 (* v v)) (sqrt 2)) 4) (sqrt (- 1 (* (* 3 v) v)))))) (log (sqrt (* (/ (* (- 1 (* v v)) (sqrt 2)) 4) (sqrt (- 1 (* (* 3 v) v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (exp (+ (log (sqrt (* (/ (* (- 1 (* v v)) (sqrt 2)) 4) (sqrt (- 1 (* (* 3 v) v)))))) (log (sqrt (* (/ (* (- 1 (* v v)) (sqrt 2)) 4) (sqrt (- 1 (* (* 3 v) v))))))))) * * * * [misc]progress: [ 9 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 10 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 11 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (* (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (149 enodes) * [exit]simplify: Simplified to (pow (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1))) 3) * [misc]simplify: Simplified (2 1) to (λ (v) (cbrt (pow (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1))) 3))) * * * * [misc]progress: [ 12 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 13 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 14 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (166 enodes) * [exit]simplify: Simplified to (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1)))) * [misc]simplify: Simplified (2 1) to (λ (v) (sqrt (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1)))))) * * * * [misc]progress: [ 15 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 16 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (77 enodes) * * [misc]simplify: iters left: 2 (89 enodes) * * [misc]simplify: iters left: 1 (104 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (* v (* v -3)))) (/ 4 (sqrt 2))) * [misc]simplify: Simplified (2 1) to (λ (v) (+ (/ (sqrt (+ 1 (* v (* v -3)))) (/ 4 (sqrt 2))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) * [enter]simplify: Simplifying (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (207 enodes) * * [misc]simplify: iters left: 2 (387 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (* -3 (* v v)))) (/ (/ 4 (* v v)) (- (sqrt 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (+ (/ (sqrt (+ 1 (* v (* v -3)))) (/ 4 (sqrt 2))) (/ (sqrt (+ 1 (* -3 (* v v)))) (/ (/ 4 (* v v)) (- (sqrt 2)))))) * * * * [misc]progress: [ 17 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (28 enodes) * * [misc]simplify: iters left: 5 (79 enodes) * * [misc]simplify: iters left: 4 (248 enodes) * [exit]simplify: Simplified to (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) 4) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (sqrt 2) (* (- v) (* v (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) 4) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (sqrt 2) (* (- v) (* v (sqrt 2)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (278 enodes) * [exit]simplify: Simplified to (* 4 (+ (* (* (* v v) 3) (* 12 (* v v))) (+ 4 (* 12 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) 4) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (sqrt 2) (* (- v) (* v (sqrt 2)))))) (* 4 (+ (* (* (* v v) 3) (* 12 (* v v))) (+ 4 (* 12 (* v v))))))) * * * * [misc]progress: [ 18 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (111 enodes) * * [misc]simplify: iters left: 4 (365 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* (sqrt 2) (sqrt (- 1 (pow (* (* 3 v) v) 3))))) (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* v v) (sqrt 2))) (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))))))) (sqrt (* (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* (sqrt 2) (sqrt (- 1 (pow (* (* 3 v) v) 3))))) (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* v v) (sqrt 2))) (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))))))) (sqrt (* (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (53 enodes) * * [misc]simplify: iters left: 4 (111 enodes) * * [misc]simplify: iters left: 3 (176 enodes) * * [misc]simplify: iters left: 2 (294 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 16 (* 16 (+ (* (* 9 v) (pow v 3)) (* (* 3 v) v))))) (sqrt (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* 9 v) (pow v 3)))) (* (sqrt (+ 1 (* (* 3 v) v))) 16)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* (sqrt 2) (sqrt (- 1 (pow (* (* 3 v) v) 3))))) (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* v v) (sqrt 2))) (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))))))) (sqrt (* (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2)))))) (* (sqrt (+ 16 (* 16 (+ (* (* 9 v) (pow v 3)) (* (* 3 v) v))))) (sqrt (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* 9 v) (pow v 3)))) (* (sqrt (+ 1 (* (* 3 v) v))) 16)))))) * * * * [misc]progress: [ 19 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (102 enodes) * * [misc]simplify: iters left: 4 (362 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) 4) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ (* (sqrt 2) (* v v)) 4)) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) 4) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ (* (sqrt 2) (* v v)) 4)) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) 4))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (98 enodes) * * [misc]simplify: iters left: 3 (189 enodes) * * [misc]simplify: iters left: 2 (408 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ 16 (* (* v 4) (* v 12))) (* (* v (* v 12)) (* v (* v 12))))) (sqrt (+ (* (* 3 v) (* (* v v) (* v 12))) (+ 4 (* v (* v 12)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) 4) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ (* (sqrt 2) (* v v)) 4)) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) 4))))) (* (sqrt (+ (+ 16 (* (* v 4) (* v 12))) (* (* v (* v 12)) (* v (* v 12))))) (sqrt (+ (* (* 3 v) (* (* v v) (* v 12))) (+ 4 (* v (* v 12)))))))) * * * * [misc]progress: [ 20 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (111 enodes) * * [misc]simplify: iters left: 4 (373 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (/ (* (sqrt 2) (* v v)) 4)) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) 4)))) (sqrt (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) 4) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (/ (* (sqrt 2) (* v v)) 4)) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) 4)))) (sqrt (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) 4) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (102 enodes) * * [misc]simplify: iters left: 3 (159 enodes) * * [misc]simplify: iters left: 2 (281 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (+ (* (* (* v 9) v) (* (* v v) 4)) (+ 4 (* (* v v) 12))))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (* v 9) (pow v 3)) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (/ (* (sqrt 2) (* v v)) 4)) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) 4)))) (sqrt (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) 4) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2)))))) (* (sqrt (* 4 (+ (* (* (* v 9) v) (* (* v v) 4)) (+ 4 (* (* v v) 12))))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (* v 9) (pow v 3)) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v))))))))) * * * * [misc]progress: [ 21 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (36 enodes) * * [misc]simplify: iters left: 5 (104 enodes) * * [misc]simplify: iters left: 4 (350 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (sqrt 2) (* v (* (- v) (sqrt 2))))))) (sqrt (+ (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (+ (* -3 (* v v)) 1)) (* (* (* (sqrt 2) v) (- v)) 4))) (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (sqrt 2) (* v (* (- v) (sqrt 2))))))) (sqrt (+ (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (+ (* -3 (* v v)) 1)) (* (* (* (sqrt 2) v) (- v)) 4))) (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (96 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (303 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ (* 48 (* v v)) (* (* 48 (* v v)) (* 3 (* v v)))) 16)) (sqrt (* (sqrt (+ (+ (* (* v 9) (pow v 3)) (* 3 (* v v))) 1)) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (sqrt 2) (* v (* (- v) (sqrt 2))))))) (sqrt (+ (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (+ (* -3 (* v v)) 1)) (* (* (* (sqrt 2) v) (- v)) 4))) (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (* (sqrt (+ (+ (* 48 (* v v)) (* (* 48 (* v v)) (* 3 (* v v)))) 16)) (sqrt (* (sqrt (+ (+ (* (* v 9) (pow v 3)) (* 3 (* v v))) 1)) 16))))) * * * * [misc]progress: [ 22 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (109 enodes) * * [misc]simplify: iters left: 4 (338 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* 9 (* v v)) (* v v))))) (* (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* v v)))) (sqrt (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* 9 (* v v)) (* v v)))) 4) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (sqrt 2) (* (- v) (* v (sqrt 2)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* 9 (* v v)) (* v v))))) (* (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* v v)))) (sqrt (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* 9 (* v v)) (* v v)))) 4) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (sqrt 2) (* (- v) (* v (sqrt 2)))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (54 enodes) * * [misc]simplify: iters left: 4 (112 enodes) * * [misc]simplify: iters left: 3 (178 enodes) * * [misc]simplify: iters left: 2 (303 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (+ (+ 4 (* (* v v) 12)) (* (* (* v v) 12) (* (* 3 v) v))))) (sqrt (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (pow v 3) (* v 9)))) (* 16 (sqrt (+ 1 (* (* 3 v) v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* 9 (* v v)) (* v v))))) (* (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* v v)))) (sqrt (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* 9 (* v v)) (* v v)))) 4) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (sqrt 2) (* (- v) (* v (sqrt 2)))))))) (* (sqrt (* 4 (+ (+ 4 (* (* v v) 12)) (* (* (* v v) 12) (* (* 3 v) v))))) (sqrt (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (pow v 3) (* v 9)))) (* 16 (sqrt (+ 1 (* (* 3 v) v))))))))) * * * * [misc]progress: [ 23 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (375 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2))) (* (sqrt (+ (* (* 3 v) v) 1)) 4))) (sqrt (* (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2))) (* (sqrt (+ (* (* 3 v) v) 1)) 4))) (sqrt (* (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (54 enodes) * * [misc]simplify: iters left: 4 (105 enodes) * * [misc]simplify: iters left: 3 (169 enodes) * * [misc]simplify: iters left: 2 (303 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (+ (* (* (* v v) (* v 9)) (* v 4)) (+ 4 (* 12 (* v v)))))) (sqrt (+ 16 (* 16 (* (* 3 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2))) (* (sqrt (+ (* (* 3 v) v) 1)) 4))) (sqrt (* (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2)))))) (* (sqrt (* 4 (+ (* (* (* v v) (* v 9)) (* v 4)) (+ 4 (* 12 (* v v)))))) (sqrt (+ 16 (* 16 (* (* 3 v) v))))))) * * * * [misc]progress: [ 24 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (117 enodes) * * [misc]simplify: iters left: 4 (391 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (/ (sqrt 2) 4)) (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* v v))))) (sqrt (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (/ (sqrt 2) 4)) (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* v v))))) (sqrt (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (101 enodes) * * [misc]simplify: iters left: 3 (153 enodes) * * [misc]simplify: iters left: 2 (267 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 16 (* 16 (+ (* (* v 9) (pow v 3)) (* (* 3 v) v))))) (sqrt (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* v 9) (pow v 3)))) (* 4 (sqrt (+ 1 (* (* 3 v) v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (/ (sqrt 2) 4)) (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* v v))))) (sqrt (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))))))) (* (sqrt (+ 16 (* 16 (+ (* (* v 9) (pow v 3)) (* (* 3 v) v))))) (sqrt (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* v 9) (pow v 3)))) (* 4 (sqrt (+ 1 (* (* 3 v) v))))))))) * * * * [misc]progress: [ 25 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (404 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (+ (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))))) (sqrt (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (sqrt 2) (- (* (* v v) (sqrt 2))))) (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (+ (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))))) (sqrt (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (sqrt 2) (- (* (* v v) (sqrt 2))))) (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (98 enodes) * * [misc]simplify: iters left: 3 (167 enodes) * * [misc]simplify: iters left: 2 (325 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (+ (+ (* (* v v) 12) 4) (* (* (* 3 v) (* v v)) (* v 12))))) (sqrt (+ (* (* v v) 12) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (+ (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))))) (sqrt (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (sqrt 2) (- (* (* v v) (sqrt 2))))) (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))))))) (* (sqrt (* 4 (+ (+ (* (* v v) 12) 4) (* (* (* 3 v) (* v v)) (* v 12))))) (sqrt (+ (* (* v v) 12) 4))))) * * * * [misc]progress: [ 26 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (385 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) 4) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (sqrt 2) (* (- v) (* v (sqrt 2))))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* v -3)) 1))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) 4) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (sqrt 2) (* (- v) (* v (sqrt 2))))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* v -3)) 1))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (96 enodes) * * [misc]simplify: iters left: 3 (154 enodes) * * [misc]simplify: iters left: 2 (274 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 16 (* 16 (+ (* (* v 9) (pow v 3)) (* (* 3 v) v))))) (sqrt (* 16 (sqrt (+ 1 (* (* 3 v) v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) 4) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (sqrt 2) (* (- v) (* v (sqrt 2))))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* v -3)) 1))))))) (* (sqrt (+ 16 (* 16 (+ (* (* v 9) (pow v 3)) (* (* 3 v) v))))) (sqrt (* 16 (sqrt (+ 1 (* (* 3 v) v)))))))) * * * * [misc]progress: [ 27 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (98 enodes) * * [misc]simplify: iters left: 4 (307 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))))) (sqrt (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))))) (sqrt (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (279 enodes) * [exit]simplify: Simplified to (* (sqrt (* (+ (* (* 3 (* v v)) (* (* v v) 12)) (+ 4 (* (* v v) 12))) 4)) (sqrt (+ (* (* 3 (* v v)) (* (* v v) 12)) (+ 4 (* (* v v) 12))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))))) (sqrt (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))))))) (* (sqrt (* (+ (* (* 3 (* v v)) (* (* v v) 12)) (+ 4 (* (* v v) 12))) 4)) (sqrt (+ (* (* 3 (* v v)) (* (* v v) 12)) (+ 4 (* (* v v) 12))))))) * * * * [misc]progress: [ 28 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (117 enodes) * * [misc]simplify: iters left: 4 (374 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) 4) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) 4) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (102 enodes) * * [misc]simplify: iters left: 3 (160 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (+ (* (pow v 3) (* v 9)) (* (* 3 v) v)) 16) 16)) (sqrt (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (pow v 3) (* v 9)))) (* 4 (sqrt (+ 1 (* (* 3 v) v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) 4) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))))))) (* (sqrt (+ (* (+ (* (pow v 3) (* v 9)) (* (* 3 v) v)) 16) 16)) (sqrt (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (pow v 3) (* v 9)))) (* 4 (sqrt (+ 1 (* (* 3 v) v))))))))) * * * * [misc]progress: [ 29 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (36 enodes) * * [misc]simplify: iters left: 5 (102 enodes) * * [misc]simplify: iters left: 4 (328 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))))) (sqrt (- (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (/ (sqrt 2) 4))) (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (/ (sqrt 2) 4)) (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))))) (sqrt (- (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (/ (sqrt 2) 4))) (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (/ (sqrt 2) 4)) (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (98 enodes) * * [misc]simplify: iters left: 3 (169 enodes) * * [misc]simplify: iters left: 2 (299 enodes) * [exit]simplify: Simplified to (* (sqrt (* (+ (* (* 4 v) (* (* v 9) (* v v))) (+ 4 (* 12 (* v v)))) 4)) (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v 9) (pow v 3))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))))) (sqrt (- (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (/ (sqrt 2) 4))) (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (/ (sqrt 2) 4)) (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* v v)))))) (* (sqrt (* (+ (* (* 4 v) (* (* v 9) (* v v))) (+ 4 (* 12 (* v v)))) 4)) (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v 9) (pow v 3))))))) * * * * [misc]progress: [ 30 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (374 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (* (* v v) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))))) (sqrt (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (* (sqrt 2) (* v (- v))) (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (* (* v v) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))))) (sqrt (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (* (sqrt 2) (* v (- v))) (sqrt 2)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * * [misc]simplify: iters left: 2 (274 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 16 (* (+ (* (* v 9) (pow v 3)) (* (* 3 v) v)) 16))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (* v 9) (pow v 3)) 1))) (sqrt (+ 1 (* (* 3 v) v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (* (* v v) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))))) (sqrt (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (* (sqrt 2) (* v (- v))) (sqrt 2)))))) (* (sqrt (+ 16 (* (+ (* (* v 9) (pow v 3)) (* (* 3 v) v)) 16))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (* v 9) (pow v 3)) 1))) (sqrt (+ 1 (* (* 3 v) v)))))))) * * * * [misc]progress: [ 31 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (110 enodes) * * [misc]simplify: iters left: 4 (354 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (/ (* 4 (sqrt 2)) 4)) (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* -3 v)) 1)))))) (sqrt (* (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) 4) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (/ (* 4 (sqrt 2)) 4)) (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* -3 v)) 1)))))) (sqrt (* (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) 4) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (96 enodes) * * [misc]simplify: iters left: 3 (160 enodes) * * [misc]simplify: iters left: 2 (284 enodes) * [exit]simplify: Simplified to (* (sqrt (* (+ (* (* 4 (* v v)) (* 9 (* v v))) (+ (* (* v v) 12) 4)) 4)) (sqrt (* (sqrt (+ (+ (* (* 9 v) (pow v 3)) (* (* v v) 3)) 1)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (/ (* 4 (sqrt 2)) 4)) (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* -3 v)) 1)))))) (sqrt (* (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) 4) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2)))))) (* (sqrt (* (+ (* (* 4 (* v v)) (* 9 (* v v))) (+ (* (* v v) 12) 4)) 4)) (sqrt (* (sqrt (+ (+ (* (* 9 v) (pow v 3)) (* (* v v) 3)) 1)) 4))))) * * * * [misc]progress: [ 32 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (108 enodes) * * [misc]simplify: iters left: 4 (338 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ (* v (* 3 v)) 1))) 4)) (* (* v v) (* (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3))))))) (sqrt (* (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ (* v (* 3 v)) 1))) 4) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (+ (sqrt 2) (- (* (* v v) (sqrt 2)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ (* v (* 3 v)) 1))) 4)) (* (* v v) (* (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3))))))) (sqrt (* (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ (* v (* 3 v)) 1))) 4) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (+ (sqrt 2) (- (* (* v v) (sqrt 2)))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (102 enodes) * * [misc]simplify: iters left: 3 (161 enodes) * * [misc]simplify: iters left: 2 (284 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (+ (* (* (* v v) (* 9 v)) (* v 4)) (+ 4 (* 12 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ (* (* 3 v) v) (+ (* (pow v 3) (* 9 v)) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ (* v (* 3 v)) 1))) 4)) (* (* v v) (* (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3))))))) (sqrt (* (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ (* v (* 3 v)) 1))) 4) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (+ (sqrt 2) (- (* (* v v) (sqrt 2)))))))) (* (sqrt (* 4 (+ (* (* (* v v) (* 9 v)) (* v 4)) (+ 4 (* 12 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ (* (* 3 v) v) (+ (* (pow v 3) (* 9 v)) 1)))))))) * * * * [misc]progress: [ 33 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (398 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* v v) (sqrt 2)))))) (sqrt (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (sqrt 2) (* (sqrt 2) (- (* v v))))) (* 4 (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* v v) (sqrt 2)))))) (sqrt (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (sqrt 2) (* (sqrt 2) (- (* v v))))) (* 4 (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (152 enodes) * * [misc]simplify: iters left: 2 (282 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (+ (+ 4 (* 12 (* v v))) (* (* 4 (* v v)) (* (* 3 v) (* 3 v)))))) (sqrt (+ 4 (* 12 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* v v) (sqrt 2)))))) (sqrt (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (sqrt 2) (* (sqrt 2) (- (* v v))))) (* 4 (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))))))) (* (sqrt (* 4 (+ (+ 4 (* 12 (* v v))) (* (* 4 (* v v)) (* (* 3 v) (* 3 v)))))) (sqrt (+ 4 (* 12 (* v v))))))) * * * * [misc]progress: [ 34 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (382 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (/ (sqrt 2) 4) (* v v)) (sqrt (+ (* (* v v) 3) 1)))))) (sqrt (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) 4) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (sqrt 2) (* v (* (- v) (sqrt 2)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (/ (sqrt 2) 4) (* v v)) (sqrt (+ (* (* v v) 3) 1)))))) (sqrt (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) 4) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (sqrt 2) (* v (* (- v) (sqrt 2)))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * * [misc]simplify: iters left: 2 (274 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 16 (* (+ (* (* v 9) (pow v 3)) (* (* 3 v) v)) 16))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (* v 9) (pow v 3)) 1))) (sqrt (+ 1 (* (* 3 v) v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (/ (sqrt 2) 4) (* v v)) (sqrt (+ (* (* v v) 3) 1)))))) (sqrt (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) 4) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (sqrt 2) (* v (* (- v) (sqrt 2)))))))) (* (sqrt (+ 16 (* (+ (* (* v 9) (pow v 3)) (* (* 3 v) v)) 16))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (* v 9) (pow v 3)) 1))) (sqrt (+ 1 (* (* 3 v) v)))))))) * * * * [misc]progress: [ 35 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (112 enodes) * * [misc]simplify: iters left: 4 (361 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (* (* 3 v) v) 1))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* (/ (sqrt 2) 4) (sqrt (+ (* (* 3 v) v) 1))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* v v)))) (sqrt (* (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) 4) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (* (* 3 v) v) 1))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* (/ (sqrt 2) 4) (sqrt (+ (* (* 3 v) v) 1))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* v v)))) (sqrt (* (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) 4) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (178 enodes) * * [misc]simplify: iters left: 2 (336 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* 16 (+ (* 9 (pow v 4)) (* (* 3 v) v))) 16)) (sqrt (+ 1 (* (* 3 v) v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (* (* 3 v) v) 1))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* (/ (sqrt 2) 4) (sqrt (+ (* (* 3 v) v) 1))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* v v)))) (sqrt (* (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) 4) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2)))))) (* (sqrt (+ (* 16 (+ (* 9 (pow v 4)) (* (* 3 v) v))) 16)) (sqrt (+ 1 (* (* 3 v) v)))))) * * * * [misc]progress: [ 36 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (119 enodes) * * [misc]simplify: iters left: 4 (379 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) 4) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))))) (sqrt (- (* (* (/ (sqrt 2) 4) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ (* 3 (* v v)) 1)) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* -3 v) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) 4) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))))) (sqrt (- (* (* (/ (sqrt 2) 4) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ (* 3 (* v v)) 1)) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* -3 v) v)))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * * [misc]simplify: iters left: 2 (274 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 16 (* (+ (* (* v 9) (pow v 3)) (* (* 3 v) v)) 16))) (sqrt (* 4 (sqrt (+ 1 (* (* 3 v) v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) 4) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))))) (sqrt (- (* (* (/ (sqrt 2) 4) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ (* 3 (* v v)) 1)) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* -3 v) v)))))))) (* (sqrt (+ 16 (* (+ (* (* v 9) (pow v 3)) (* (* 3 v) v)) 16))) (sqrt (* 4 (sqrt (+ 1 (* (* 3 v) v)))))))) * * * * [misc]progress: [ 37 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (36 enodes) * * [misc]simplify: iters left: 5 (102 enodes) * * [misc]simplify: iters left: 4 (315 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (+ (* (* (- (* v v)) (* (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (+ (* (* (- (* v v)) (* (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (154 enodes) * * [misc]simplify: iters left: 2 (289 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* 16 (* 3 (* v v))) (+ 1 (* 3 (* v v)))) 16)) (sqrt (* (sqrt (+ (+ (* (* 9 v) (pow v 3)) (* 3 (* v v))) 1)) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (+ (* (* (- (* v v)) (* (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))))))) (* (sqrt (+ (* (* 16 (* 3 (* v v))) (+ 1 (* 3 (* v v)))) 16)) (sqrt (* (sqrt (+ (+ (* (* 9 v) (pow v 3)) (* 3 (* v v))) 1)) 16))))) * * * * [misc]progress: [ 38 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (381 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))))) (sqrt (- (* (* (sqrt 2) (sqrt (+ 1 (* v (* v -3))))) (* (sqrt (+ (* (* 3 v) v) 1)) 4)) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (* v v) (sqrt 2)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))))) (sqrt (- (* (* (sqrt 2) (sqrt (+ 1 (* v (* v -3))))) (* (sqrt (+ (* (* 3 v) v) 1)) 4)) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (53 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (149 enodes) * * [misc]simplify: iters left: 2 (262 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* 16 (+ (* (* 9 v) (pow v 3)) (* (* 3 v) v))) 16)) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))))) (sqrt (- (* (* (sqrt 2) (sqrt (+ 1 (* v (* v -3))))) (* (sqrt (+ (* (* 3 v) v) 1)) 4)) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (+ (* 16 (+ (* (* 9 v) (pow v 3)) (* (* 3 v) v))) 16)) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) 16))))) * * * * [misc]progress: [ 39 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (110 enodes) * * [misc]simplify: iters left: 4 (364 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* 9 (* v v)) (* v v)))) (* (sqrt (+ (* -3 (* v v)) 1)) (sqrt 2))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* 9 (* v v)) (* v v)))) 4) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (* (- v) (* v (sqrt 2))) (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* 9 (* v v)) (* v v)))) (* (sqrt (+ (* -3 (* v v)) 1)) (sqrt 2))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* 9 (* v v)) (* v v)))) 4) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (* (- v) (* v (sqrt 2))) (sqrt 2)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (96 enodes) * * [misc]simplify: iters left: 3 (159 enodes) * * [misc]simplify: iters left: 2 (284 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* v v) 3) (+ (* (* 9 v) (pow v 3)) 1))) 4)) (sqrt (* 4 (+ (* (* (* 9 v) v) (* (* v v) 4)) (+ 4 (* (* v v) 12)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* 9 (* v v)) (* v v)))) (* (sqrt (+ (* -3 (* v v)) 1)) (sqrt 2))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* 9 (* v v)) (* v v)))) 4) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (* (- v) (* v (sqrt 2))) (sqrt 2)))))) (* (sqrt (* (sqrt (+ (* (* v v) 3) (+ (* (* 9 v) (pow v 3)) 1))) 4)) (sqrt (* 4 (+ (* (* (* 9 v) v) (* (* v v) 4)) (+ 4 (* (* v v) 12)))))))) * * * * [misc]progress: [ 40 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (119 enodes) * * [misc]simplify: iters left: 4 (381 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (sqrt 2) (* (- v) (* v (sqrt 2))))))) (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt 2)) (sqrt (+ 1 (* (* -3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (* v v) (/ (sqrt 2) 4)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (sqrt 2) (* (- v) (* v (sqrt 2))))))) (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt 2)) (sqrt (+ 1 (* (* -3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (* v v) (/ (sqrt 2) 4)) 4))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * * [misc]simplify: iters left: 2 (274 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 16 (* (+ (* (* v 9) (pow v 3)) (* (* 3 v) v)) 16))) (sqrt (* 4 (sqrt (+ 1 (* (* 3 v) v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (sqrt 2) (* (- v) (* v (sqrt 2))))))) (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt 2)) (sqrt (+ 1 (* (* -3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (* v v) (/ (sqrt 2) 4)) 4))))) (* (sqrt (+ 16 (* (+ (* (* v 9) (pow v 3)) (* (* 3 v) v)) 16))) (sqrt (* 4 (sqrt (+ 1 (* (* 3 v) v)))))))) * * * * [misc]progress: [ 41 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (37 enodes) * * [misc]simplify: iters left: 5 (106 enodes) * * [misc]simplify: iters left: 4 (337 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* v (* -3 v)) 1)) (sqrt 2)) (+ (* (* 4 v) (- v)) 4))) (sqrt (* (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) 4) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (* (- v) (* v (sqrt 2))) (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* v (* -3 v)) 1)) (sqrt 2)) (+ (* (* 4 v) (- v)) 4))) (sqrt (* (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) 4) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (* (- v) (* v (sqrt 2))) (sqrt 2)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 4))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (160 enodes) * * [misc]simplify: iters left: 2 (281 enodes) * [exit]simplify: Simplified to (* (sqrt (* (+ (+ 4 (* (* v v) 12)) (* (* (* v v) 3) (* (* v v) 12))) 4)) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* v (* -3 v)) 1)) (sqrt 2)) (+ (* (* 4 v) (- v)) 4))) (sqrt (* (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) 4) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (* (- v) (* v (sqrt 2))) (sqrt 2)))))) (* (sqrt (* (+ (+ 4 (* (* v v) 12)) (* (* (* v v) 3) (* (* v v) 12))) 4)) 4))) * * * * [misc]progress: [ 42 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3)))) * * [misc]simplify: iters left: 6 (38 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (417 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) 4) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (* (sqrt 2) (* v (- v))) (sqrt 2))))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ (* (* -3 v) v) 1))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* -3 v) v) 1))) 3)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) 4) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (* (sqrt 2) (* v (- v))) (sqrt 2))))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ (* (* -3 v) v) 1))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* -3 v) v) 1))) 3)))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * * [misc]simplify: iters left: 6 (31 enodes) * * [misc]simplify: iters left: 5 (92 enodes) * * [misc]simplify: iters left: 4 (299 enodes) * [exit]simplify: Simplified to (* (fabs (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4)) (sqrt (- (* (* (* (/ (sqrt 2) 4) (* v (- v))) (sqrt (- 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (* v (- v))) (sqrt (- 1 (* 3 (* v v)))))) (* (* (sqrt (- 1 (* 3 (* v v)))) (- (* (/ (sqrt 2) 4) (* v (- v))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (* 3 (* v v)))) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) 4) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (* (sqrt 2) (* v (- v))) (sqrt 2))))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ (* (* -3 v) v) 1))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* -3 v) v) 1))) 3)))) (* (fabs (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4)) (sqrt (- (* (* (* (/ (sqrt 2) 4) (* v (- v))) (sqrt (- 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (* v (- v))) (sqrt (- 1 (* 3 (* v v)))))) (* (* (sqrt (- 1 (* 3 (* v v)))) (- (* (/ (sqrt 2) 4) (* v (- v))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (* 3 (* v v)))) (/ (sqrt 2) 4)))))))) * * * * [misc]progress: [ 43 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (38 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (416 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2))))) (sqrt (* (* (sqrt (+ (* v (* v -3)) 1)) (+ (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* v (- v))))) (* (sqrt (+ (* v (* v -3)) 1)) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* v (- v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* 4 (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2))))) (sqrt (* (* (sqrt (+ (* v (* v -3)) 1)) (+ (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* v (- v))))) (* (sqrt (+ (* v (* v -3)) 1)) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* v (- v)))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (73 enodes) * * [misc]simplify: iters left: 4 (199 enodes) * [exit]simplify: Simplified to (* (sqrt (* (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))) 16)) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* -3 v)) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* 4 (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2))))) (sqrt (* (* (sqrt (+ (* v (* v -3)) 1)) (+ (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* v (- v))))) (* (sqrt (+ (* v (* v -3)) 1)) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* v (- v)))))))) (* (sqrt (* (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))) 16)) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* -3 v)) 1))))))) * * * * [misc]progress: [ 44 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (111 enodes) * * [misc]simplify: iters left: 4 (367 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (* (sqrt 2) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* 4 (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2)))))) (sqrt (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (sqrt 2) (* (sqrt 2) (* v (- v))))) (* 4 (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (* (sqrt 2) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* 4 (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2)))))) (sqrt (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (sqrt 2) (* (sqrt 2) (* v (- v))))) (* 4 (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (53 enodes) * * [misc]simplify: iters left: 4 (111 enodes) * * [misc]simplify: iters left: 3 (179 enodes) * * [misc]simplify: iters left: 2 (299 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ 1 (* (* 3 v) v))) 16) (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* v 9) (pow v 3)))))) (sqrt (* 4 (+ (+ (* 12 (* v v)) 4) (* (* 12 (* v v)) (* (* 3 v) v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (* (sqrt 2) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* 4 (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2)))))) (sqrt (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (sqrt 2) (* (sqrt 2) (* v (- v))))) (* 4 (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))))))) (* (sqrt (* (* (sqrt (+ 1 (* (* 3 v) v))) 16) (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* v 9) (pow v 3)))))) (sqrt (* 4 (+ (+ (* 12 (* v v)) 4) (* (* 12 (* v v)) (* (* 3 v) v)))))))) * * * * [misc]progress: [ 45 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (91 enodes) * * [misc]simplify: iters left: 4 (280 enodes) * [exit]simplify: Simplified to (- (* (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (* (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (105 enodes) * * [misc]simplify: iters left: 3 (175 enodes) * * [misc]simplify: iters left: 2 (272 enodes) * * [misc]simplify: iters left: 1 (345 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (pow v 4) 9))) (* (sqrt (+ 1 (* 3 (* v v)))) 16)) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (* (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (pow v 4) 9))) (* (sqrt (+ 1 (* 3 (* v v)))) 16)))) * * * * [misc]progress: [ 46 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (408 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt 2) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (sqrt (+ (* (* (- (* v v)) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (sqrt (+ (* 3 (* v v)) 1)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt 2) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (sqrt (+ (* (* (- (* v v)) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (sqrt (+ (* 3 (* v v)) 1)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (197 enodes) * * [misc]simplify: iters left: 2 (373 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 16 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ (* (* 3 v) v) (+ (* (* v 9) (pow v 3)) 1))))) (sqrt (+ (* (* v v) (* (* v 9) (* v 4))) (+ (* 12 (* v v)) 4)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt 2) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (sqrt (+ (* (* (- (* v v)) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (sqrt (+ (* 3 (* v v)) 1)))))) (* (sqrt (* (* 16 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ (* (* 3 v) v) (+ (* (* v 9) (pow v 3)) 1))))) (sqrt (+ (* (* v v) (* (* v 9) (* v 4))) (+ (* 12 (* v v)) 4)))))) * * * * [misc]progress: [ 47 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (369 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) (* 4 (/ (sqrt 2) 4))) (* (* v v) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))))))) (sqrt (- (* (sqrt 2) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* 4 (sqrt (+ (* v (* 3 v)) 1))))) (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* v v) (sqrt 2))) (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) (* 4 (/ (sqrt 2) 4))) (* (* v v) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))))))) (sqrt (- (* (sqrt 2) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* 4 (sqrt (+ (* v (* 3 v)) 1))))) (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* v v) (sqrt 2))) (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) 4))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (160 enodes) * * [misc]simplify: iters left: 2 (254 enodes) * * [misc]simplify: iters left: 1 (303 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* 16 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) (* 4 (/ (sqrt 2) 4))) (* (* v v) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))))))) (sqrt (- (* (sqrt 2) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* 4 (sqrt (+ (* v (* 3 v)) 1))))) (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* v v) (sqrt 2))) (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) 4))))) (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* 16 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v))))))))) * * * * [misc]progress: [ 48 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (376 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* v (* 3 v)) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt 2) (* v v))) (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) 4)))) (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (* 4 (* (sqrt 2) (- (* v v)))) (sqrt (+ 1 (* v (* -3 v))))) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* v (* 3 v)) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt 2) (* v v))) (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) 4)))) (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (* 4 (* (sqrt 2) (- (* v v)))) (sqrt (+ 1 (* v (* -3 v))))) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (104 enodes) * * [misc]simplify: iters left: 3 (167 enodes) * * [misc]simplify: iters left: 2 (265 enodes) * * [misc]simplify: iters left: 1 (314 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* 16 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* v (* 3 v)) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt 2) (* v v))) (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) 4)))) (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (* 4 (* (sqrt 2) (- (* v v)))) (sqrt (+ 1 (* v (* -3 v))))) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))))))) (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* 16 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) 16))))) * * * * [misc]progress: [ 49 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (365 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* 4 (sqrt (+ (* v (* 3 v)) 1)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* 4 (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* 4 (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))))) (* (* (sqrt 2) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* 4 (sqrt (+ (* v (* 3 v)) 1))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* 4 (sqrt (+ (* v (* 3 v)) 1)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* 4 (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* 4 (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))))) (* (* (sqrt 2) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* 4 (sqrt (+ (* v (* 3 v)) 1))) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (166 enodes) * * [misc]simplify: iters left: 2 (260 enodes) * * [misc]simplify: iters left: 1 (307 enodes) * [exit]simplify: Simplified to (* (* 16 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* 4 (sqrt (+ (* v (* 3 v)) 1)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* 4 (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* 4 (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))))) (* (* (sqrt 2) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* 4 (sqrt (+ (* v (* 3 v)) 1))) (* v v)))))) (* (* 16 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1)))))) * * * * [misc]progress: [ 50 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (109 enodes) * * [misc]simplify: iters left: 4 (338 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (sqrt 2)) (* (sqrt (+ (* (* 3 v) v) 1)) 4)) (* (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))))) (sqrt (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (* (sqrt 2) (* v (- v))) (sqrt 2))) (* (sqrt (+ (* (* 3 v) v) 1)) 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (sqrt 2)) (* (sqrt (+ (* (* 3 v) v) 1)) 4)) (* (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))))) (sqrt (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (* (sqrt 2) (* v (- v))) (sqrt 2))) (* (sqrt (+ (* (* 3 v) v) 1)) 4)))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (54 enodes) * * [misc]simplify: iters left: 4 (112 enodes) * * [misc]simplify: iters left: 3 (175 enodes) * * [misc]simplify: iters left: 2 (287 enodes) * * [misc]simplify: iters left: 1 (386 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* 9 (pow v 4)))) (* 16 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (+ (* 48 (* v v)) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (sqrt 2)) (* (sqrt (+ (* (* 3 v) v) 1)) 4)) (* (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))))) (sqrt (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (* (sqrt 2) (* v (- v))) (sqrt 2))) (* (sqrt (+ (* (* 3 v) v) 1)) 4)))) (* (sqrt (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* 9 (pow v 4)))) (* 16 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (+ (* 48 (* v v)) 16))))) * * * * [misc]progress: [ 51 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (119 enodes) * * [misc]simplify: iters left: 4 (404 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (* v (* 3 v)) 1)) (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* 4 (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))))))) (sqrt (- (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (sqrt 2)) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (/ (sqrt 2) 4) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* v (* 3 v)) 1)) (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* 4 (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))))))) (sqrt (- (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (sqrt 2)) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (/ (sqrt 2) 4) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (104 enodes) * * [misc]simplify: iters left: 3 (160 enodes) * * [misc]simplify: iters left: 2 (255 enodes) * * [misc]simplify: iters left: 1 (299 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 16 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* v (* 3 v)) 1)) (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* 4 (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))))))) (sqrt (- (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (sqrt 2)) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (/ (sqrt 2) 4) (* v v)))))) (* (sqrt (* (* 16 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v))))))))) * * * * [misc]progress: [ 52 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (394 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* 4 (sqrt (+ (* (* v v) 3) 1)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* 4 (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (/ (sqrt 2) 4) (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* 4 (sqrt (+ (* (* v v) 3) 1)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* 4 (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (/ (sqrt 2) 4) (* v v))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (180 enodes) * * [misc]simplify: iters left: 2 (315 enodes) * * [misc]simplify: iters left: 1 (443 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* 16 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (+ (* v (* 12 v)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* 4 (sqrt (+ (* (* v v) 3) 1)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* 4 (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (/ (sqrt 2) 4) (* v v))))))) (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* 16 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (+ (* v (* 12 v)) 4))))) * * * * [misc]progress: [ 53 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (385 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (* (sqrt (+ (* (* v -3) v) 1)) (* v v))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* 4 (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (* (sqrt (+ (* (* v -3) v) 1)) (* v v))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* 4 (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (105 enodes) * * [misc]simplify: iters left: 3 (164 enodes) * * [misc]simplify: iters left: 2 (259 enodes) * * [misc]simplify: iters left: 1 (304 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))) (* (sqrt (+ 1 (* (* 3 v) v))) 16))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (* (sqrt (+ (* (* v -3) v) 1)) (* v v))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* 4 (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))))))) (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))) (* (sqrt (+ 1 (* (* 3 v) v))) 16))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) 16))))) * * * * [misc]progress: [ 54 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (383 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)) (* (sqrt (+ (* (* v v) 3) 1)) 4)) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* 9 (* v v)) (* v v)))) 4)))) (sqrt (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* 9 (* v v)) (* v v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)) (* (sqrt (+ (* (* v v) 3) 1)) 4)) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* 9 (* v v)) (* v v)))) 4)))) (sqrt (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* 9 (* v v)) (* v v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (106 enodes) * * [misc]simplify: iters left: 3 (167 enodes) * * [misc]simplify: iters left: 2 (280 enodes) * * [misc]simplify: iters left: 1 (433 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))) (* (sqrt (+ 1 (* (* 3 v) v))) 16))) (sqrt (+ (+ 4 (* (pow v 3) (* v 36))) (* 12 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)) (* (sqrt (+ (* (* v v) 3) 1)) 4)) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* 9 (* v v)) (* v v)))) 4)))) (sqrt (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* 9 (* v v)) (* v v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))))))) (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))) (* (sqrt (+ 1 (* (* 3 v) v))) 16))) (sqrt (+ (+ 4 (* (pow v 3) (* v 36))) (* 12 (* v v))))))) * * * * [misc]progress: [ 55 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (110 enodes) * * [misc]simplify: iters left: 4 (334 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* 3 (* v v)) 1)) 4)) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (sqrt 2))) (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* 3 (* v v)) 1)) 4)) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (sqrt 2))) (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (104 enodes) * * [misc]simplify: iters left: 3 (164 enodes) * * [misc]simplify: iters left: 2 (259 enodes) * * [misc]simplify: iters left: 1 (309 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* 16 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* 3 (* v v)) 1)) 4)) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (sqrt 2))) (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* 16 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v))))))))) * * * * [misc]progress: [ 56 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (375 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) 4) (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* v v) (sqrt 2))) (* 4 (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) 4) (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* v v) (sqrt 2))) (* 4 (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (106 enodes) * * [misc]simplify: iters left: 3 (178 enodes) * * [misc]simplify: iters left: 2 (288 enodes) * * [misc]simplify: iters left: 1 (367 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ 1 (* (* 3 v) v))) 16) (sqrt (+ (+ 1 (* (* 3 v) v)) (* (pow v 4) 9))))) (sqrt (+ (+ 1 (* (* 3 v) v)) (* (pow v 4) 9)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) 4) (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* v v) (sqrt 2))) (* 4 (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))))))) (* (sqrt (* (* (sqrt (+ 1 (* (* 3 v) v))) 16) (sqrt (+ (+ 1 (* (* 3 v) v)) (* (pow v 4) 9))))) (sqrt (+ (+ 1 (* (* 3 v) v)) (* (pow v 4) 9)))))) * * * * [misc]progress: [ 57 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (368 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (- (* v v)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) (/ (sqrt 2) 4))) (* (* (sqrt (+ (* v (* 3 v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* 4 (sqrt (+ (* v (* 3 v)) 1)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (- (* v v)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) (/ (sqrt 2) 4))) (* (* (sqrt (+ (* v (* 3 v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* 4 (sqrt (+ (* v (* 3 v)) 1)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) 4))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (243 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))) (* 16 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (- (* v v)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) (/ (sqrt 2) 4))) (* (* (sqrt (+ (* v (* 3 v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* 4 (sqrt (+ (* v (* 3 v)) 1)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) 4))))) (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))) (* 16 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1)))))))) * * * * [misc]progress: [ 58 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (122 enodes) * * [misc]simplify: iters left: 4 (380 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (sqrt (+ (* v (* 3 v)) 1)) (* 4 (sqrt 2)))) (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* v v) (sqrt 2))) (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ (* v (* 3 v)) 1))) 4)))) (sqrt (- (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (/ (sqrt 2) 4) 4)) (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ (* v (* 3 v)) 1))) (* (sqrt (- 1 (* v (* 3 v)))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (sqrt (+ (* v (* 3 v)) 1)) (* 4 (sqrt 2)))) (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* v v) (sqrt 2))) (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ (* v (* 3 v)) 1))) 4)))) (sqrt (- (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (/ (sqrt 2) 4) 4)) (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ (* v (* 3 v)) 1))) (* (sqrt (- 1 (* v (* 3 v)))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (104 enodes) * * [misc]simplify: iters left: 3 (166 enodes) * * [misc]simplify: iters left: 2 (260 enodes) * * [misc]simplify: iters left: 1 (311 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 16 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (sqrt (+ (* v (* 3 v)) 1)) (* 4 (sqrt 2)))) (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* v v) (sqrt 2))) (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ (* v (* 3 v)) 1))) 4)))) (sqrt (- (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (/ (sqrt 2) 4) 4)) (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ (* v (* 3 v)) 1))) (* (sqrt (- 1 (* v (* 3 v)))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (* 16 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) 4))))) * * * * [misc]progress: [ 59 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (119 enodes) * * [misc]simplify: iters left: 4 (391 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (sqrt 2) (* v v))) (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) 4)))) (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* v v) (* (* (sqrt 2) (sqrt (+ (* (* 3 v) v) 1))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (sqrt 2) (* v v))) (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) 4)))) (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* v v) (* (* (sqrt 2) (sqrt (+ (* (* 3 v) v) 1))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (104 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (246 enodes) * * [misc]simplify: iters left: 1 (275 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* 16 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (sqrt 2) (* v v))) (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) 4)))) (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* v v) (* (* (sqrt 2) (sqrt (+ (* (* 3 v) v) 1))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))))))) (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* 16 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v))))))))) * * * * [misc]progress: [ 60 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (112 enodes) * * [misc]simplify: iters left: 4 (364 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (sqrt 2)) (* 4 (sqrt (+ (* v (* 3 v)) 1)))) (* (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) 4) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (sqrt 2)) (* 4 (sqrt (+ (* v (* 3 v)) 1)))) (* (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) 4) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (108 enodes) * * [misc]simplify: iters left: 3 (169 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * * [misc]simplify: iters left: 1 (375 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ 1 (* (* 3 v) v))) 16) (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))))) (sqrt (+ (* 12 (* v v)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (sqrt 2)) (* 4 (sqrt (+ (* v (* 3 v)) 1)))) (* (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) 4) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (* (sqrt (+ 1 (* (* 3 v) v))) 16) (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))))) (sqrt (+ (* 12 (* v v)) 4))))) * * * * [misc]progress: [ 61 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (411 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4)) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (+ (* (* v v) 3) 1)) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ (* (sqrt 2) (* v v)) 4))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* 4 (sqrt (+ (* (* v v) 3) 1)))) (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* 4 (sqrt 2))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4)) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (+ (* (* v v) 3) 1)) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ (* (sqrt 2) (* v v)) 4))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* 4 (sqrt (+ (* (* v v) 3) 1)))) (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* 4 (sqrt 2))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (243 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))) (* 16 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4)) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (+ (* (* v v) 3) 1)) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ (* (sqrt 2) (* v v)) 4))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* 4 (sqrt (+ (* (* v v) 3) 1)))) (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* 4 (sqrt 2))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))))) (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))) (* 16 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1)))))))) * * * * [misc]progress: [ 62 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (370 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) 4) (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* v v) (sqrt 2))) (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) 4)))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (* v (* 3 v)) 1))) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (* v (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* v (sqrt (+ (* v (* 3 v)) 1))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) 4) (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* v v) (sqrt 2))) (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) 4)))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (* v (* 3 v)) 1))) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (* v (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* v (sqrt (+ (* v (* 3 v)) 1))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (106 enodes) * * [misc]simplify: iters left: 3 (176 enodes) * * [misc]simplify: iters left: 2 (289 enodes) * * [misc]simplify: iters left: 1 (395 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (pow v 4) 9))) (* 16 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (+ 1 (* (* 3 v) v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) 4) (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* v v) (sqrt 2))) (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) 4)))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (* v (* 3 v)) 1))) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (* v (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* v (sqrt (+ (* v (* 3 v)) 1))))))) (* (sqrt (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (pow v 4) 9))) (* 16 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (+ 1 (* (* 3 v) v)))))) * * * * [misc]progress: [ 63 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (123 enodes) * * [misc]simplify: iters left: 4 (395 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* v v) (sqrt 2))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) 4)))) (sqrt (- (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (* 4 (sqrt 2)) 4)) (* (* (sqrt (+ (* (* v v) 3) 1)) (sqrt 2)) (* (sqrt (- 1 (* (* v v) 3))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* v v) (sqrt 2))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) 4)))) (sqrt (- (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (* 4 (sqrt 2)) 4)) (* (* (sqrt (+ (* (* v v) 3) 1)) (sqrt 2)) (* (sqrt (- 1 (* (* v v) 3))) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (104 enodes) * * [misc]simplify: iters left: 3 (169 enodes) * * [misc]simplify: iters left: 2 (264 enodes) * * [misc]simplify: iters left: 1 (315 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 16 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))))) (sqrt (* 4 (sqrt (+ 1 (* (* 3 v) v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* v v) (sqrt 2))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) 4)))) (sqrt (- (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (* 4 (sqrt 2)) 4)) (* (* (sqrt (+ (* (* v v) 3) 1)) (sqrt 2)) (* (sqrt (- 1 (* (* v v) 3))) (* v v)))))) (* (sqrt (* (* 16 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))))) (sqrt (* 4 (sqrt (+ 1 (* (* 3 v) v)))))))) * * * * [misc]progress: [ 64 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (381 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (* (sqrt 2) 4) (sqrt (+ 1 (* v (* -3 v)))))) (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (- 1 (pow (* (* v v) 3) 3)))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (* (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (* (sqrt 2) 4) (sqrt (+ 1 (* v (* -3 v)))))) (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (- 1 (pow (* (* v v) 3) 3)))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (* (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) 4))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (166 enodes) * * [misc]simplify: iters left: 2 (261 enodes) * * [misc]simplify: iters left: 1 (315 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* (sqrt (+ 1 (* (* 3 v) v))) 16))) (sqrt (* 16 (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (* (sqrt 2) 4) (sqrt (+ 1 (* v (* -3 v)))))) (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (- 1 (pow (* (* v v) 3) 3)))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (* (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) 4))))) (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* (sqrt (+ 1 (* (* 3 v) v))) 16))) (sqrt (* 16 (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1)))))))) * * * * [misc]progress: [ 65 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (346 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt 2) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* 4 (sqrt (+ (* (* v v) 3) 1))))) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* v v) (sqrt 2))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) 4)))) (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (+ (* (* v -3) v) 1))) (sqrt (+ (* (* v v) 3) 1))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt 2) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* 4 (sqrt (+ (* (* v v) 3) 1))))) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* v v) (sqrt 2))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) 4)))) (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (+ (* (* v -3) v) 1))) (sqrt (+ (* (* v v) 3) 1))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (53 enodes) * * [misc]simplify: iters left: 4 (104 enodes) * * [misc]simplify: iters left: 3 (161 enodes) * * [misc]simplify: iters left: 2 (249 enodes) * * [misc]simplify: iters left: 1 (278 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))) (* (sqrt (+ 1 (* (* 3 v) v))) 16))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt 2) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* 4 (sqrt (+ (* (* v v) 3) 1))))) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* v v) (sqrt 2))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) 4)))) (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (+ (* (* v -3) v) 1))) (sqrt (+ (* (* v v) 3) 1))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))) (* (sqrt (+ 1 (* (* 3 v) v))) 16))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) 16))))) * * * * [misc]progress: [ 66 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (123 enodes) * * [misc]simplify: iters left: 4 (406 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (* (* v v) 3) 1)) 4)) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* v v) (sqrt 2))) (* 4 (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* v v) 3)))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (* (* v v) 3) 1)) 4)) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* v v) (sqrt 2))) (* 4 (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* v v) 3)))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (106 enodes) * * [misc]simplify: iters left: 3 (166 enodes) * * [misc]simplify: iters left: 2 (254 enodes) * * [misc]simplify: iters left: 1 (283 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* (pow v 4) 9) 1))) 4)) (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* (pow v 4) 9) 1))) (* (sqrt (+ 1 (* v (* 3 v)))) 16)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (* (* v v) 3) 1)) 4)) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* v v) (sqrt 2))) (* 4 (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* v v) 3)))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* (pow v 4) 9) 1))) 4)) (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* (pow v 4) 9) 1))) (* (sqrt (+ 1 (* v (* 3 v)))) 16)))))) * * * * [misc]progress: [ 67 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (122 enodes) * * [misc]simplify: iters left: 4 (377 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)) (* 4 (sqrt (+ (* (* v v) 3) 1)))) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* v v) (sqrt 2))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) 4)))) (sqrt (- (* (* (sqrt 2) (sqrt (+ 1 (* v (* -3 v))))) (sqrt (+ (* (* v v) 3) 1))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)) (* 4 (sqrt (+ (* (* v v) 3) 1)))) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* v v) (sqrt 2))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) 4)))) (sqrt (- (* (* (sqrt 2) (sqrt (+ 1 (* v (* -3 v))))) (sqrt (+ (* (* v v) 3) 1))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (106 enodes) * * [misc]simplify: iters left: 3 (166 enodes) * * [misc]simplify: iters left: 2 (254 enodes) * * [misc]simplify: iters left: 1 (283 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ 1 (* v (* 3 v)))))) (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* (pow v 4) 9) 1))) (* (sqrt (+ 1 (* v (* 3 v)))) 16)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)) (* 4 (sqrt (+ (* (* v v) 3) 1)))) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* v v) (sqrt 2))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) 4)))) (sqrt (- (* (* (sqrt 2) (sqrt (+ 1 (* v (* -3 v))))) (sqrt (+ (* (* v v) 3) 1))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) (* (sqrt (* 4 (sqrt (+ 1 (* v (* 3 v)))))) (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* (pow v 4) 9) 1))) (* (sqrt (+ 1 (* v (* 3 v)))) 16)))))) * * * * [misc]progress: [ 68 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (367 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt 2) (sqrt (+ 1 (* (* -3 v) v)))) (+ 4 (* (* 4 v) (- v))))) (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (sqrt 2)))) (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* 4 (sqrt 2))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt 2) (sqrt (+ 1 (* (* -3 v) v)))) (+ 4 (* (* 4 v) (- v))))) (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (sqrt 2)))) (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* 4 (sqrt 2))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 4))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (163 enodes) * * [misc]simplify: iters left: 2 (249 enodes) * * [misc]simplify: iters left: 1 (281 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* 9 (pow v 4)))) (* (sqrt (+ 1 (* (* 3 v) v))) 16))) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt 2) (sqrt (+ 1 (* (* -3 v) v)))) (+ 4 (* (* 4 v) (- v))))) (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (sqrt 2)))) (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* 4 (sqrt 2))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)))))) (* (sqrt (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* 9 (pow v 4)))) (* (sqrt (+ 1 (* (* 3 v) v))) 16))) 4))) * * * * [misc]progress: [ 69 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3)))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (126 enodes) * * [misc]simplify: iters left: 4 (444 enodes) * [exit]simplify: Simplified to (* (sqrt (- (pow (* (sqrt (+ (* (* v -3) v) 1)) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))) 3))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (* (* v v) 3) 1)) 4)) (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* 4 (sqrt 2))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (pow (* (sqrt (+ (* (* v -3) v) 1)) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))) 3))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (* (* v v) 3) 1)) 4)) (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* 4 (sqrt 2))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (97 enodes) * * [misc]simplify: iters left: 4 (308 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (sqrt (- 1 (* (* 3 v) v))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* 3 v) v))) (/ (sqrt 2) 4))) (* (* (* (- (* v v)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 v) v)))) (* (sqrt (- 1 (* (* 3 v) v))) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))))) (sqrt (* (* (sqrt (+ 1 (* (* 3 v) v))) 16) (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (pow (* (sqrt (+ (* (* v -3) v) 1)) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))) 3))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (* (* v v) 3) 1)) 4)) (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* 4 (sqrt 2))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))))) (* (sqrt (+ (* (* (sqrt (- 1 (* (* 3 v) v))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* 3 v) v))) (/ (sqrt 2) 4))) (* (* (* (- (* v v)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 v) v)))) (* (sqrt (- 1 (* (* 3 v) v))) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))))) (sqrt (* (* (sqrt (+ 1 (* (* 3 v) v))) 16) (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v))))))))) * * * * [misc]progress: [ 70 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (128 enodes) * * [misc]simplify: iters left: 4 (446 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* (* v -3) v) 1)) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* (- v) v)))) (* (* (+ 1 (* (- v) v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (sqrt (+ (* v (* 3 v)) 1)) 4)) (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* v v) (sqrt 2))) (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* (* v -3) v) 1)) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* (- v) v)))) (* (* (+ 1 (* (- v) v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (sqrt (+ (* v (* 3 v)) 1)) 4)) (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* v v) (sqrt 2))) (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) 4))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (30 enodes) * * [misc]simplify: iters left: 5 (78 enodes) * * [misc]simplify: iters left: 4 (208 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ 1 (* 3 (* v v)))) 16) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* -3 v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* (* v -3) v) 1)) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* (- v) v)))) (* (* (+ 1 (* (- v) v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (sqrt (+ (* v (* 3 v)) 1)) 4)) (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* v v) (sqrt 2))) (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) 4))))) (* (sqrt (* (* (sqrt (+ 1 (* 3 (* v v)))) 16) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* -3 v))))))))) * * * * [misc]progress: [ 71 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (102 enodes) * * [misc]simplify: iters left: 4 (364 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (+ (* (* 4 (* (* v (- v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (sqrt 2))))) (sqrt (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (sqrt 2) (* (- v) (* v (sqrt 2))))) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (+ (* (* 4 (* (* v (- v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (sqrt 2))))) (sqrt (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (sqrt 2) (* (- v) (* v (sqrt 2))))) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) 4)))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (99 enodes) * * [misc]simplify: iters left: 3 (232 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* 3 (* v v)) (* (* v v) 12)) (+ (* (* v v) 12) 4))) (sqrt (+ (* (* 3 (* v v)) (* 48 (* v v))) (+ (* 48 (* v v)) 16)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (+ (* (* 4 (* (* v (- v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (sqrt 2))))) (sqrt (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (sqrt 2) (* (- v) (* v (sqrt 2))))) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) 4)))) (* (sqrt (+ (* (* 3 (* v v)) (* (* v v) 12)) (+ (* (* v v) 12) 4))) (sqrt (+ (* (* 3 (* v v)) (* 48 (* v v))) (+ (* 48 (* v v)) 16)))))) * * * * [misc]progress: [ 72 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (407 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (+ (* (sqrt 2) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4))))) (sqrt (- (* 4 (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (+ (* (sqrt 2) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4))))) (sqrt (- (* 4 (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (108 enodes) * * [misc]simplify: iters left: 3 (197 enodes) * * [misc]simplify: iters left: 2 (364 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ (* (* v v) 12) 4) (* (* (* v v) 12) (* (* 3 v) v)))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 3) (* v 9)) 1))) (* 16 (sqrt (+ 1 (* (* 3 v) v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (+ (* (sqrt 2) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4))))) (sqrt (- (* 4 (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (+ (+ (* (* v v) 12) 4) (* (* (* v v) 12) (* (* 3 v) v)))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 3) (* v 9)) 1))) (* 16 (sqrt (+ 1 (* (* 3 v) v))))))))) * * * * [misc]progress: [ 73 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (30 enodes) * * [misc]simplify: iters left: 5 (82 enodes) * * [misc]simplify: iters left: 4 (274 enodes) * [exit]simplify: Simplified to (- (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt 2))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (/ (sqrt 2) 4))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt 2))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (/ (sqrt 2) 4))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (338 enodes) * [exit]simplify: Simplified to (+ (* (* 3 (* v v)) (* (* v v) 12)) (+ 4 (* (* v v) 12))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt 2))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (/ (sqrt 2) 4))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4))) (+ (* (* 3 (* v v)) (* (* v v) 12)) (+ 4 (* (* v v) 12))))) * * * * [misc]progress: [ 74 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (113 enodes) * * [misc]simplify: iters left: 4 (397 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (/ (* (sqrt 2) (* v v)) 4)) (* 4 (sqrt (+ (+ 1 (* v (* 3 v))) (* (* 9 (* v v)) (* v v)))))))) (sqrt (- (* (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (* 9 (* v v)) (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (/ (* (sqrt 2) (* v v)) 4)) (* 4 (sqrt (+ (+ 1 (* v (* 3 v))) (* (* 9 (* v v)) (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (/ (* (sqrt 2) (* v v)) 4)) (* 4 (sqrt (+ (+ 1 (* v (* 3 v))) (* (* 9 (* v v)) (* v v)))))))) (sqrt (- (* (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (* 9 (* v v)) (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (/ (* (sqrt 2) (* v v)) 4)) (* 4 (sqrt (+ (+ 1 (* v (* 3 v))) (* (* 9 (* v v)) (* v v))))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (95 enodes) * * [misc]simplify: iters left: 3 (184 enodes) * * [misc]simplify: iters left: 2 (366 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ 4 (* (* v 12) v)) (* (* (* v 4) (* v v)) (* v 9)))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* v 9) (pow v 3))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (/ (* (sqrt 2) (* v v)) 4)) (* 4 (sqrt (+ (+ 1 (* v (* 3 v))) (* (* 9 (* v v)) (* v v)))))))) (sqrt (- (* (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (* 9 (* v v)) (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (/ (* (sqrt 2) (* v v)) 4)) (* 4 (sqrt (+ (+ 1 (* v (* 3 v))) (* (* 9 (* v v)) (* v v))))))))) (* (sqrt (+ (+ 4 (* (* v 12) v)) (* (* (* v 4) (* v v)) (* v 9)))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* v 9) (pow v 3))))))))) * * * * [misc]progress: [ 75 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (38 enodes) * * [misc]simplify: iters left: 5 (108 enodes) * * [misc]simplify: iters left: 4 (391 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (sqrt 2))) (* (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ 1 (* 3 (* v v))))) (* (* 4 (* v (* (- v) (sqrt 2)))) (sqrt (+ (* v (* v -3)) 1)))))) (sqrt (* (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ 1 (* 3 (* v v))))) (+ (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt 2)) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (sqrt 2))) (* (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ 1 (* 3 (* v v))))) (* (* 4 (* v (* (- v) (sqrt 2)))) (sqrt (+ (* v (* v -3)) 1)))))) (sqrt (* (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ 1 (* 3 (* v v))))) (+ (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt 2)) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (181 enodes) * * [misc]simplify: iters left: 2 (352 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ (* (* 12 v) v) 4) (* (* 4 (* v v)) (* (* v v) 9)))) (sqrt (* 16 (sqrt (+ (* v (* 3 v)) (+ (* (pow v 3) (* v 9)) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (sqrt 2))) (* (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ 1 (* 3 (* v v))))) (* (* 4 (* v (* (- v) (sqrt 2)))) (sqrt (+ (* v (* v -3)) 1)))))) (sqrt (* (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ 1 (* 3 (* v v))))) (+ (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt 2)) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4)))))) (* (sqrt (+ (+ (* (* 12 v) v) 4) (* (* 4 (* v v)) (* (* v v) 9)))) (sqrt (* 16 (sqrt (+ (* v (* 3 v)) (+ (* (pow v 3) (* v 9)) 1)))))))) * * * * [misc]progress: [ 76 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (391 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ (* (sqrt 2) (* v v)) 4)) (* 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))))) (* (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (* v v)) (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ (* (sqrt 2) (* v v)) 4)) (* 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))))) (* (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (* v v)) (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3)))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (108 enodes) * * [misc]simplify: iters left: 3 (198 enodes) * * [misc]simplify: iters left: 2 (365 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ (* v (* v 12)) 4) (* (* (* v v) 9) (* 4 (* v v))))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 3) (* 9 v)) 1))) (* 16 (sqrt (+ 1 (* (* 3 v) v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ (* (sqrt 2) (* v v)) 4)) (* 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))))) (* (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (* v v)) (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3)))))))) (* (sqrt (+ (+ (* v (* v 12)) 4) (* (* (* v v) 9) (* 4 (* v v))))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 3) (* 9 v)) 1))) (* 16 (sqrt (+ 1 (* (* 3 v) v))))))))) * * * * [misc]progress: [ 77 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (401 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* v v))))) (sqrt (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (sqrt 2) (- (* (* v v) (sqrt 2)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* v v))))) (sqrt (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (sqrt 2) (- (* (* v v) (sqrt 2)))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (98 enodes) * * [misc]simplify: iters left: 3 (182 enodes) * * [misc]simplify: iters left: 2 (367 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* 9 (* v v)) (* (* v v) 4)) (+ (* (* v 12) v) 4))) (sqrt (+ (* 16 (* (* 3 v) v)) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* v v))))) (sqrt (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (sqrt 2) (- (* (* v v) (sqrt 2)))))))) (* (sqrt (+ (* (* 9 (* v v)) (* (* v v) 4)) (+ (* (* v 12) v) 4))) (sqrt (+ (* 16 (* (* 3 v) v)) 16))))) * * * * [misc]progress: [ 78 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (110 enodes) * * [misc]simplify: iters left: 4 (356 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (+ (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt 2)) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4))))) (sqrt (- (* (sqrt 2) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* v v)) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (+ (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt 2)) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4))))) (sqrt (- (* (sqrt 2) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* v v)) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (sqrt 2) 4)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (197 enodes) * * [misc]simplify: iters left: 2 (390 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ 4 (* (* 12 v) v)) (* (* v v) (* 36 (* v v))))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 3) (* v 9)) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (+ (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt 2)) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4))))) (sqrt (- (* (sqrt 2) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* v v)) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (sqrt 2) 4)))))) (* (sqrt (+ (+ 4 (* (* 12 v) v)) (* (* v v) (* 36 (* v v))))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 3) (* v 9)) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v))))))))) * * * * [misc]progress: [ 79 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (421 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2))))) (sqrt (* (sqrt (+ 1 (* (* v v) 3))) (+ (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2))))) (sqrt (* (sqrt (+ 1 (* (* v v) 3))) (+ (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (178 enodes) * * [misc]simplify: iters left: 2 (368 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ (* (* v v) 12) 4) (* (* (* v v) 12) (* 3 (* v v))))) (sqrt (+ (* (* v v) 12) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2))))) (sqrt (* (sqrt (+ 1 (* (* v v) 3))) (+ (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)))))) (* (sqrt (+ (+ (* (* v v) 12) 4) (* (* (* v v) 12) (* 3 (* v v))))) (sqrt (+ (* (* v v) 12) 4))))) * * * * [misc]progress: [ 80 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (123 enodes) * * [misc]simplify: iters left: 4 (411 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (+ (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4)) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt 2))))) (sqrt (- (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt 2) 4)) (* (* (sqrt (+ 1 (* (* v v) -3))) (* (* v v) (sqrt 2))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (+ (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4)) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt 2))))) (sqrt (- (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt 2) 4)) (* (* (sqrt (+ 1 (* (* v v) -3))) (* (* v v) (sqrt 2))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (333 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ (* (* 12 v) v) 4) (* (* 4 (* v v)) (* (* v v) 9)))) (sqrt (* 16 (sqrt (+ 1 (* (* v v) 3)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (+ (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4)) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt 2))))) (sqrt (- (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt 2) 4)) (* (* (sqrt (+ 1 (* (* v v) -3))) (* (* v v) (sqrt 2))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (+ (+ (* (* 12 v) v) 4) (* (* 4 (* v v)) (* (* v v) 9)))) (sqrt (* 16 (sqrt (+ 1 (* (* v v) 3)))))))) * * * * [misc]progress: [ 81 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (36 enodes) * * [misc]simplify: iters left: 5 (102 enodes) * * [misc]simplify: iters left: 4 (331 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt 2) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* 4 (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))))))) (sqrt (- (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (sqrt 2)) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt 2) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* 4 (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))))))) (sqrt (- (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (sqrt 2)) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (177 enodes) * * [misc]simplify: iters left: 2 (351 enodes) * [exit]simplify: Simplified to (+ (* (* (* v v) 12) (* (* v v) 3)) (+ 4 (* (* v v) 12))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt 2) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* 4 (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))))))) (sqrt (- (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (sqrt 2)) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* v v)))))) (+ (* (* (* v v) 12) (* (* v v) 3)) (+ 4 (* (* v v) 12))))) * * * * [misc]progress: [ 82 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (383 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))))))) (sqrt (- (* (/ (sqrt 2) 4) (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (- 1 (pow (* (* 3 v) v) 3))))) (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))))))) (sqrt (- (* (/ (sqrt 2) 4) (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (- 1 (pow (* (* 3 v) v) 3))))) (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (177 enodes) * * [misc]simplify: iters left: 2 (350 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ 4 (* v (* v 12))) (* (* (* v v) 4) (* (* v v) 9)))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (* 9 v) (pow v 3)) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))))))) (sqrt (- (* (/ (sqrt 2) 4) (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (- 1 (pow (* (* 3 v) v) 3))))) (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* v v)))))) (* (sqrt (+ (+ 4 (* v (* v 12))) (* (* (* v v) 4) (* (* v v) 9)))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (* 9 v) (pow v 3)) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v))))))))) * * * * [misc]progress: [ 83 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (94 enodes) * * [misc]simplify: iters left: 4 (294 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) (+ (* (sqrt 2) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* 4 (* (/ (sqrt 2) 4) (- (* v v)))) (sqrt (- 1 (pow (* v (* 3 v)) 3))))))) (sqrt (- (/ (* (sqrt 2) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (/ 4 (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) (+ (* (sqrt 2) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* 4 (* (/ (sqrt 2) 4) (- (* v v)))) (sqrt (- 1 (pow (* v (* 3 v)) 3))))))) (sqrt (- (/ (* (sqrt 2) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (/ 4 (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (342 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ (* v (* v 12)) 4) (* (* 3 v) (* (* v v) (* v 12))))) (sqrt (+ (+ (* (pow v 3) (* 9 v)) (* 3 (* v v))) 1))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) (+ (* (sqrt 2) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* 4 (* (/ (sqrt 2) 4) (- (* v v)))) (sqrt (- 1 (pow (* v (* 3 v)) 3))))))) (sqrt (- (/ (* (sqrt 2) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (/ 4 (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))))))) (* (sqrt (+ (+ (* v (* v 12)) 4) (* (* 3 v) (* (* v v) (* v 12))))) (sqrt (+ (+ (* (pow v 3) (* 9 v)) (* 3 (* v v))) 1))))) * * * * [misc]progress: [ 84 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (378 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (sqrt 2) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4)))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (sqrt 2) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4)))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (173 enodes) * * [misc]simplify: iters left: 2 (358 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* v v) 12) (* (* v v) 3)) (+ 4 (* (* v v) 12)))) (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* v 9) (pow v 3)))) (sqrt (+ 1 (* (* v v) 3)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (sqrt 2) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4)))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* v v)))))) (* (sqrt (+ (* (* (* v v) 12) (* (* v v) 3)) (+ 4 (* (* v v) 12)))) (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* v 9) (pow v 3)))) (sqrt (+ 1 (* (* v v) 3)))))))) * * * * [misc]progress: [ 85 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (109 enodes) * * [misc]simplify: iters left: 4 (367 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (+ (* (* 4 (* (* v (- v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt 2) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (+ (* (* 4 (* (* v (- v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt 2) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (175 enodes) * * [misc]simplify: iters left: 2 (350 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ 4 (* (* v 12) v)) (* (* 3 v) (* (* v 12) (* v v))))) (sqrt (* (sqrt (+ (* 3 (* v v)) (+ (* (* 9 v) (pow v 3)) 1))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (+ (* (* 4 (* (* v (- v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt 2) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))))))) (* (sqrt (+ (+ 4 (* (* v 12) v)) (* (* 3 v) (* (* v 12) (* v v))))) (sqrt (* (sqrt (+ (* 3 (* v v)) (+ (* (* 9 v) (pow v 3)) 1))) 4))))) * * * * [misc]progress: [ 86 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (386 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* v v) (/ (sqrt 2) 4))) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) 4)))) (sqrt (- (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (sqrt (+ 1 (* (* v v) 3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* v v) (/ (sqrt 2) 4))) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) 4)))) (sqrt (- (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (sqrt (+ 1 (* (* v v) 3))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (177 enodes) * * [misc]simplify: iters left: 2 (351 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* 12 v) (* v v)) (* 3 v)) (+ (* 12 (* v v)) 4))) (sqrt (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* 9 v) (pow v 3))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* v v) (/ (sqrt 2) 4))) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) 4)))) (sqrt (- (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (sqrt (+ 1 (* (* v v) 3))))))) (* (sqrt (+ (* (* (* 12 v) (* v v)) (* 3 v)) (+ (* 12 (* v v)) 4))) (sqrt (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* 9 v) (pow v 3))))))))) * * * * [misc]progress: [ 87 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (418 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (+ (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt 2)) (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (+ (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt 2)) (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (165 enodes) * * [misc]simplify: iters left: 2 (341 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ 4 (* (* 12 v) v)) (* (* (* 3 v) (* v v)) (* 12 v)))) (sqrt (+ 4 (* (* 12 v) v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (+ (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt 2)) (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))))))) (* (sqrt (+ (+ 4 (* (* 12 v) v)) (* (* (* 3 v) (* v v)) (* 12 v)))) (sqrt (+ 4 (* (* 12 v) v)))))) * * * * [misc]progress: [ 88 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (108 enodes) * * [misc]simplify: iters left: 4 (352 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ 1 (* (* 3 v) v))))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))) (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (/ (* (sqrt 2) (* v v)) 4)) (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ 1 (* (* 3 v) v))))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))) (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (/ (* (sqrt 2) (* v v)) 4)) (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (173 enodes) * * [misc]simplify: iters left: 2 (358 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* v v) 12) (* (* v v) 3)) (+ 4 (* (* v v) 12)))) (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* v 9) (pow v 3)))) (sqrt (+ 1 (* (* v v) 3)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ 1 (* (* 3 v) v))))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))) (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (/ (* (sqrt 2) (* v v)) 4)) (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))))))) (* (sqrt (+ (* (* (* v v) 12) (* (* v v) 3)) (+ 4 (* (* v v) 12)))) (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* v 9) (pow v 3)))) (sqrt (+ 1 (* (* v v) 3)))))))) * * * * [misc]progress: [ 89 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (386 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt 2) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (* (sqrt 2) (* v v)) 4)) (* 4 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt 2) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (* (sqrt 2) (* v v)) 4)) (* 4 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (202 enodes) * * [misc]simplify: iters left: 2 (441 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ (* v (* v 12)) (* 36 (pow v 4))) 4)) (sqrt (+ 1 (* (* v v) 3)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt 2) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (* (sqrt 2) (* v v)) 4)) (* 4 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (+ (+ (* v (* v 12)) (* 36 (pow v 4))) 4)) (sqrt (+ 1 (* (* v v) 3)))))) * * * * [misc]progress: [ 90 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (405 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (- 1 (* (* v v) 3))) (* (* v v) (sqrt 2))) (sqrt (+ 1 (* (* v v) 3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (- 1 (* (* v v) 3))) (* (* v v) (sqrt 2))) (sqrt (+ 1 (* (* v v) 3))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (173 enodes) * * [misc]simplify: iters left: 2 (358 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* v v) 12) (* (* v v) 3)) (+ 4 (* (* v v) 12)))) (sqrt (* 4 (sqrt (+ 1 (* (* v v) 3)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (- 1 (* (* v v) 3))) (* (* v v) (sqrt 2))) (sqrt (+ 1 (* (* v v) 3))))))) (* (sqrt (+ (* (* (* v v) 12) (* (* v v) 3)) (+ 4 (* (* v v) 12)))) (sqrt (* 4 (sqrt (+ 1 (* (* v v) 3)))))))) * * * * [misc]progress: [ 91 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (111 enodes) * * [misc]simplify: iters left: 4 (373 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (+ (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)) (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (+ (* (* (* 4 (sqrt 2)) (- (* v v))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* v v) 3)))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (+ (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)) (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (+ (* (* (* 4 (sqrt 2)) (- (* v v))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* v v) 3)))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (179 enodes) * * [misc]simplify: iters left: 2 (356 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* v v) (* (* v 9) (* v 4))) (+ 4 (* v (* v 12))))) (sqrt (* (sqrt (+ (* (* v v) 3) (+ (* (* v 9) (pow v 3)) 1))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (+ (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)) (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (+ (* (* (* 4 (sqrt 2)) (- (* v v))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* v v) 3)))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))))))) (* (sqrt (+ (* (* v v) (* (* v 9) (* v 4))) (+ 4 (* v (* v 12))))) (sqrt (* (sqrt (+ (* (* v v) 3) (+ (* (* v 9) (pow v 3)) 1))) 16))))) * * * * [misc]progress: [ 92 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (123 enodes) * * [misc]simplify: iters left: 4 (411 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (* 9 (* v v)) (* v v)))) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (sqrt 2))))) (sqrt (- (* (* (sqrt (+ 1 (* v (* 3 v)))) 4) (* (sqrt 2) (sqrt (- 1 (* v (* 3 v)))))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (* (* v v) (sqrt 2)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (* 9 (* v v)) (* v v)))) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (sqrt 2))))) (sqrt (- (* (* (sqrt (+ 1 (* v (* 3 v)))) 4) (* (sqrt 2) (sqrt (- 1 (* v (* 3 v)))))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (172 enodes) * * [misc]simplify: iters left: 2 (347 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* 9 (* v v)) (* 4 (* v v))) (+ (* (* v 12) v) 4))) (sqrt (* 16 (sqrt (+ 1 (* 3 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (* 9 (* v v)) (* v v)))) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (sqrt 2))))) (sqrt (- (* (* (sqrt (+ 1 (* v (* 3 v)))) 4) (* (sqrt 2) (sqrt (- 1 (* v (* 3 v)))))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (+ (* (* 9 (* v v)) (* 4 (* v v))) (+ (* (* v 12) v) 4))) (sqrt (* 16 (sqrt (+ 1 (* 3 (* v v))))))))) * * * * [misc]progress: [ 93 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (38 enodes) * * [misc]simplify: iters left: 5 (103 enodes) * * [misc]simplify: iters left: 4 (336 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* v v) 3)))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (+ (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (/ (sqrt 2) 4) 4) (- (* v v))) (sqrt (- 1 (pow (* (* v v) 3) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* v v) 3)))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (+ (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (/ (sqrt 2) 4) 4) (- (* v v))) (sqrt (- 1 (pow (* (* v v) 3) 3)))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (174 enodes) * * [misc]simplify: iters left: 2 (335 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (pow v 3) (* 9 v)) (* (* 3 v) v)) 1)) 4)) (sqrt (+ (+ (* 12 (* v v)) 4) (* (* v 4) (* (* v v) (* 9 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* v v) 3)))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (+ (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (/ (sqrt 2) 4) 4) (- (* v v))) (sqrt (- 1 (pow (* (* v v) 3) 3)))))))) (* (sqrt (* (sqrt (+ (+ (* (pow v 3) (* 9 v)) (* (* 3 v) v)) 1)) 4)) (sqrt (+ (+ (* 12 (* v v)) 4) (* (* v 4) (* (* v v) (* 9 v)))))))) * * * * [misc]progress: [ 94 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (401 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (+ (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4)) (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (- (* (* (sqrt 2) (sqrt (+ (* (* v -3) v) 1))) (sqrt (+ 1 (* (* v v) 3)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (+ (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4)) (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (- (* (* (sqrt 2) (sqrt (+ (* (* v -3) v) 1))) (sqrt (+ 1 (* (* v v) 3)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (173 enodes) * * [misc]simplify: iters left: 2 (358 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* v v) 12) (* (* v v) 3)) (+ 4 (* (* v v) 12)))) (sqrt (* 4 (sqrt (+ 1 (* (* v v) 3)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (+ (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4)) (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (- (* (* (sqrt 2) (sqrt (+ (* (* v -3) v) 1))) (sqrt (+ 1 (* (* v v) 3)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) (* (sqrt (+ (* (* (* v v) 12) (* (* v v) 3)) (+ 4 (* (* v v) 12)))) (sqrt (* 4 (sqrt (+ 1 (* (* v v) 3)))))))) * * * * [misc]progress: [ 95 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (109 enodes) * * [misc]simplify: iters left: 4 (370 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (+ (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (sqrt 2)) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v (- v)) (/ (sqrt 2) 4)) 4))))) (sqrt (* (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2)) (+ (* (* 4 v) (- v)) 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (+ (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (sqrt 2)) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v (- v)) (/ (sqrt 2) 4)) 4))))) (sqrt (* (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2)) (+ (* (* 4 v) (- v)) 4)))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 4))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (178 enodes) * * [misc]simplify: iters left: 2 (354 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ (* v (* 12 v)) 4) (* (* (* v 4) (* v 9)) (* v v)))) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (+ (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (sqrt 2)) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v (- v)) (/ (sqrt 2) 4)) 4))))) (sqrt (* (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2)) (+ (* (* 4 v) (- v)) 4)))) (* (sqrt (+ (+ (* v (* 12 v)) 4) (* (* (* v 4) (* v 9)) (* v v)))) 4))) * * * * [misc]progress: [ 96 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3)))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (441 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* v v) (/ (sqrt 2) 4))) (* 4 (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v v) 3)))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) 3)))) 3)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* v v) (/ (sqrt 2) 4))) (* 4 (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v v) 3)))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) 3)))) 3)))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * * [misc]simplify: iters left: 6 (31 enodes) * * [misc]simplify: iters left: 5 (90 enodes) * * [misc]simplify: iters left: 4 (290 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (- (* (* (* (/ (sqrt 2) 4) (* (- v) v)) (sqrt (+ (* (* -3 v) v) 1))) (* (* (/ (sqrt 2) 4) (* (- v) v)) (sqrt (+ (* (* -3 v) v) 1)))) (* (* (sqrt (+ (* (* -3 v) v) 1)) (- (* (/ (sqrt 2) 4) (* (- v) v)) (/ (sqrt 2) 4))) (* (/ (sqrt 2) 4) (sqrt (+ (* (* -3 v) v) 1))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* v v) (/ (sqrt 2) 4))) (* 4 (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v v) 3)))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) 3)))) 3)))) (* (sqrt (* 4 (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (- (* (* (* (/ (sqrt 2) 4) (* (- v) v)) (sqrt (+ (* (* -3 v) v) 1))) (* (* (/ (sqrt 2) 4) (* (- v) v)) (sqrt (+ (* (* -3 v) v) 1)))) (* (* (sqrt (+ (* (* -3 v) v) 1)) (- (* (/ (sqrt 2) 4) (* (- v) v)) (/ (sqrt 2) 4))) (* (/ (sqrt 2) 4) (sqrt (+ (* (* -3 v) v) 1))))))))) * * * * [misc]progress: [ 97 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (439 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt 2) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* v v))))) (sqrt (* (* (sqrt (- 1 (* 3 (* v v)))) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))) (* (sqrt (- 1 (* 3 (* v v)))) (+ (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt 2) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* v v))))) (sqrt (* (* (sqrt (- 1 (* 3 (* v v)))) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))) (* (sqrt (- 1 (* 3 (* v v)))) (+ (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (71 enodes) * * [misc]simplify: iters left: 4 (192 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v)))))) (sqrt (* (* (+ (* v v) 1) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt 2) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* v v))))) (sqrt (* (* (sqrt (- 1 (* 3 (* v v)))) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))) (* (sqrt (- 1 (* 3 (* v v)))) (+ (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4))))))) (* (sqrt (* 4 (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v)))))) (sqrt (* (* (+ (* v v) 1) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v)))))))) * * * * [misc]progress: [ 98 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (111 enodes) * * [misc]simplify: iters left: 4 (370 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (/ (sqrt 2) 4)))))) (sqrt (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (* (sqrt 2) (- (* v v))) (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (/ (sqrt 2) 4)))))) (sqrt (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (* (sqrt 2) (- (* v v))) (sqrt 2)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (162 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* 3 (* v v)) (+ (* (pow v 3) (* v 9)) 1))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (+ (* (* 4 v) (* (* v v) (* v 9))) (+ (* (* v v) 12) 4)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (/ (sqrt 2) 4)))))) (sqrt (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (* (sqrt 2) (- (* v v))) (sqrt 2)))))) (* (sqrt (* (sqrt (+ (* 3 (* v v)) (+ (* (pow v 3) (* v 9)) 1))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (+ (* (* 4 v) (* (* v v) (* v 9))) (+ (* (* v v) 12) 4)) 4))))) * * * * [misc]progress: [ 99 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (367 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ 1 (* v (* 3 v)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3))))) (* (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) 4) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt 2) (* v v)))))) (sqrt (- (* (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) 4) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ 1 (* v (* 3 v)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3))))) (* (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) 4) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt 2) (* v v)))))) (sqrt (- (* (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) 4) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (104 enodes) * * [misc]simplify: iters left: 3 (163 enodes) * * [misc]simplify: iters left: 2 (252 enodes) * * [misc]simplify: iters left: 1 (297 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* v v) 3) (+ (* 9 (pow v 4)) 1))) (* 4 (sqrt (+ 1 (* (* v v) 3)))))) (sqrt (* (* 16 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (+ (* (* v v) 3) (+ (* 9 (pow v 4)) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ 1 (* v (* 3 v)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3))))) (* (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) 4) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt 2) (* v v)))))) (sqrt (- (* (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) 4) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))))))) (* (sqrt (* (sqrt (+ (* (* v v) 3) (+ (* 9 (pow v 4)) 1))) (* 4 (sqrt (+ 1 (* (* v v) 3)))))) (sqrt (* (* 16 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (+ (* (* v v) 3) (+ (* 9 (pow v 4)) 1)))))))) * * * * [misc]progress: [ 100 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (113 enodes) * * [misc]simplify: iters left: 4 (400 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* 4 (/ (sqrt 2) 4))) (* (* v v) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) 4) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ (* (sqrt 2) (* v v)) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* 4 (/ (sqrt 2) 4))) (* (* v v) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) 4) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ (* (sqrt 2) (* v v)) 4)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (96 enodes) * * [misc]simplify: iters left: 3 (178 enodes) * * [misc]simplify: iters left: 2 (342 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* (* v 9) (pow v 3)) 1))) (* 4 (sqrt (+ 1 (* v (* 3 v))))))) (sqrt (+ (+ (* (* 12 v) v) 4) (* (* v 9) (* (* v v) (* v 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* 4 (/ (sqrt 2) 4))) (* (* v v) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) 4) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ (* (sqrt 2) (* v v)) 4)))))) (* (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* (* v 9) (pow v 3)) 1))) (* 4 (sqrt (+ 1 (* v (* 3 v))))))) (sqrt (+ (+ (* (* 12 v) v) 4) (* (* v 9) (* (* v v) (* v 4)))))))) * * * * [misc]progress: [ 101 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (90 enodes) * * [misc]simplify: iters left: 4 (273 enodes) * [exit]simplify: Simplified to (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (* (sqrt 2) (* v v)) 4)) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (* (sqrt 2) (* v v)) 4)) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (148 enodes) * * [misc]simplify: iters left: 2 (253 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* v (* 3 v)) (+ (* (pow v 4) 9) 1))) (* 4 (sqrt (+ 1 (* v (* 3 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (* (sqrt 2) (* v v)) 4)) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4))) (* (sqrt (+ (* v (* 3 v)) (+ (* (pow v 4) 9) 1))) (* 4 (sqrt (+ 1 (* v (* 3 v)))))))) * * * * [misc]progress: [ 102 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (384 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* 4 (/ (sqrt 2) 4))) (* (* v v) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (- 1 (* (* v v) 3))) (* (* (* (sqrt 2) (- v)) v) 4)) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* 4 (/ (sqrt 2) 4))) (* (* v v) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (- 1 (* (* v v) 3))) (* (* (* (sqrt 2) (- v)) v) 4)) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (98 enodes) * * [misc]simplify: iters left: 3 (179 enodes) * * [misc]simplify: iters left: 2 (281 enodes) * * [misc]simplify: iters left: 1 (300 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* (pow v 4) 9) 1))) (* 4 (sqrt (+ 1 (* v (* 3 v))))))) (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* (pow v 4) 9) 1))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* 4 (/ (sqrt 2) 4))) (* (* v v) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (- 1 (* (* v v) 3))) (* (* (* (sqrt 2) (- v)) v) 4)) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))))))) (* (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* (pow v 4) 9) 1))) (* 4 (sqrt (+ 1 (* v (* 3 v))))))) (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* (pow v 4) 9) 1))) 16))))) * * * * [misc]progress: [ 103 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (119 enodes) * * [misc]simplify: iters left: 4 (405 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* v v) (/ (sqrt 2) 4)))))) (sqrt (- (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (+ 1 (* (* 3 v) v))) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* v v) (/ (sqrt 2) 4)))))) (sqrt (- (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (+ 1 (* (* 3 v) v))) 4))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (106 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (262 enodes) * * [misc]simplify: iters left: 1 (320 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* (sqrt (+ 1 (* (* 3 v) v))) 16)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* v v) (/ (sqrt 2) 4)))))) (sqrt (- (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (+ 1 (* (* 3 v) v))) 4))))) (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* (sqrt (+ 1 (* (* 3 v) v))) 16)))))) * * * * [misc]progress: [ 104 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (117 enodes) * * [misc]simplify: iters left: 4 (387 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* 4 (/ (sqrt 2) 4))) (* (* v v) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (* (sqrt 2) (- (* v v))) (sqrt 2))) (* (sqrt (+ 1 (* (* v v) 3))) 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* 4 (/ (sqrt 2) 4))) (* (* v v) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (* (sqrt 2) (- (* v v))) (sqrt 2))) (* (sqrt (+ 1 (* (* v v) 3))) 4)))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (101 enodes) * * [misc]simplify: iters left: 3 (154 enodes) * * [misc]simplify: iters left: 2 (261 enodes) * * [misc]simplify: iters left: 1 (346 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (pow v 4) 9))) (* 4 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (+ (* 48 (* v v)) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* 4 (/ (sqrt 2) 4))) (* (* v v) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (* (sqrt 2) (- (* v v))) (sqrt 2))) (* (sqrt (+ 1 (* (* v v) 3))) 4)))) (* (sqrt (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (pow v 4) 9))) (* 4 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (+ (* 48 (* v v)) 16))))) * * * * [misc]progress: [ 105 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (422 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v)))))) (* (* (sqrt (+ 1 (* v (* 3 v)))) 4) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (/ (* (sqrt 2) (* v v)) 4))))) (sqrt (- (* (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) 4) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (/ (* (sqrt 2) (* v v)) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v)))))) (* (* (sqrt (+ 1 (* v (* 3 v)))) 4) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (/ (* (sqrt 2) (* v v)) 4))))) (sqrt (- (* (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) 4) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (/ (* (sqrt 2) (* v v)) 4)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (136 enodes) * * [misc]simplify: iters left: 2 (225 enodes) * * [misc]simplify: iters left: 1 (257 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v)))))) (* (* (sqrt (+ 1 (* v (* 3 v)))) 4) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (/ (* (sqrt 2) (* v v)) 4))))) (sqrt (- (* (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) 4) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (/ (* (sqrt 2) (* v v)) 4)))))) (* (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v))))))) * * * * [misc]progress: [ 106 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (110 enodes) * * [misc]simplify: iters left: 4 (354 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) 4) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (/ (sqrt 2) 4) (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) 4) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (/ (sqrt 2) 4) (* v v))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (292 enodes) * * [misc]simplify: iters left: 1 (424 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (+ (* (* v 12) v) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) 4) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (/ (sqrt 2) 4) (* v v))))))) (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (+ (* (* v 12) v) 4))))) * * * * [misc]progress: [ 107 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (123 enodes) * * [misc]simplify: iters left: 4 (413 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (/ (sqrt 2) 4)))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (/ (sqrt 2) 4)))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (174 enodes) * * [misc]simplify: iters left: 2 (296 enodes) * * [misc]simplify: iters left: 1 (345 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (* 16 (sqrt (+ 1 (* (* 3 v) v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (/ (sqrt 2) 4)))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (* 16 (sqrt (+ 1 (* (* 3 v) v)))))))) * * * * [misc]progress: [ 108 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (382 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3))))))) (sqrt (- (* (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) 4) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (/ (* (sqrt 2) (* v v)) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3))))))) (sqrt (- (* (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) 4) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (/ (* (sqrt 2) (* v v)) 4)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (95 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * * [misc]simplify: iters left: 2 (269 enodes) * * [misc]simplify: iters left: 1 (456 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 3 (* v v)) (+ (* 9 (pow v 4)) 1))))) (sqrt (+ (+ (* (* v 36) (pow v 3)) 4) (* 12 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3))))))) (sqrt (- (* (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) 4) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (/ (* (sqrt 2) (* v v)) 4)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 3 (* v v)) (+ (* 9 (pow v 4)) 1))))) (sqrt (+ (+ (* (* v 36) (pow v 3)) 4) (* 12 (* v v))))))) * * * * [misc]progress: [ 109 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (374 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (/ (sqrt 2) 4) (* 4 (sqrt (+ 1 (* (* v v) 3))))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) 4) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* v v) (/ (sqrt 2) 4))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (* 4 (sqrt (+ 1 (* (* v v) 3))))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) 4) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* v v) (/ (sqrt 2) 4))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (238 enodes) * * [misc]simplify: iters left: 1 (282 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (* 4 (sqrt (+ 1 (* (* v v) 3))))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) 4) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* v v) (/ (sqrt 2) 4))))))) (* (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v))))))) * * * * [misc]progress: [ 110 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (113 enodes) * * [misc]simplify: iters left: 4 (369 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* v (* 3 v)) 3))))))) (sqrt (- (* (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* 4 (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v)))))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (/ (* (sqrt 2) (* v v)) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* v (* 3 v)) 3))))))) (sqrt (- (* (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* 4 (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v)))))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (/ (* (sqrt 2) (* v v)) 4)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (151 enodes) * * [misc]simplify: iters left: 2 (248 enodes) * * [misc]simplify: iters left: 1 (301 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 3 (* v v)) (+ (* 9 (pow v 4)) 1))))) (sqrt (+ (* 3 (* v v)) (+ (* 9 (pow v 4)) 1)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* v (* 3 v)) 3))))))) (sqrt (- (* (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* 4 (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v)))))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (/ (* (sqrt 2) (* v v)) 4)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 3 (* v v)) (+ (* 9 (pow v 4)) 1))))) (sqrt (+ (* 3 (* v v)) (+ (* 9 (pow v 4)) 1)))))) * * * * [misc]progress: [ 111 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (106 enodes) * * [misc]simplify: iters left: 4 (319 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4)))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4)))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (149 enodes) * * [misc]simplify: iters left: 2 (252 enodes) * * [misc]simplify: iters left: 1 (326 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* 9 (pow v 4)) 1))) (* 4 (sqrt (+ 1 (* v (* 3 v))))))) (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ (* v (* 3 v)) (+ (* 9 (pow v 4)) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4)))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* 9 (pow v 4)) 1))) (* 4 (sqrt (+ 1 (* v (* 3 v))))))) (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ (* v (* 3 v)) (+ (* 9 (pow v 4)) 1)))))))) * * * * [misc]progress: [ 112 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (382 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (* 4 (sqrt 2)) 4)) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* 3 (* v v)))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (* 4 (sqrt 2)) 4)) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* 3 (* v v)))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (149 enodes) * * [misc]simplify: iters left: 2 (250 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ (* v (* 3 v)) (+ (* (pow v 4) 9) 1))))) (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* (pow v 4) 9) 1))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (* 4 (sqrt 2)) 4)) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* 3 (* v v)))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ (* v (* 3 v)) (+ (* (pow v 4) 9) 1))))) (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* (pow v 4) 9) 1))) 4))))) * * * * [misc]progress: [ 113 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (112 enodes) * * [misc]simplify: iters left: 4 (360 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))))))) (sqrt (- (* (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (sqrt (+ 1 (* (* 3 v) v))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))))))) (sqrt (- (* (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (sqrt (+ 1 (* (* 3 v) v))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (166 enodes) * * [misc]simplify: iters left: 2 (274 enodes) * * [misc]simplify: iters left: 1 (310 enodes) * [exit]simplify: Simplified to (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))))))) (sqrt (- (* (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (sqrt (+ 1 (* (* 3 v) v))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))))))) (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1)))))) * * * * [misc]progress: [ 114 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (385 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4) (/ (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ 4 (* (* v v) (sqrt 2))))))) (sqrt (* (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2)))) (sqrt (+ 1 (* 3 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4) (/ (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ 4 (* (* v v) (sqrt 2))))))) (sqrt (* (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2)))) (sqrt (+ 1 (* 3 (* v v))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (259 enodes) * * [misc]simplify: iters left: 1 (362 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* 3 (* v v)) (+ (* (pow v 4) 9) 1))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (+ (* 12 (* v v)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4) (/ (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ 4 (* (* v v) (sqrt 2))))))) (sqrt (* (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2)))) (sqrt (+ 1 (* 3 (* v v))))))) (* (sqrt (* (sqrt (+ (* 3 (* v v)) (+ (* (pow v 4) 9) 1))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (+ (* 12 (* v v)) 4))))) * * * * [misc]progress: [ 115 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (392 enodes) * [exit]simplify: Simplified to (* (sqrt (- (/ (* (sqrt 2) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (/ 4 (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))))) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ 1 (* v (* 3 v)))))))) (sqrt (- (* (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) 4) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (/ (* (sqrt 2) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (/ 4 (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))))) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ 1 (* v (* 3 v)))))))) (sqrt (- (* (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) 4) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (149 enodes) * * [misc]simplify: iters left: 2 (252 enodes) * * [misc]simplify: iters left: 1 (326 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* 9 (pow v 4)) 1))) (* 4 (sqrt (+ 1 (* v (* 3 v))))))) (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ (* v (* 3 v)) (+ (* 9 (pow v 4)) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (/ (* (sqrt 2) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (/ 4 (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))))) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ 1 (* v (* 3 v)))))))) (sqrt (- (* (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) 4) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))))))) (* (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* 9 (pow v 4)) 1))) (* 4 (sqrt (+ 1 (* v (* 3 v))))))) (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ (* v (* 3 v)) (+ (* 9 (pow v 4)) 1)))))))) * * * * [misc]progress: [ 116 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (104 enodes) * * [misc]simplify: iters left: 4 (314 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) 4)))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* 3 v) v)))) (* (* v (- v)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) 4)))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* 3 v) v)))) (* (* v (- v)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (179 enodes) * * [misc]simplify: iters left: 2 (309 enodes) * * [misc]simplify: iters left: 1 (402 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* (* v v) 3))) (sqrt (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (+ (* (* v v) 3) (+ (* 9 (pow v 4)) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) 4)))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* 3 v) v)))) (* (* v (- v)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))))) (* (sqrt (+ 1 (* (* v v) 3))) (sqrt (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (+ (* (* v v) 3) (+ (* 9 (pow v 4)) 1)))))))) * * * * [misc]progress: [ 117 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (380 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (* 4 (sqrt 2)) 4)) (* (* (sqrt 2) (sqrt (- 1 (* (* v v) 3)))) (* (sqrt (+ 1 (* (* v v) 3))) (* v v))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) 4) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (* 4 (sqrt 2)) 4)) (* (* (sqrt 2) (sqrt (- 1 (* (* v v) 3)))) (* (sqrt (+ 1 (* (* v v) 3))) (* v v))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) 4) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (148 enodes) * * [misc]simplify: iters left: 2 (249 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* 3 (* v v)) (+ (* (pow v 4) 9) 1))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (* 4 (sqrt 2)) 4)) (* (* (sqrt 2) (sqrt (- 1 (* (* v v) 3)))) (* (sqrt (+ 1 (* (* v v) 3))) (* v v))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) 4) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))))) (* (sqrt (* (sqrt (+ (* 3 (* v v)) (+ (* (pow v 4) 9) 1))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * * * * [misc]progress: [ 118 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (385 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v)))))) (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (* (sqrt 2) (* v v)) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (* (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v)))))) (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (* (sqrt 2) (* v v)) 4)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (95 enodes) * * [misc]simplify: iters left: 3 (148 enodes) * * [misc]simplify: iters left: 2 (237 enodes) * * [misc]simplify: iters left: 1 (290 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* 3 (* v v)) (+ (* (pow v 4) 9) 1))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 16 (sqrt (+ (* 3 (* v v)) (+ (* (pow v 4) 9) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (* (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v)))))) (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (* (sqrt 2) (* v v)) 4)))))) (* (sqrt (* (sqrt (+ (* 3 (* v v)) (+ (* (pow v 4) 9) 1))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 16 (sqrt (+ (* 3 (* v v)) (+ (* (pow v 4) 9) 1)))))))) * * * * [misc]progress: [ 119 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (122 enodes) * * [misc]simplify: iters left: 4 (379 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) 4) (/ (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ 4 (* (* v v) (sqrt 2))))))) (sqrt (- (* (* (sqrt (- 1 (* (* v v) 3))) (sqrt 2)) (* (sqrt (+ 1 (* (* v v) 3))) 4)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) 4) (/ (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ 4 (* (* v v) (sqrt 2))))))) (sqrt (- (* (* (sqrt (- 1 (* (* v v) 3))) (sqrt 2)) (* (sqrt (+ 1 (* (* v v) 3))) 4)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (237 enodes) * * [misc]simplify: iters left: 1 (281 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) 4) (/ (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ 4 (* (* v v) (sqrt 2))))))) (sqrt (- (* (* (sqrt (- 1 (* (* v v) 3))) (sqrt 2)) (* (sqrt (+ 1 (* (* v v) 3))) 4)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) 16))))) * * * * [misc]progress: [ 120 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (400 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (- 1 (* (* v v) 3))) (sqrt 2)) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (/ (sqrt 2) 4) 4)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* v v) 3))) (sqrt 2)) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (/ (sqrt 2) 4) 4)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (229 enodes) * * [misc]simplify: iters left: 1 (262 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* 9 (pow v 4)))))) (sqrt (* (sqrt (+ (+ 1 (* 3 (* v v))) (* 9 (pow v 4)))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* v v) 3))) (sqrt 2)) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (/ (sqrt 2) 4) 4)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* 9 (pow v 4)))))) (sqrt (* (sqrt (+ (+ 1 (* 3 (* v v))) (* 9 (pow v 4)))) 4))))) * * * * [misc]progress: [ 121 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (111 enodes) * * [misc]simplify: iters left: 4 (334 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (/ (sqrt 2) 4)) 4)) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v)))))))) (sqrt (- (* (sqrt (+ 1 (* 3 (* v v)))) (* (sqrt 2) (sqrt (- 1 (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (/ (sqrt 2) 4)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (/ (sqrt 2) 4)) 4)) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v)))))))) (sqrt (- (* (sqrt (+ 1 (* 3 (* v v)))) (* (sqrt 2) (sqrt (- 1 (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (/ (sqrt 2) 4)) 4))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (148 enodes) * * [misc]simplify: iters left: 2 (249 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* 3 (* v v)) (+ (* (pow v 4) 9) 1))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (/ (sqrt 2) 4)) 4)) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v)))))))) (sqrt (- (* (sqrt (+ 1 (* 3 (* v v)))) (* (sqrt 2) (sqrt (- 1 (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (/ (sqrt 2) 4)) 4))))) (* (sqrt (* (sqrt (+ (* 3 (* v v)) (+ (* (pow v 4) 9) 1))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * * * * [misc]progress: [ 122 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (117 enodes) * * [misc]simplify: iters left: 4 (367 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt 2) (sqrt (- 1 (* (* v v) 3)))) (+ (* (* 4 v) (- v)) 4))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) 4) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (* (sqrt 2) (* v v)) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt 2) (sqrt (- 1 (* (* v v) 3)))) (+ (* (* 4 v) (- v)) 4))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) 4) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (* (sqrt 2) (* v v)) 4)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (176 enodes) * * [misc]simplify: iters left: 2 (305 enodes) * * [misc]simplify: iters left: 1 (353 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v)))))) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt 2) (sqrt (- 1 (* (* v v) 3)))) (+ (* (* 4 v) (- v)) 4))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) 4) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (* (sqrt 2) (* v v)) 4)))))) (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v)))))) 4))) * * * * [misc]progress: [ 123 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3)))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (124 enodes) * * [misc]simplify: iters left: 4 (440 enodes) * [exit]simplify: Simplified to (* (sqrt (* (pow (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 v) v)))) 3) (+ (* (* (* v v) (* v v)) (- (* v v))) 1))) (sqrt (- (* (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) 4) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (pow (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 v) v)))) 3) (+ (* (* (* v v) (* v v)) (- (* v v))) 1))) (sqrt (- (* (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) 4) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * * [misc]simplify: iters left: 6 (33 enodes) * * [misc]simplify: iters left: 5 (93 enodes) * * [misc]simplify: iters left: 4 (293 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* 4 (sqrt (+ 1 (* (* v v) 3)))))) (sqrt (+ (* (* (sqrt (+ (* (* -3 v) v) 1)) (- (* (/ (sqrt 2) 4) (* (- v) v)) (/ (sqrt 2) 4))) (* (* (/ (sqrt 2) 4) (* (- v) v)) (sqrt (+ (* (* -3 v) v) 1)))) (* (* (sqrt (+ (* (* -3 v) v) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* -3 v) v) 1)) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (pow (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 v) v)))) 3) (+ (* (* (* v v) (* v v)) (- (* v v))) 1))) (sqrt (- (* (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) 4) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))))))) (* (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* 4 (sqrt (+ 1 (* (* v v) 3)))))) (sqrt (+ (* (* (sqrt (+ (* (* -3 v) v) 1)) (- (* (/ (sqrt 2) 4) (* (- v) v)) (/ (sqrt 2) 4))) (* (* (/ (sqrt 2) 4) (* (- v) v)) (sqrt (+ (* (* -3 v) v) 1)))) (* (* (sqrt (+ (* (* -3 v) v) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* -3 v) v) 1)) (/ (sqrt 2) 4)))))))) * * * * [misc]progress: [ 124 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (126 enodes) * * [misc]simplify: iters left: 4 (440 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (- 1 (* (* v v) 3))) (+ (* (* (- v) v) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (sqrt (- 1 (* (* v v) 3))) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* (* v v) 3))) (+ (* (* (- v) v) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (sqrt (- 1 (* (* v v) 3))) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) 4))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (29 enodes) * * [misc]simplify: iters left: 5 (74 enodes) * * [misc]simplify: iters left: 4 (195 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))))) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* -3 v) v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* (* v v) 3))) (+ (* (* (- v) v) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (sqrt (- 1 (* (* v v) 3))) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) 4))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))))) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* -3 v) v)))))))) * * * * [misc]progress: [ 125 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (36 enodes) * * [misc]simplify: iters left: 5 (104 enodes) * * [misc]simplify: iters left: 4 (350 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* 3 (* v v)))) (* (- (* (sqrt 2) (* v v))) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* 3 (* v v)))) (* (- (* (sqrt 2) (* v v))) 4)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (96 enodes) * * [misc]simplify: iters left: 3 (156 enodes) * * [misc]simplify: iters left: 2 (277 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* 9 v) (pow v 3)) (* 3 (* v v))) 1)) 16)) (sqrt (* (+ (* (* (* v v) (* 9 v)) (* v 4)) (+ 4 (* (* v v) 12))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* 3 (* v v)))) (* (- (* (sqrt 2) (* v v))) 4)))))) (* (sqrt (* (sqrt (+ (+ (* (* 9 v) (pow v 3)) (* 3 (* v v))) 1)) 16)) (sqrt (* (+ (* (* (* v v) (* 9 v)) (* v 4)) (+ 4 (* (* v v) 12))) 4))))) * * * * [misc]progress: [ 126 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (376 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* v (* 3 v)))) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v (* 3 v)) (* v (* 3 v))))) (* 4 (sqrt 2))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* v v))))) (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt (- 1 (* v (* 3 v)))) (* (* (* (sqrt 2) (- v)) v) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* v (* 3 v)))) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v (* 3 v)) (* v (* 3 v))))) (* 4 (sqrt 2))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* v v))))) (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt (- 1 (* v (* 3 v)))) (* (* (* (sqrt 2) (- v)) v) 4)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (267 enodes) * * [misc]simplify: iters left: 1 (322 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))))) (sqrt (* (* 16 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* v (* 3 v)))) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v (* 3 v)) (* v (* 3 v))))) (* 4 (sqrt 2))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* v v))))) (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt (- 1 (* v (* 3 v)))) (* (* (* (sqrt 2) (- v)) v) 4)))))) (* (sqrt (* 16 (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))))) (sqrt (* (* 16 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1)))))))) * * * * [misc]progress: [ 127 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (38 enodes) * * [misc]simplify: iters left: 5 (108 enodes) * * [misc]simplify: iters left: 4 (391 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (sqrt 2) 4)) (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* 9 (* v v)) (* v v)))) (* (sqrt (- 1 (* (* 3 v) v))) (* (* (* (sqrt 2) v) (- v)) 4))))) (sqrt (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* 9 (* v v)) (* v v)))) (+ (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (sqrt 2)) (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (sqrt 2) 4)) (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* 9 (* v v)) (* v v)))) (* (sqrt (- 1 (* (* 3 v) v))) (* (* (* (sqrt 2) v) (- v)) 4))))) (sqrt (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* 9 (* v v)) (* v v)))) (+ (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (sqrt 2)) (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (181 enodes) * * [misc]simplify: iters left: 2 (353 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ (* v (* 3 v)) (+ (* (pow v 3) (* 9 v)) 1))))) (sqrt (+ (* (* 4 (* v v)) (* 9 (* v v))) (+ (* v (* v 12)) 4)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (sqrt 2) 4)) (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* 9 (* v v)) (* v v)))) (* (sqrt (- 1 (* (* 3 v) v))) (* (* (* (sqrt 2) v) (- v)) 4))))) (sqrt (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* 9 (* v v)) (* v v)))) (+ (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (sqrt 2)) (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))))))) (* (sqrt (* 16 (sqrt (+ (* v (* 3 v)) (+ (* (pow v 3) (* 9 v)) 1))))) (sqrt (+ (* (* 4 (* v v)) (* 9 (* v v))) (+ (* v (* v 12)) 4)))))) * * * * [misc]progress: [ 128 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (383 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 9 (* v v)) (* v v)))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* v v))))) (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 9 (* v v)) (* v v)))) (* (* 4 (* (- (* v v)) (sqrt 2))) (sqrt (- 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 9 (* v v)) (* v v)))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* v v))))) (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 9 (* v v)) (* v v)))) (* (* 4 (* (- (* v v)) (sqrt 2))) (sqrt (- 1 (* 3 (* v v))))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (95 enodes) * * [misc]simplify: iters left: 3 (154 enodes) * * [misc]simplify: iters left: 2 (255 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (pow v 4) 9))) 16)) (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (pow v 4) 9))) (* 4 (sqrt (+ 1 (* (* v v) 3))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 9 (* v v)) (* v v)))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* v v))))) (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 9 (* v v)) (* v v)))) (* (* 4 (* (- (* v v)) (sqrt 2))) (sqrt (- 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (pow v 4) 9))) 16)) (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (pow v 4) 9))) (* 4 (sqrt (+ 1 (* (* v v) 3))))))))) * * * * [misc]progress: [ 129 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (31 enodes) * * [misc]simplify: iters left: 5 (84 enodes) * * [misc]simplify: iters left: 4 (266 enodes) * [exit]simplify: Simplified to (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* 4 (* v (* (- v) (sqrt 2)))) (sqrt (- 1 (* 3 (* v v))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* 4 (* v (* (- v) (sqrt 2)))) (sqrt (- 1 (* 3 (* v v))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (225 enodes) * * [misc]simplify: iters left: 1 (269 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (pow v 4) 9))) 16) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* 4 (* v (* (- v) (sqrt 2)))) (sqrt (- 1 (* 3 (* v v))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (pow v 4) 9))) 16))) * * * * [misc]progress: [ 130 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (385 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (sqrt 2) 4)) (* (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (- 1 (* (* v v) 3)))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) 4) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2))) (* (* (* (sqrt (+ 1 (* (* v v) 3))) (* (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (sqrt 2) 4)) (* (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (- 1 (* (* v v) 3)))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) 4) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2))) (* (* (* (sqrt (+ 1 (* (* v v) 3))) (* (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* v v))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (104 enodes) * * [misc]simplify: iters left: 3 (172 enodes) * * [misc]simplify: iters left: 2 (267 enodes) * * [misc]simplify: iters left: 1 (323 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) 16)) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* 16 (sqrt (+ 1 (* (* 3 v) v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (sqrt 2) 4)) (* (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (- 1 (* (* v v) 3)))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) 4) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2))) (* (* (* (sqrt (+ 1 (* (* v v) 3))) (* (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* v v))))) (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) 16)) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* 16 (sqrt (+ 1 (* (* 3 v) v))))))))) * * * * [misc]progress: [ 131 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (381 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* 3 (* v v)))) (* (* (- (* v v)) (sqrt 2)) 4))))) (sqrt (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (+ (sqrt 2) (* (- (* v v)) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* 3 (* v v)))) (* (* (- (* v v)) (sqrt 2)) 4))))) (sqrt (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (+ (sqrt 2) (* (- (* v v)) (sqrt 2))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (96 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (267 enodes) * * [misc]simplify: iters left: 1 (371 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (pow v 4) 9))) 16)) (sqrt (+ 16 (* (* v v) 48)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* 3 (* v v)))) (* (* (- (* v v)) (sqrt 2)) 4))))) (sqrt (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (+ (sqrt 2) (* (- (* v v)) (sqrt 2))))))) (* (sqrt (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (pow v 4) 9))) 16)) (sqrt (+ 16 (* (* v v) 48)))))) * * * * [misc]progress: [ 132 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (123 enodes) * * [misc]simplify: iters left: 4 (413 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (- 1 (* (* v v) 3))) (* (* (sqrt 2) (- (* v v))) 4)) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (sqrt 2) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (sqrt (+ 1 (* (* v v) 3))) 4)) (* (/ (sqrt 2) 4) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (- 1 (* (* v v) 3))) (* (* (sqrt 2) (- (* v v))) 4)) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (sqrt 2) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (sqrt (+ 1 (* (* v v) 3))) 4)) (* (/ (sqrt 2) 4) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (243 enodes) * * [misc]simplify: iters left: 1 (300 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))) 16)) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (- 1 (* (* v v) 3))) (* (* (sqrt 2) (- (* v v))) 4)) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (sqrt 2) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (sqrt (+ 1 (* (* v v) 3))) 4)) (* (/ (sqrt 2) 4) (* v v)))))) (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))) 16)) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v))))))))) * * * * [misc]progress: [ 133 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (123 enodes) * * [misc]simplify: iters left: 4 (413 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (- 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (+ (* (sqrt 2) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (- 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (+ (* (sqrt 2) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (153 enodes) * * [misc]simplify: iters left: 2 (274 enodes) * * [misc]simplify: iters left: 1 (375 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ (* (* v v) 3) (+ (* (pow v 4) 9) 1))))) (sqrt (+ 4 (* (* v v) 12)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (- 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (+ (* (sqrt 2) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (* 16 (sqrt (+ (* (* v v) 3) (+ (* (pow v 4) 9) 1))))) (sqrt (+ 4 (* (* v v) 12)))))) * * * * [misc]progress: [ 134 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (112 enodes) * * [misc]simplify: iters left: 4 (347 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt 2))) (* (sqrt (- 1 (* 3 (* v v)))) (* v v))))) (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (- 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt 2))) (* (sqrt (- 1 (* 3 (* v v)))) (* v v))))) (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (- 1 (* 3 (* v v))))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (233 enodes) * * [misc]simplify: iters left: 1 (280 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) 16)) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt 2))) (* (sqrt (- 1 (* 3 (* v v)))) (* v v))))) (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (- 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) 16)) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) 16))))) * * * * [misc]progress: [ 135 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (111 enodes) * * [misc]simplify: iters left: 4 (369 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (* 4 (* (sqrt 2) (- (* v v)))) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))))) (sqrt (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (* 4 (* (sqrt 2) (- (* v v)))) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))))) (sqrt (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (255 enodes) * * [misc]simplify: iters left: 1 (414 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ (* (* v v) 3) (+ (* 9 (pow v 4)) 1))))) (sqrt (+ 4 (+ (* (* 36 v) (pow v 3)) (* v (* v 12)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (* 4 (* (sqrt 2) (- (* v v)))) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))))) (sqrt (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))))))) (* (sqrt (* 16 (sqrt (+ (* (* v v) 3) (+ (* 9 (pow v 4)) 1))))) (sqrt (+ 4 (+ (* (* 36 v) (pow v 3)) (* v (* v 12)))))))) * * * * [misc]progress: [ 136 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (122 enodes) * * [misc]simplify: iters left: 4 (383 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (sqrt 2) 4)) (* (* (sqrt (- 1 (* (* v v) 3))) (* (- (* (sqrt 2) (* v v))) 4)) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (sqrt (+ 1 (* (* v v) 3))) (* 4 (/ (sqrt 2) 4)))) (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (sqrt 2) 4)) (* (* (sqrt (- 1 (* (* v v) 3))) (* (- (* (sqrt 2) (* v v))) 4)) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (sqrt (+ 1 (* (* v v) 3))) (* 4 (/ (sqrt 2) 4)))) (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (149 enodes) * * [misc]simplify: iters left: 2 (241 enodes) * * [misc]simplify: iters left: 1 (293 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ (* (* v v) 3) (+ (* 9 (pow v 4)) 1))))) (sqrt (* (sqrt (+ (* (* v v) 3) (+ (* 9 (pow v 4)) 1))) (* 4 (sqrt (+ 1 (* (* v v) 3))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (sqrt 2) 4)) (* (* (sqrt (- 1 (* (* v v) 3))) (* (- (* (sqrt 2) (* v v))) 4)) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (sqrt (+ 1 (* (* v v) 3))) (* 4 (/ (sqrt 2) 4)))) (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))))) (* (sqrt (* 16 (sqrt (+ (* (* v v) 3) (+ (* 9 (pow v 4)) 1))))) (sqrt (* (sqrt (+ (* (* v v) 3) (+ (* 9 (pow v 4)) 1))) (* 4 (sqrt (+ 1 (* (* v v) 3))))))))) * * * * [misc]progress: [ 137 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (108 enodes) * * [misc]simplify: iters left: 4 (360 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* 3 (* v v)))) (* (- (* (sqrt 2) (* v v))) 4)) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v)))))))) (sqrt (- (/ (* (sqrt 2) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (/ 4 (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* 3 (* v v)))) (* (- (* (sqrt 2) (* v v))) 4)) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v)))))))) (sqrt (- (/ (* (sqrt 2) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (/ 4 (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (152 enodes) * * [misc]simplify: iters left: 2 (255 enodes) * * [misc]simplify: iters left: 1 (346 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ (+ (* (pow v 4) 9) (* 3 (* v v))) 1)))) (sqrt (+ (+ (* (pow v 4) 9) (* 3 (* v v))) 1))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* 3 (* v v)))) (* (- (* (sqrt 2) (* v v))) 4)) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v)))))))) (sqrt (- (/ (* (sqrt 2) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (/ 4 (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* v v)))))) (* (sqrt (* 16 (sqrt (+ (+ (* (pow v 4) 9) (* 3 (* v v))) 1)))) (sqrt (+ (+ (* (pow v 4) 9) (* 3 (* v v))) 1))))) * * * * [misc]progress: [ 138 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (381 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (sqrt 2) 4)) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (- 1 (* (* v v) 3))) (* (* (sqrt 2) (- (* v v))) 4))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (sqrt 2) 4)) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (- 1 (* (* v v) 3))) (* (* (sqrt 2) (- (* v v))) 4))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (247 enodes) * * [misc]simplify: iters left: 1 (313 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* 9 (pow v 4)))) 16)) (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* 9 (pow v 4)))) (sqrt (+ 1 (* v (* 3 v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (sqrt 2) 4)) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (- 1 (* (* v v) 3))) (* (* (sqrt 2) (- (* v v))) 4))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))))) (* (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* 9 (pow v 4)))) 16)) (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* 9 (pow v 4)))) (sqrt (+ 1 (* v (* 3 v))))))))) * * * * [misc]progress: [ 139 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (38 enodes) * * [misc]simplify: iters left: 5 (101 enodes) * * [misc]simplify: iters left: 4 (315 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* 3 (* v v)))) (* (* (sqrt 2) (- (* v v))) 4))))) (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (* 4 (sqrt 2)) 4)) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* 3 (* v v)))) (* (* (sqrt 2) (- (* v v))) 4))))) (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (* 4 (sqrt 2)) 4)) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (244 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* (pow v 4) 9) 1))) 16)) (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* (pow v 4) 9) 1))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* 3 (* v v)))) (* (* (sqrt 2) (- (* v v))) 4))))) (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (* 4 (sqrt 2)) 4)) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* (pow v 4) 9) 1))) 16)) (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* (pow v 4) 9) 1))) 4))))) * * * * [misc]progress: [ 140 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (386 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (+ (* (* v -3) v) 1)) (* (- (* (sqrt 2) (* v v))) 4)) (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ 1 (* v (* 3 v)))))))) (sqrt (- (* (* (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ 1 (* v (* 3 v))))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) 4)) (* (* (* (sqrt 2) (sqrt (+ 1 (* v (* 3 v))))) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (+ (* (* v -3) v) 1)) (* (- (* (sqrt 2) (* v v))) 4)) (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ 1 (* v (* 3 v)))))))) (sqrt (- (* (* (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ 1 (* v (* 3 v))))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) 4)) (* (* (* (sqrt 2) (sqrt (+ 1 (* v (* 3 v))))) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* v v))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (149 enodes) * * [misc]simplify: iters left: 2 (244 enodes) * * [misc]simplify: iters left: 1 (291 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (pow v 4) 9))) 16)) (sqrt (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ (+ 1 (* (* 3 v) v)) (* (pow v 4) 9)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (+ (* (* v -3) v) 1)) (* (- (* (sqrt 2) (* v v))) 4)) (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ 1 (* v (* 3 v)))))))) (sqrt (- (* (* (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ 1 (* v (* 3 v))))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) 4)) (* (* (* (sqrt 2) (sqrt (+ 1 (* v (* 3 v))))) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* v v))))) (* (sqrt (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (pow v 4) 9))) 16)) (sqrt (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ (+ 1 (* (* 3 v) v)) (* (pow v 4) 9)))))))) * * * * [misc]progress: [ 141 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (123 enodes) * * [misc]simplify: iters left: 4 (402 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (- 1 (* (* v v) 3))) (* (- (* (sqrt 2) (* v v))) 4))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (- 1 (* (* v v) 3))) (* (- (* (sqrt 2) (* v v))) 4))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v v) 3)))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (253 enodes) * * [misc]simplify: iters left: 1 (348 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) 16)) (sqrt (+ 4 (* (* 12 v) v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (- 1 (* (* v v) 3))) (* (- (* (sqrt 2) (* v v))) 4))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v v) 3)))))))) (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) 16)) (sqrt (+ 4 (* (* 12 v) v)))))) * * * * [misc]progress: [ 142 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (403 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 9 (* v v)) (* v v)))) (* (sqrt (- 1 (* 3 (* v v)))) (* (- (* (sqrt 2) (* v v))) 4))))) (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 9 (* v v)) (* v v)))) (sqrt (- 1 (* (* 9 (* v v)) (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 9 (* v v)) (* v v)))) (* (sqrt (- 1 (* 3 (* v v)))) (* (- (* (sqrt 2) (* v v))) 4))))) (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 9 (* v v)) (* v v)))) (sqrt (- 1 (* (* 9 (* v v)) (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (247 enodes) * * [misc]simplify: iters left: 1 (313 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* 9 (pow v 4)))) 16)) (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* 9 (pow v 4)))) (sqrt (+ 1 (* v (* 3 v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 9 (* v v)) (* v v)))) (* (sqrt (- 1 (* 3 (* v v)))) (* (- (* (sqrt 2) (* v v))) 4))))) (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 9 (* v v)) (* v v)))) (sqrt (- 1 (* (* 9 (* v v)) (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* 9 (pow v 4)))) 16)) (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* 9 (pow v 4)))) (sqrt (+ 1 (* v (* 3 v))))))))) * * * * [misc]progress: [ 143 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (117 enodes) * * [misc]simplify: iters left: 4 (373 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) (* (* 4 (* v (* (- v) (sqrt 2)))) (sqrt (- 1 (* v (* 3 v)))))))) (sqrt (+ (* (* (sqrt (+ 1 (* v (* 3 v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (sqrt (+ 1 (* v (* 3 v)))) (/ (sqrt 2) 4)) (* (* (- v) v) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) (* (* 4 (* v (* (- v) (sqrt 2)))) (sqrt (- 1 (* v (* 3 v)))))))) (sqrt (+ (* (* (sqrt (+ 1 (* v (* 3 v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (sqrt (+ 1 (* v (* 3 v)))) (/ (sqrt 2) 4)) (* (* (- v) v) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (258 enodes) * * [misc]simplify: iters left: 1 (351 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt (* 16 (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) (* (* 4 (* v (* (- v) (sqrt 2)))) (sqrt (- 1 (* v (* 3 v)))))))) (sqrt (+ (* (* (sqrt (+ 1 (* v (* 3 v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (sqrt (+ 1 (* v (* 3 v)))) (/ (sqrt 2) 4)) (* (* (- v) v) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))))))) (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt (* 16 (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1)))))))) * * * * [misc]progress: [ 144 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (111 enodes) * * [misc]simplify: iters left: 4 (345 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt 2)) (* (* v v) (sqrt (- 1 (* (* 3 v) v))))))) (sqrt (+ (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (sqrt 2) 4)) (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (sqrt (- 1 (* (* 3 v) v))) (* (* (* (sqrt 2) v) (- v)) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt 2)) (* (* v v) (sqrt (- 1 (* (* 3 v) v))))))) (sqrt (+ (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (sqrt 2) 4)) (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (sqrt (- 1 (* (* 3 v) v))) (* (* (* (sqrt 2) v) (- v)) 4)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (247 enodes) * * [misc]simplify: iters left: 1 (313 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* 9 (pow v 4)))) 16)) (sqrt (* 4 (sqrt (+ 1 (* v (* 3 v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt 2)) (* (* v v) (sqrt (- 1 (* (* 3 v) v))))))) (sqrt (+ (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (sqrt 2) 4)) (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (sqrt (- 1 (* (* 3 v) v))) (* (* (* (sqrt 2) v) (- v)) 4)))))) (* (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* 9 (pow v 4)))) 16)) (sqrt (* 4 (sqrt (+ 1 (* v (* 3 v))))))))) * * * * [misc]progress: [ 145 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (37 enodes) * * [misc]simplify: iters left: 5 (106 enodes) * * [misc]simplify: iters left: 4 (339 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (* 4 (* (sqrt 2) (* v (- v)))) (sqrt (- 1 (* (* 3 v) v))))))) (sqrt (+ (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))) (* (* (* (sqrt 2) 4) (* v (- v))) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (* 4 (* (sqrt 2) (* v (- v)))) (sqrt (- 1 (* (* 3 v) v))))))) (sqrt (+ (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))) (* (* (* (sqrt 2) 4) (* v (- v))) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (225 enodes) * * [misc]simplify: iters left: 1 (254 enodes) * [exit]simplify: Simplified to (* 16 (sqrt (+ (* (* v v) 3) (+ (* 9 (pow v 4)) 1)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (* 4 (* (sqrt 2) (* v (- v)))) (sqrt (- 1 (* (* 3 v) v))))))) (sqrt (+ (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))) (* (* (* (sqrt 2) 4) (* v (- v))) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) (* 16 (sqrt (+ (* (* v v) 3) (+ (* 9 (pow v 4)) 1)))))) * * * * [misc]progress: [ 146 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (119 enodes) * * [misc]simplify: iters left: 4 (367 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (* (sqrt 2) (* (- v) v))) (sqrt (- 1 (* 3 (* v v)))))))) (sqrt (- (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt 2) (sqrt (- 1 (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (sqrt 2) (* v v)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (* (sqrt 2) (* (- v) v))) (sqrt (- 1 (* 3 (* v v)))))))) (sqrt (- (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt 2) (sqrt (- 1 (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (sqrt 2) (* v v)) 4))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (138 enodes) * * [misc]simplify: iters left: 2 (220 enodes) * * [misc]simplify: iters left: 1 (252 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ (* (* v v) 3) (+ (* (pow v 4) 9) 1))))) (sqrt (* 16 (sqrt (+ 1 (* (* v v) 3)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (* (sqrt 2) (* (- v) v))) (sqrt (- 1 (* 3 (* v v)))))))) (sqrt (- (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt 2) (sqrt (- 1 (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (sqrt 2) (* v v)) 4))))) (* (sqrt (* 16 (sqrt (+ (* (* v v) 3) (+ (* (pow v 4) 9) 1))))) (sqrt (* 16 (sqrt (+ 1 (* (* v v) 3)))))))) * * * * [misc]progress: [ 147 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (110 enodes) * * [misc]simplify: iters left: 4 (371 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (* 4 (* (sqrt 2) (* v (- v)))) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ 1 (* (* 3 v) v))))))) (sqrt (- (* (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ 1 (* (* 3 v) v)))) (* (sqrt 2) (sqrt (- 1 (* (* 3 v) v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (* 4 (* (sqrt 2) (* v (- v)))) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ 1 (* (* 3 v) v))))))) (sqrt (- (* (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ 1 (* (* 3 v) v)))) (* (sqrt 2) (sqrt (- 1 (* (* 3 v) v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (225 enodes) * * [misc]simplify: iters left: 1 (257 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) (* 3 (* v v))) 1)) 4)) (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) (* 3 (* v v))) 1)) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (* 4 (* (sqrt 2) (* v (- v)))) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ 1 (* (* 3 v) v))))))) (sqrt (- (* (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ 1 (* (* 3 v) v)))) (* (sqrt 2) (sqrt (- 1 (* (* 3 v) v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) (* (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) (* 3 (* v v))) 1)) 4)) (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) (* 3 (* v v))) 1)) 16))))) * * * * [misc]progress: [ 148 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (371 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v (* 3 v)) (* v (* 3 v))))) (* (* 4 (* (* (- v) v) (sqrt 2))) (sqrt (- 1 (* v (* 3 v)))))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* v (* 3 v))))) (sqrt (+ 1 (* v (* 3 v))))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* (* v v) (/ (sqrt 2) 4)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v (* 3 v)) (* v (* 3 v))))) (* (* 4 (* (* (- v) v) (sqrt 2))) (sqrt (- 1 (* v (* 3 v)))))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* v (* 3 v))))) (sqrt (+ 1 (* v (* 3 v))))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* (* v v) (/ (sqrt 2) 4)) 4))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (247 enodes) * * [misc]simplify: iters left: 1 (313 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* 9 (pow v 4)))) 16)) (sqrt (* 4 (sqrt (+ 1 (* v (* 3 v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v (* 3 v)) (* v (* 3 v))))) (* (* 4 (* (* (- v) v) (sqrt 2))) (sqrt (- 1 (* v (* 3 v)))))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* v (* 3 v))))) (sqrt (+ 1 (* v (* 3 v))))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* (* v v) (/ (sqrt 2) 4)) 4))))) (* (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* 9 (pow v 4)))) 16)) (sqrt (* 4 (sqrt (+ 1 (* v (* 3 v))))))))) * * * * [misc]progress: [ 149 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (36 enodes) * * [misc]simplify: iters left: 5 (98 enodes) * * [misc]simplify: iters left: 4 (299 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2)) (+ 4 (* (* 4 v) (- v))))) (sqrt (+ (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (sqrt 2) 4)) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (* (* (* 4 v) (- v)) (sqrt 2)) (sqrt (- 1 (* (* 3 v) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2)) (+ 4 (* (* 4 v) (- v))))) (sqrt (+ (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (sqrt 2) 4)) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (* (* (* 4 v) (- v)) (sqrt 2)) (sqrt (- 1 (* (* 3 v) v)))))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* 4 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (* 4 4))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (223 enodes) * * [misc]simplify: iters left: 1 (255 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) (* 3 (* v v))) 1)) 16)) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2)) (+ 4 (* (* 4 v) (- v))))) (sqrt (+ (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (sqrt 2) 4)) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (* (* (* 4 v) (- v)) (sqrt 2)) (sqrt (- 1 (* (* 3 v) v)))))))) (* (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) (* 3 (* v v))) 1)) 16)) 4))) * * * * [misc]progress: [ 150 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3)))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (113 enodes) * * [misc]simplify: iters left: 4 (410 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) (* (sqrt (- 1 (* v (* 3 v)))) (* (* (sqrt 2) (* (- v) v)) 4))))) (sqrt (* (+ (* (* (* v v) (* v v)) (- (* v v))) 1) (pow (* (/ (sqrt 2) 4) (sqrt (- 1 (* v (* 3 v))))) 3)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) (* (sqrt (- 1 (* v (* 3 v)))) (* (* (sqrt 2) (* (- v) v)) 4))))) (sqrt (* (+ (* (* (* v v) (* v v)) (- (* v v))) 1) (pow (* (/ (sqrt 2) 4) (sqrt (- 1 (* v (* 3 v))))) 3)))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * * [misc]simplify: iters left: 6 (31 enodes) * * [misc]simplify: iters left: 5 (88 enodes) * * [misc]simplify: iters left: 4 (290 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) 16)) (sqrt (- (* (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (+ (* v (* -3 v)) 1))) (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (+ (* v (* -3 v)) 1)))) (* (* (sqrt (+ (* v (* -3 v)) 1)) (- (* (/ (sqrt 2) 4) (- (* v v))) (/ (sqrt 2) 4))) (* (/ (sqrt 2) 4) (sqrt (+ (* v (* -3 v)) 1))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) (* (sqrt (- 1 (* v (* 3 v)))) (* (* (sqrt 2) (* (- v) v)) 4))))) (sqrt (* (+ (* (* (* v v) (* v v)) (- (* v v))) 1) (pow (* (/ (sqrt 2) 4) (sqrt (- 1 (* v (* 3 v))))) 3)))) (* (sqrt (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) 16)) (sqrt (- (* (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (+ (* v (* -3 v)) 1))) (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (+ (* v (* -3 v)) 1)))) (* (* (sqrt (+ (* v (* -3 v)) 1)) (- (* (/ (sqrt 2) 4) (- (* v v))) (/ (sqrt 2) 4))) (* (/ (sqrt 2) 4) (sqrt (+ (* v (* -3 v)) 1))))))))) * * * * [misc]progress: [ 151 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (406 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (- 1 (* 3 (* v v)))))))) (sqrt (* (* (sqrt (- 1 (* 3 (* v v)))) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* v (- v))))) (* (sqrt (- 1 (* 3 (* v v)))) (+ (* (/ (sqrt 2) 4) (* v (- v))) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (- 1 (* 3 (* v v)))))))) (sqrt (* (* (sqrt (- 1 (* 3 (* v v)))) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* v (- v))))) (* (sqrt (- 1 (* 3 (* v v)))) (+ (* (/ (sqrt 2) 4) (* v (- v))) (/ (sqrt 2) 4)))))) (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (69 enodes) * * [misc]simplify: iters left: 4 (192 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 16)) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (- 1 (* 3 (* v v)))))))) (sqrt (* (* (sqrt (- 1 (* 3 (* v v)))) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* v (- v))))) (* (sqrt (- 1 (* 3 (* v v)))) (+ (* (/ (sqrt 2) 4) (* v (- v))) (/ (sqrt 2) 4)))))) (* (sqrt (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 16)) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v)))))))) * * * * [misc]progress: [ 152 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (109 enodes) * * [misc]simplify: iters left: 4 (340 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) (sqrt (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))) (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) (sqrt (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))) (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) 4)))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (54 enodes) * * [misc]simplify: iters left: 4 (112 enodes) * * [misc]simplify: iters left: 3 (183 enodes) * * [misc]simplify: iters left: 2 (301 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* (* 3 v) v) 1)) 16) (sqrt (+ (+ (* (* 3 v) v) (* (pow v 3) (* v 9))) 1)))) (sqrt (* 4 (+ (* (* 9 (* v v)) (* (* v v) 4)) (+ (* 12 (* v v)) 4))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) (sqrt (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))) (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) 4)))) (* (sqrt (* (* (sqrt (+ (* (* 3 v) v) 1)) 16) (sqrt (+ (+ (* (* 3 v) v) (* (pow v 3) (* v 9))) 1)))) (sqrt (* 4 (+ (* (* 9 (* v v)) (* (* v v) 4)) (+ (* 12 (* v v)) 4))))))) * * * * [misc]progress: [ 153 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (366 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* 3 (* v v)) 1)) 4)))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* 3 (* v v)) 1)) 4)) (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* 3 (* v v)) 1)) 4)))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* 3 (* v v)) 1)) 4)) (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (161 enodes) * * [misc]simplify: iters left: 2 (251 enodes) * * [misc]simplify: iters left: 1 (288 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ (* (* v v) 3) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* (* v v) 3) 1)) 16)) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* 3 (* v v)) 1)) 4)))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* 3 (* v v)) 1)) 4)) (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (+ (+ (* (* v v) 3) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* (* v v) 3) 1)) 16)))) * * * * [misc]progress: [ 154 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (395 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* 4 (sqrt (+ (* (* 3 v) v) 1)))))) (sqrt (- (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (sqrt 2))) (* (* 4 (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (/ (* (sqrt 2) (* v v)) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* 4 (sqrt (+ (* (* 3 v) v) 1)))))) (sqrt (- (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (sqrt 2))) (* (* 4 (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (/ (* (sqrt 2) (* v v)) 4)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (191 enodes) * * [misc]simplify: iters left: 2 (367 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (* 9 v) (pow v 3))) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 16))) (sqrt (+ (* (* v (* 3 v)) (* (* 12 v) v)) (+ (* (* 12 v) v) 4)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* 4 (sqrt (+ (* (* 3 v) v) 1)))))) (sqrt (- (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (sqrt 2))) (* (* 4 (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (/ (* (sqrt 2) (* v v)) 4)))))) (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (* 9 v) (pow v 3))) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 16))) (sqrt (+ (* (* v (* 3 v)) (* (* 12 v) v)) (+ (* (* 12 v) v) 4)))))) * * * * [misc]progress: [ 155 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (119 enodes) * * [misc]simplify: iters left: 4 (406 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (* v v))))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (/ (sqrt 2) 4))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (* v v))))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (/ (sqrt 2) 4))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (104 enodes) * * [misc]simplify: iters left: 3 (173 enodes) * * [misc]simplify: iters left: 2 (264 enodes) * * [misc]simplify: iters left: 1 (296 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 16))) (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 4)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (* v v))))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (/ (sqrt 2) 4))))))) (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 16))) (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 4)))))) * * * * [misc]progress: [ 156 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (385 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (sqrt 2) 4)) (* (* (* 4 (* (sqrt 2) (* (- v) v))) (sqrt (+ (* (* v -3) v) 1))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (* 4 (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)) (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (sqrt 2) 4)) (* (* (* 4 (* (sqrt 2) (* (- v) v))) (sqrt (+ (* (* v -3) v) 1))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (* 4 (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)) (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (105 enodes) * * [misc]simplify: iters left: 3 (182 enodes) * * [misc]simplify: iters left: 2 (292 enodes) * * [misc]simplify: iters left: 1 (319 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 16))) (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (sqrt 2) 4)) (* (* (* 4 (* (sqrt 2) (* (- v) v))) (sqrt (+ (* (* v -3) v) 1))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (* 4 (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)) (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (* v v)))))) (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 16))) (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) 16))))) * * * * [misc]progress: [ 157 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (91 enodes) * * [misc]simplify: iters left: 4 (277 enodes) * [exit]simplify: Simplified to (- (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) 4) (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* 4 (sqrt (+ (* (* v v) 3) 1)))) (* (* v v) (sqrt 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) 4) (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* 4 (sqrt (+ (* (* v v) 3) 1)))) (* (* v v) (sqrt 2)))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (101 enodes) * * [misc]simplify: iters left: 3 (181 enodes) * * [misc]simplify: iters left: 2 (296 enodes) * * [misc]simplify: iters left: 1 (310 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ (* v (* 3 v)) (* 9 (pow v 4))) 1)) (* 16 (sqrt (+ (* v (* 3 v)) 1)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) 4) (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* 4 (sqrt (+ (* (* v v) 3) 1)))) (* (* v v) (sqrt 2)))) (* (sqrt (+ (+ (* v (* 3 v)) (* 9 (pow v 4))) 1)) (* 16 (sqrt (+ (* v (* 3 v)) 1)))))) * * * * [misc]progress: [ 158 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (111 enodes) * * [misc]simplify: iters left: 4 (365 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) 4) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (sqrt 2))) (* (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (sqrt (+ (* v (* 3 v)) 1)) 4)) (* (sqrt 2) (* v v))))) (sqrt (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) 4) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (sqrt 2))) (* (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (sqrt (+ (* v (* 3 v)) 1)) 4)) (* (sqrt 2) (* v v))))) (sqrt (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (53 enodes) * * [misc]simplify: iters left: 4 (111 enodes) * * [misc]simplify: iters left: 3 (186 enodes) * * [misc]simplify: iters left: 2 (309 enodes) * * [misc]simplify: iters left: 1 (384 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 16 (sqrt (+ (* 3 (* v v)) 1))) (sqrt (+ (+ (* 3 (* v v)) (* (pow v 4) 9)) 1)))) (sqrt (+ 16 (* (* v v) 48)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) 4) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (sqrt 2))) (* (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (sqrt (+ (* v (* 3 v)) 1)) 4)) (* (sqrt 2) (* v v))))) (sqrt (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2)))))) (* (sqrt (* (* 16 (sqrt (+ (* 3 (* v v)) 1))) (sqrt (+ (+ (* 3 (* v v)) (* (pow v 4) 9)) 1)))) (sqrt (+ 16 (* (* v v) 48)))))) * * * * [misc]progress: [ 159 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (369 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (sqrt 2))) (* (* 4 (sqrt (+ (* v (* 3 v)) 1))) (/ (sqrt (- 1 (pow (* v (* 3 v)) 3))) (/ 4 (* (* v v) (sqrt 2))))))) (sqrt (+ (* (* (* (sqrt (+ (* v (* 3 v)) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (- (* v v))) (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (sqrt 2))) (* (* 4 (sqrt (+ (* v (* 3 v)) 1))) (/ (sqrt (- 1 (pow (* v (* 3 v)) 3))) (/ 4 (* (* v v) (sqrt 2))))))) (sqrt (+ (* (* (* (sqrt (+ (* v (* 3 v)) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (- (* v v))) (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (246 enodes) * * [misc]simplify: iters left: 1 (283 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 16))) (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 4)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (sqrt 2))) (* (* 4 (sqrt (+ (* v (* 3 v)) 1))) (/ (sqrt (- 1 (pow (* v (* 3 v)) 3))) (/ 4 (* (* v v) (sqrt 2))))))) (sqrt (+ (* (* (* (sqrt (+ (* v (* 3 v)) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (- (* v v))) (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))))))) (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 16))) (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 4)))))) * * * * [misc]progress: [ 160 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (408 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (+ (* (* v v) 3) 1))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v))))) (sqrt (- (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)) (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (+ (* (* v v) 3) 1))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v))))) (sqrt (- (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)) (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (175 enodes) * * [misc]simplify: iters left: 2 (302 enodes) * * [misc]simplify: iters left: 1 (421 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* v (* 3 v)) 1)) 16) (sqrt (+ (+ (* v (* 3 v)) (* 9 (pow v 4))) 1)))) (sqrt (+ (* v (* 12 v)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (+ (* (* v v) 3) 1))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v))))) (sqrt (- (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)) (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (* v v)))))) (* (sqrt (* (* (sqrt (+ (* v (* 3 v)) 1)) 16) (sqrt (+ (+ (* v (* 3 v)) (* 9 (pow v 4))) 1)))) (sqrt (+ (* v (* 12 v)) 4))))) * * * * [misc]progress: [ 161 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (377 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt 2) 4)) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (sqrt 2)) (* (* v v) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (sqrt (- (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt 2) 4)) (* (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (sqrt 2))) (* (sqrt (+ 1 (* (* -3 v) v))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt 2) 4)) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (sqrt 2)) (* (* v v) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (sqrt (- (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt 2) 4)) (* (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (sqrt 2))) (* (sqrt (+ 1 (* (* -3 v) v))) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (102 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (249 enodes) * * [misc]simplify: iters left: 1 (287 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* 3 (* v v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* 3 (* v v)) 1)) 16))) (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt 2) 4)) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (sqrt 2)) (* (* v v) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (sqrt (- (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt 2) 4)) (* (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (sqrt 2))) (* (sqrt (+ 1 (* (* -3 v) v))) (* v v)))))) (* (sqrt (* (sqrt (+ (+ (* 3 (* v v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* 3 (* v v)) 1)) 16))) (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) 16))))) * * * * [misc]progress: [ 162 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (112 enodes) * * [misc]simplify: iters left: 4 (364 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (108 enodes) * * [misc]simplify: iters left: 3 (187 enodes) * * [misc]simplify: iters left: 2 (325 enodes) * * [misc]simplify: iters left: 1 (454 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) (* 9 (pow v 4))) 1)) (* 16 (sqrt (+ (* (* v v) 3) 1))))) (sqrt (+ (+ 4 (* (* 12 v) v)) (* (* v v) (* (* 12 v) (* 3 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* v v)))))) (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) (* 9 (pow v 4))) 1)) (* 16 (sqrt (+ (* (* v v) 3) 1))))) (sqrt (+ (+ 4 (* (* 12 v) v)) (* (* v v) (* (* 12 v) (* 3 v)))))))) * * * * [misc]progress: [ 163 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (119 enodes) * * [misc]simplify: iters left: 4 (395 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2))) (* 4 (sqrt (+ (* 3 (* v v)) 1)))))) (sqrt (- (/ (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (sqrt 2)) (/ 4 (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2))) (* 4 (sqrt (+ (* 3 (* v v)) 1)))))) (sqrt (- (/ (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (sqrt 2)) (/ 4 (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (104 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (249 enodes) * * [misc]simplify: iters left: 1 (283 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) (* 9 (pow v 4))) 1)) (* (sqrt (+ (* (* v v) 3) 1)) 16))) (sqrt (* (sqrt (+ (+ (* (* v v) 3) (* 9 (pow v 4))) 1)) (* (sqrt (+ (* (* v v) 3) 1)) 4)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2))) (* 4 (sqrt (+ (* 3 (* v v)) 1)))))) (sqrt (- (/ (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (sqrt 2)) (/ 4 (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)))))) (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) (* 9 (pow v 4))) 1)) (* (sqrt (+ (* (* v v) 3) 1)) 16))) (sqrt (* (sqrt (+ (+ (* (* v v) 3) (* 9 (pow v 4))) 1)) (* (sqrt (+ (* (* v v) 3) 1)) 4)))))) * * * * [misc]progress: [ 164 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (371 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (- (* v v))) (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2)))) (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (sqrt (- 1 (pow (* (* v v) 3) 3))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (- (* v v))) (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2)))) (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (sqrt (- 1 (pow (* (* v v) 3) 3))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (165 enodes) * * [misc]simplify: iters left: 2 (267 enodes) * * [misc]simplify: iters left: 1 (314 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* v (* 3 v)) 1)) 16) (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)))) (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (- (* v v))) (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2)))) (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (sqrt (- 1 (pow (* (* v v) 3) 3))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))))))) (* (sqrt (* (* (sqrt (+ (* v (* 3 v)) 1)) 16) (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)))) (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1))))) * * * * [misc]progress: [ 165 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (411 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* v v))))) (sqrt (+ (* (* (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (- (* v v))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* v v))))) (sqrt (+ (* (* (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (- (* v v))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (156 enodes) * * [misc]simplify: iters left: 2 (248 enodes) * * [misc]simplify: iters left: 1 (284 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 16))) (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (sqrt (+ (* v (* 3 v)) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* v v))))) (sqrt (+ (* (* (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (- (* v v))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 16))) (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (sqrt (+ (* v (* 3 v)) 1))))))) * * * * [misc]progress: [ 166 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (123 enodes) * * [misc]simplify: iters left: 4 (400 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* 4 (sqrt 2))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (sqrt 2))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* v v))))) (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (* 4 (sqrt 2)) 4)) (* (* (sqrt (- 1 (* 3 (* v v)))) (* (* v v) (sqrt 2))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* 4 (sqrt 2))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (sqrt 2))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* v v))))) (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (* 4 (sqrt 2)) 4)) (* (* (sqrt (- 1 (* 3 (* v v)))) (* (* v v) (sqrt 2))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (102 enodes) * * [misc]simplify: iters left: 3 (160 enodes) * * [misc]simplify: iters left: 2 (250 enodes) * * [misc]simplify: iters left: 1 (290 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* 9 (pow v 4))) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 16))) (sqrt (* 4 (sqrt (+ (+ (* v (* 3 v)) (* 9 (pow v 4))) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* 4 (sqrt 2))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (sqrt 2))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* v v))))) (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (* 4 (sqrt 2)) 4)) (* (* (sqrt (- 1 (* 3 (* v v)))) (* (* v v) (sqrt 2))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* 9 (pow v 4))) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 16))) (sqrt (* 4 (sqrt (+ (+ (* v (* 3 v)) (* 9 (pow v 4))) 1))))))) * * * * [misc]progress: [ 167 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (110 enodes) * * [misc]simplify: iters left: 4 (333 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* 3 (* v v)) 1)))))) (sqrt (- (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt 2)) (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* 3 (* v v)) 1)))))) (sqrt (- (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt 2)) (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (104 enodes) * * [misc]simplify: iters left: 3 (179 enodes) * * [misc]simplify: iters left: 2 (280 enodes) * * [misc]simplify: iters left: 1 (309 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 16))) (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 4)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* 3 (* v v)) 1)))))) (sqrt (- (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt 2)) (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (* v v)))))) (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 16))) (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 4)))))) * * * * [misc]progress: [ 168 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (386 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)) (* (* (sqrt (+ (* (* v v) 3) 1)) 4) (* v v))))) (sqrt (* (sqrt (+ (* (* v v) 3) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)) (* (* (sqrt (+ (* (* v v) 3) 1)) 4) (* v v))))) (sqrt (* (sqrt (+ (* (* v v) 3) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (106 enodes) * * [misc]simplify: iters left: 3 (165 enodes) * * [misc]simplify: iters left: 2 (276 enodes) * * [misc]simplify: iters left: 1 (358 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) (* 9 (pow v 4))) 1)) (* (sqrt (+ (* (* v v) 3) 1)) 16))) (sqrt (+ 4 (* v (* v 12))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)) (* (* (sqrt (+ (* (* v v) 3) 1)) 4) (* v v))))) (sqrt (* (sqrt (+ (* (* v v) 3) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))))) (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) (* 9 (pow v 4))) 1)) (* (sqrt (+ (* (* v v) 3) 1)) 16))) (sqrt (+ 4 (* v (* v 12))))))) * * * * [misc]progress: [ 169 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (367 enodes) * [exit]simplify: Simplified to (* (sqrt (- (/ (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (/ (/ 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ (* 3 (* v v)) 1)))))) (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (sqrt (+ (* 3 (* v v)) 1)))) (* (* v v) (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (/ (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (/ (/ 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ (* 3 (* v v)) 1)))))) (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (sqrt (+ (* 3 (* v v)) 1)))) (* (* v v) (sqrt 2)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (156 enodes) * * [misc]simplify: iters left: 2 (248 enodes) * * [misc]simplify: iters left: 1 (284 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 16))) (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (sqrt (+ (* v (* 3 v)) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (/ (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (/ (/ 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ (* 3 (* v v)) 1)))))) (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (sqrt (+ (* 3 (* v v)) 1)))) (* (* v v) (sqrt 2)))))) (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 16))) (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (sqrt (+ (* v (* 3 v)) 1))))))) * * * * [misc]progress: [ 170 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (376 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (sqrt 2)) (* 4 (sqrt (+ (* (* 3 v) v) 1))))))) (sqrt (+ (* (* (sqrt (+ (* (* 3 v) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (+ (* (* 3 v) v) 1)) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (- (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (sqrt 2)) (* 4 (sqrt (+ (* (* 3 v) v) 1))))))) (sqrt (+ (* (* (sqrt (+ (* (* 3 v) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (+ (* (* 3 v) v) 1)) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (- (* v v))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (109 enodes) * * [misc]simplify: iters left: 3 (180 enodes) * * [misc]simplify: iters left: 2 (299 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* 3 (* v v)) 1)) (sqrt (* (* (sqrt (+ (* 3 (* v v)) 1)) 16) (sqrt (+ (+ (* 3 (* v v)) (* 9 (pow v 4))) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (sqrt 2)) (* 4 (sqrt (+ (* (* 3 v) v) 1))))))) (sqrt (+ (* (* (sqrt (+ (* (* 3 v) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (+ (* (* 3 v) v) 1)) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (- (* v v))))))) (* (sqrt (+ (* 3 (* v v)) 1)) (sqrt (* (* (sqrt (+ (* 3 (* v v)) 1)) 16) (sqrt (+ (+ (* 3 (* v v)) (* 9 (pow v 4))) 1))))))) * * * * [misc]progress: [ 171 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (122 enodes) * * [misc]simplify: iters left: 4 (385 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* 4 (sqrt 2))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt 2)) (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (* v v))))) (sqrt (- (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (* 4 (sqrt 2)) 4)) (* (sqrt (+ 1 (* v (* v -3)))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* 3 (* v v)) 1))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* 4 (sqrt 2))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt 2)) (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (* v v))))) (sqrt (- (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (* 4 (sqrt 2)) 4)) (* (sqrt (+ 1 (* v (* v -3)))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* 3 (* v v)) 1))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (102 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (247 enodes) * * [misc]simplify: iters left: 1 (283 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 16))) (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* 4 (sqrt 2))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt 2)) (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (* v v))))) (sqrt (- (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (* 4 (sqrt 2)) 4)) (* (sqrt (+ 1 (* v (* v -3)))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* 3 (* v v)) 1))))))) (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 16))) (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) 4))))) * * * * [misc]progress: [ 172 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (348 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* (sqrt (+ (* (* 3 v) v) 1)) (* 4 (sqrt 2))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* v v))))) (sqrt (+ (* (* (- (* v v)) (* (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (* (sqrt 2) 4) (sqrt (+ (* (* v -3) v) 1))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* (sqrt (+ (* (* 3 v) v) 1)) (* 4 (sqrt 2))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* v v))))) (sqrt (+ (* (* (- (* v v)) (* (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (* (sqrt 2) 4) (sqrt (+ (* (* v -3) v) 1))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (53 enodes) * * [misc]simplify: iters left: 4 (104 enodes) * * [misc]simplify: iters left: 3 (161 enodes) * * [misc]simplify: iters left: 2 (246 enodes) * * [misc]simplify: iters left: 1 (283 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) (* (pow v 4) 9)) 1)) (* 16 (sqrt (+ (* (* v v) 3) 1))))) (sqrt (* (sqrt (+ (+ (* (* v v) 3) (* (pow v 4) 9)) 1)) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* (sqrt (+ (* (* 3 v) v) 1)) (* 4 (sqrt 2))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* v v))))) (sqrt (+ (* (* (- (* v v)) (* (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (* (sqrt 2) 4) (sqrt (+ (* (* v -3) v) 1))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))))))) (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) (* (pow v 4) 9)) 1)) (* 16 (sqrt (+ (* (* v v) 3) 1))))) (sqrt (* (sqrt (+ (+ (* (* v v) 3) (* (pow v 4) 9)) 1)) 16))))) * * * * [misc]progress: [ 173 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (384 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* 4 (sqrt 2)) (sqrt (+ 1 (* v (* v -3))))) (sqrt (+ (* (* v v) 3) 1))) (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (* (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)) (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (* 4 (sqrt 2)) (sqrt (+ 1 (* v (* v -3))))) (sqrt (+ (* (* v v) 3) 1))) (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (* (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)) (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (161 enodes) * * [misc]simplify: iters left: 2 (251 enodes) * * [misc]simplify: iters left: 1 (286 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) (* (pow v 4) 9)) 1)) (* 16 (sqrt (+ (* (* v v) 3) 1))))) (sqrt (* 16 (sqrt (+ (* (* v v) 3) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (* 4 (sqrt 2)) (sqrt (+ 1 (* v (* v -3))))) (sqrt (+ (* (* v v) 3) 1))) (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (* (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)) (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (* v v)))))) (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) (* (pow v 4) 9)) 1)) (* 16 (sqrt (+ (* (* v v) 3) 1))))) (sqrt (* 16 (sqrt (+ (* (* v v) 3) 1))))))) * * * * [misc]progress: [ 174 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (122 enodes) * * [misc]simplify: iters left: 4 (382 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (- (* v v))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (* (sqrt 2) (sqrt (+ 1 (* v (* -3 v))))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (- (* v v))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (* (sqrt 2) (sqrt (+ 1 (* v (* -3 v))))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (102 enodes) * * [misc]simplify: iters left: 3 (173 enodes) * * [misc]simplify: iters left: 2 (268 enodes) * * [misc]simplify: iters left: 1 (307 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ (+ (* (* 3 v) v) (* (pow v 4) 9)) 1)))) (sqrt (* (* (sqrt (+ (* (* 3 v) v) 1)) 16) (sqrt (+ (+ (* (* 3 v) v) (* (pow v 4) 9)) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (- (* v v))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (* (sqrt 2) (sqrt (+ 1 (* v (* -3 v))))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (* 4 (sqrt (+ (+ (* (* 3 v) v) (* (pow v 4) 9)) 1)))) (sqrt (* (* (sqrt (+ (* (* 3 v) v) 1)) 16) (sqrt (+ (+ (* (* 3 v) v) (* (pow v 4) 9)) 1))))))) * * * * [misc]progress: [ 175 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (123 enodes) * * [misc]simplify: iters left: 4 (411 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)) (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (* v v))))) (sqrt (- (* (* (sqrt (- 1 (* (* v v) 3))) (sqrt 2)) (sqrt (+ (* (* v v) 3) 1))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (/ (sqrt 2) 4)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)) (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (* v v))))) (sqrt (- (* (* (sqrt (- 1 (* (* v v) 3))) (sqrt 2)) (sqrt (+ (* (* v v) 3) 1))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (/ (sqrt 2) 4)) 4))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (102 enodes) * * [misc]simplify: iters left: 3 (173 enodes) * * [misc]simplify: iters left: 2 (268 enodes) * * [misc]simplify: iters left: 1 (307 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) 4)) (sqrt (* (* (sqrt (+ (* (* 3 v) v) 1)) 16) (sqrt (+ (+ (* (* 3 v) v) (* (pow v 4) 9)) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)) (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (* v v))))) (sqrt (- (* (* (sqrt (- 1 (* (* v v) 3))) (sqrt 2)) (sqrt (+ (* (* v v) 3) 1))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (/ (sqrt 2) 4)) 4))))) (* (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) 4)) (sqrt (* (* (sqrt (+ (* (* 3 v) v) 1)) 16) (sqrt (+ (+ (* (* 3 v) v) (* (pow v 4) 9)) 1))))))) * * * * [misc]progress: [ 176 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (367 enodes) * [exit]simplify: Simplified to (* (sqrt (* (+ (* (- v) v) 1) (* (* (sqrt 2) 4) (sqrt (+ 1 (* (* -3 v) v)))))) (sqrt (- (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (sqrt (+ (* 3 (* v v)) 1)))) (* (* v v) (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (+ (* (- v) v) 1) (* (* (sqrt 2) 4) (sqrt (+ 1 (* (* -3 v) v)))))) (sqrt (- (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (sqrt (+ (* 3 (* v v)) 1)))) (* (* v v) (sqrt 2)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 4))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (160 enodes) * * [misc]simplify: iters left: 2 (249 enodes) * * [misc]simplify: iters left: 1 (286 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* 3 (* v v)) 1)) 16) (sqrt (+ (+ (* 3 (* v v)) (* 9 (pow v 4))) 1)))) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (+ (* (- v) v) 1) (* (* (sqrt 2) 4) (sqrt (+ 1 (* (* -3 v) v)))))) (sqrt (- (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (sqrt (+ (* 3 (* v v)) 1)))) (* (* v v) (sqrt 2)))))) (* (sqrt (* (* (sqrt (+ (* 3 (* v v)) 1)) 16) (sqrt (+ (+ (* 3 (* v v)) (* 9 (pow v 4))) 1)))) 4))) * * * * [misc]progress: [ 177 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3)))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (126 enodes) * * [misc]simplify: iters left: 4 (445 enodes) * [exit]simplify: Simplified to (* (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ (* (* v v) -3) 1))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1))) 3))) (sqrt (- (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* v v) (sqrt 2))) (* 4 (sqrt (+ (* (* 3 v) v) 1))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ (* (* v v) -3) 1))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1))) 3))) (sqrt (- (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* v v) (sqrt 2))) (* 4 (sqrt (+ (* (* 3 v) v) 1))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (97 enodes) * * [misc]simplify: iters left: 4 (307 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (sqrt (- 1 (* v (* 3 v)))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* v (* 3 v)))) (/ (sqrt 2) 4))) (* (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (- 1 (* v (* 3 v))))) (* (sqrt (- 1 (* v (* 3 v)))) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))))) (sqrt (* (* 16 (sqrt (+ (* v (* 3 v)) 1))) (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ (* v (* 3 v)) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ (* (* v v) -3) 1))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1))) 3))) (sqrt (- (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* v v) (sqrt 2))) (* 4 (sqrt (+ (* (* 3 v) v) 1))))))) (* (sqrt (+ (* (* (sqrt (- 1 (* v (* 3 v)))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* v (* 3 v)))) (/ (sqrt 2) 4))) (* (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (- 1 (* v (* 3 v))))) (* (sqrt (- 1 (* v (* 3 v)))) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))))) (sqrt (* (* 16 (sqrt (+ (* v (* 3 v)) 1))) (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ (* v (* 3 v)) 1)))))))) * * * * [misc]progress: [ 178 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (128 enodes) * * [misc]simplify: iters left: 4 (448 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* v (* v -3)) 1)) (- (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4)))) (* (sqrt (+ (* v (* v -3)) 1)) (+ (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))))) (sqrt (- (* (* 4 (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v)))))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (sqrt 2))) (* (* (* (sqrt (+ (* v (* 3 v)) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* v (* v -3)) 1)) (- (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4)))) (* (sqrt (+ (* v (* v -3)) 1)) (+ (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))))) (sqrt (- (* (* 4 (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v)))))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (sqrt 2))) (* (* (* (sqrt (+ (* v (* 3 v)) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* v v))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (30 enodes) * * [misc]simplify: iters left: 5 (78 enodes) * * [misc]simplify: iters left: 4 (208 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 16 (sqrt (+ (* (* v v) 3) 1))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))))) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* -3 v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* v (* v -3)) 1)) (- (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4)))) (* (sqrt (+ (* v (* v -3)) 1)) (+ (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))))) (sqrt (- (* (* 4 (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v)))))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (sqrt 2))) (* (* (* (sqrt (+ (* v (* 3 v)) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* v v))))) (* (sqrt (* (* 16 (sqrt (+ (* (* v v) 3) 1))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))))) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* -3 v))))))))) * * * * [misc]progress: [ 179 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (372 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (sqrt 2) (* (sqrt 2) (* (- v) v)))) (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))))) (sqrt (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (* (sqrt 2) (* (- v) v)) (sqrt 2))) (* 4 (sqrt (+ (* (* 3 v) v) 1)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (sqrt 2) (* (sqrt 2) (* (- v) v)))) (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))))) (sqrt (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (* (sqrt 2) (* (- v) v)) (sqrt 2))) (* 4 (sqrt (+ (* (* 3 v) v) 1)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (54 enodes) * * [misc]simplify: iters left: 4 (105 enodes) * * [misc]simplify: iters left: 3 (167 enodes) * * [misc]simplify: iters left: 2 (305 enodes) * [exit]simplify: Simplified to (* (sqrt (* (+ (* (* v v) 12) 4) 4)) (sqrt (* 4 (+ (+ (* (* v v) 12) 4) (* (* (* v v) 3) (* (* v v) 12)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (sqrt 2) (* (sqrt 2) (* (- v) v)))) (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))))) (sqrt (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (* (sqrt 2) (* (- v) v)) (sqrt 2))) (* 4 (sqrt (+ (* (* 3 v) v) 1)))))) (* (sqrt (* (+ (* (* v v) 12) 4) 4)) (sqrt (* 4 (+ (+ (* (* v v) 12) 4) (* (* (* v v) 3) (* (* v v) 12)))))))) * * * * [misc]progress: [ 180 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (109 enodes) * * [misc]simplify: iters left: 4 (337 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt 2) (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* 4 (sqrt 2))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v))))) (sqrt (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (+ (* (* v (- v)) (sqrt 2)) (sqrt 2))) (* 4 (sqrt (+ (* 3 (* v v)) 1)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt 2) (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* 4 (sqrt 2))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v))))) (sqrt (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (+ (* (* v (- v)) (sqrt 2)) (sqrt 2))) (* 4 (sqrt (+ (* 3 (* v v)) 1)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (54 enodes) * * [misc]simplify: iters left: 4 (112 enodes) * * [misc]simplify: iters left: 3 (201 enodes) * * [misc]simplify: iters left: 2 (333 enodes) * * [misc]simplify: iters left: 1 (413 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* v v) 48) 16)) (sqrt (* (sqrt (+ (* 9 (pow v 4)) (+ (* v (* 3 v)) 1))) (* (sqrt (+ (* v (* 3 v)) 1)) 16)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt 2) (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* 4 (sqrt 2))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v))))) (sqrt (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (+ (* (* v (- v)) (sqrt 2)) (sqrt 2))) (* 4 (sqrt (+ (* 3 (* v v)) 1)))))) (* (sqrt (+ (* (* v v) 48) 16)) (sqrt (* (sqrt (+ (* 9 (pow v 4)) (+ (* v (* 3 v)) 1))) (* (sqrt (+ (* v (* 3 v)) 1)) 16)))))) * * * * [misc]progress: [ 181 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (402 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) (+ (* (sqrt 2) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4))))) (sqrt (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) (+ (* (sqrt 2) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4))))) (sqrt (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (98 enodes) * * [misc]simplify: iters left: 3 (181 enodes) * * [misc]simplify: iters left: 2 (368 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (+ 4 (* v (* 12 v))))) (sqrt (+ (+ 4 (* v (* 12 v))) (* (* v 4) (* (* v v) (* 9 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) (+ (* (sqrt 2) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4))))) (sqrt (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2)))))) (* (sqrt (* 4 (+ 4 (* v (* 12 v))))) (sqrt (+ (+ 4 (* v (* 12 v))) (* (* v 4) (* (* v v) (* 9 v)))))))) * * * * [misc]progress: [ 182 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (117 enodes) * * [misc]simplify: iters left: 4 (387 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* v v))))) (sqrt (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (sqrt 2) (* (- v) (* v (sqrt 2))))) (* (sqrt (+ (* (* 3 v) v) 1)) 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* v v))))) (sqrt (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (sqrt 2) (* (- v) (* v (sqrt 2))))) (* (sqrt (+ (* (* 3 v) v) 1)) 4)))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (101 enodes) * * [misc]simplify: iters left: 3 (153 enodes) * * [misc]simplify: iters left: 2 (262 enodes) * * [misc]simplify: iters left: 1 (353 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 16 (* (* v v) 48))) (sqrt (* (* (sqrt (+ (* (* v v) 3) 1)) 4) (sqrt (+ (* 9 (pow v 4)) (+ (* (* v v) 3) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* v v))))) (sqrt (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (sqrt 2) (* (- v) (* v (sqrt 2))))) (* (sqrt (+ (* (* 3 v) v) 1)) 4)))) (* (sqrt (+ 16 (* (* v v) 48))) (sqrt (* (* (sqrt (+ (* (* v v) 3) 1)) 4) (sqrt (+ (* 9 (pow v 4)) (+ (* (* v v) 3) 1)))))))) * * * * [misc]progress: [ 183 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (385 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (* (sqrt 2) (* (- v) v)) (sqrt 2))) (* (sqrt (+ (* (* v v) 3) 1)) 4))) (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (* (sqrt (+ (* (* v -3) v) 1)) (* (- (* (sqrt 2) (* v v))) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (* (sqrt 2) (* (- v) v)) (sqrt 2))) (* (sqrt (+ (* (* v v) 3) 1)) 4))) (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (* (sqrt (+ (* (* v -3) v) 1)) (* (- (* (sqrt 2) (* v v))) 4)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (96 enodes) * * [misc]simplify: iters left: 3 (153 enodes) * * [misc]simplify: iters left: 2 (268 enodes) * * [misc]simplify: iters left: 1 (383 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 16 (* 48 (* v v)))) (sqrt (* 16 (sqrt (+ (* (pow v 4) 9) (+ (* (* v v) 3) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (* (sqrt 2) (* (- v) v)) (sqrt 2))) (* (sqrt (+ (* (* v v) 3) 1)) 4))) (sqrt (+ (* (* (sqrt 2) 4) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (* (sqrt (+ (* (* v -3) v) 1)) (* (- (* (sqrt 2) (* v v))) 4)))))) (* (sqrt (+ 16 (* 48 (* v v)))) (sqrt (* 16 (sqrt (+ (* (pow v 4) 9) (+ (* (* v v) 3) 1)))))))) * * * * [misc]progress: [ 184 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (111 enodes) * * [misc]simplify: iters left: 4 (373 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) 4)) (* (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* v v)) (* (sqrt 2) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) (sqrt (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (* (sqrt 2) (* v (- v))) (sqrt 2))) (* (sqrt (+ (* (* 3 v) v) 1)) 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) 4)) (* (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* v v)) (* (sqrt 2) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) (sqrt (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (* (sqrt 2) (* v (- v))) (sqrt 2))) (* (sqrt (+ (* (* 3 v) v) 1)) 4)))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (53 enodes) * * [misc]simplify: iters left: 4 (111 enodes) * * [misc]simplify: iters left: 3 (173 enodes) * * [misc]simplify: iters left: 2 (280 enodes) * * [misc]simplify: iters left: 1 (368 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* 48 (* v v)) 16)) (sqrt (* (sqrt (+ (* 9 (pow v 4)) (+ (* 3 (* v v)) 1))) (* 16 (sqrt (+ (* 3 (* v v)) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) 4)) (* (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* v v)) (* (sqrt 2) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) (sqrt (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (* (sqrt 2) (* v (- v))) (sqrt 2))) (* (sqrt (+ (* (* 3 v) v) 1)) 4)))) (* (sqrt (+ (* 48 (* v v)) 16)) (sqrt (* (sqrt (+ (* 9 (pow v 4)) (+ (* 3 (* v v)) 1))) (* 16 (sqrt (+ (* 3 (* v v)) 1)))))))) * * * * [misc]progress: [ 185 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (59 enodes) * * [misc]simplify: iters left: 4 (176 enodes) * [exit]simplify: Simplified to (* (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (+ (sqrt 2) (- (* (* v v) (sqrt 2))))) (* 4 (sqrt (+ (* (* v v) 3) 1)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (+ (sqrt 2) (- (* (* v v) (sqrt 2))))) (* 4 (sqrt (+ (* (* v v) 3) 1)))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * * [misc]simplify: iters left: 1 (73 enodes) * [exit]simplify: Simplified to (+ 16 (* 48 (* v v))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (+ (sqrt 2) (- (* (* v v) (sqrt 2))))) (* 4 (sqrt (+ (* (* v v) 3) 1)))) (+ 16 (* 48 (* v v))))) * * * * [misc]progress: [ 186 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (111 enodes) * * [misc]simplify: iters left: 4 (379 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) (sqrt (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (sqrt 2) (* (- (* v v)) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) (sqrt (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (sqrt 2) (* (- (* v v)) (sqrt 2))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (101 enodes) * * [misc]simplify: iters left: 3 (154 enodes) * * [misc]simplify: iters left: 2 (265 enodes) * * [misc]simplify: iters left: 1 (355 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (sqrt (+ (* 9 (pow v 4)) (+ (* v (* 3 v)) 1))))) (sqrt (+ 16 (* 48 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) (sqrt (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (sqrt 2) (* (- (* v v)) (sqrt 2))))))) (* (sqrt (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (sqrt (+ (* 9 (pow v 4)) (+ (* v (* 3 v)) 1))))) (sqrt (+ 16 (* 48 (* v v))))))) * * * * [misc]progress: [ 187 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (31 enodes) * * [misc]simplify: iters left: 5 (82 enodes) * * [misc]simplify: iters left: 4 (290 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) (+ (* (* 4 (* (/ (sqrt 2) 4) (- (* v v)))) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (sqrt 2) (sqrt (- 1 (* (* (* v v) (* v v)) 9))))))) (sqrt (* (* 4 (sqrt (+ (* v (* 3 v)) 1))) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (+ (sqrt 2) (* (- (* v v)) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) (+ (* (* 4 (* (/ (sqrt 2) 4) (- (* v v)))) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (sqrt 2) (sqrt (- 1 (* (* (* v v) (* v v)) 9))))))) (sqrt (* (* 4 (sqrt (+ (* v (* 3 v)) 1))) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (+ (sqrt 2) (* (- (* v v)) (sqrt 2))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (68 enodes) * * [misc]simplify: iters left: 1 (93 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 4 (* v (* 12 v)))) (sqrt (+ (* 48 (* v v)) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) (+ (* (* 4 (* (/ (sqrt 2) 4) (- (* v v)))) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (sqrt 2) (sqrt (- 1 (* (* (* v v) (* v v)) 9))))))) (sqrt (* (* 4 (sqrt (+ (* v (* 3 v)) 1))) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (+ (sqrt 2) (* (- (* v v)) (sqrt 2))))))) (* (sqrt (+ 4 (* v (* 12 v)))) (sqrt (+ (* 48 (* v v)) 16))))) * * * * [misc]progress: [ 188 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (84 enodes) * * [misc]simplify: iters left: 4 (275 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (* (sqrt (+ (* (* (* v v) -9) (* v v)) 1)) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))))) (sqrt (- (* (* (sqrt 2) 4) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* (sqrt (- 1 (* (* v v) 3))) (* (* v v) (sqrt 2))) (* 4 (sqrt (+ (* (* v v) 3) 1))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (* (sqrt (+ (* (* (* v v) -9) (* v v)) 1)) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))))) (sqrt (- (* (* (sqrt 2) 4) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* (sqrt (- 1 (* (* v v) 3))) (* (* v v) (sqrt 2))) (* 4 (sqrt (+ (* (* v v) 3) 1))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (50 enodes) * * [misc]simplify: iters left: 1 (75 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 16)) (sqrt (+ 16 (* 48 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (* (sqrt (+ (* (* (* v v) -9) (* v v)) 1)) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))))) (sqrt (- (* (* (sqrt 2) 4) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* (sqrt (- 1 (* (* v v) 3))) (* (* v v) (sqrt 2))) (* 4 (sqrt (+ (* (* v v) 3) 1))))))) (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 16)) (sqrt (+ 16 (* 48 (* v v))))))) * * * * [misc]progress: [ 189 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (395 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* v v) (sqrt 2)))))) (sqrt (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (* (- v) (* v (sqrt 2))) (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* v v) (sqrt 2)))))) (sqrt (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (* (- v) (* v (sqrt 2))) (sqrt 2)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (180 enodes) * * [misc]simplify: iters left: 2 (338 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (+ 4 (* (* v v) 12)))) (sqrt (+ (* (* (* v v) (* v v)) 36) (+ 4 (* (* v v) 12))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* v v) (sqrt 2)))))) (sqrt (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (* (- v) (* v (sqrt 2))) (sqrt 2)))))) (* (sqrt (* 4 (+ 4 (* (* v v) 12)))) (sqrt (+ (* (* (* v v) (* v v)) 36) (+ 4 (* (* v v) 12))))))) * * * * [misc]progress: [ 190 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (108 enodes) * * [misc]simplify: iters left: 4 (339 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))))) (sqrt (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (sqrt 2) (* (- (* v v)) (sqrt 2)))) (* 4 (sqrt (+ (* (* 3 v) v) 1)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))))) (sqrt (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (sqrt 2) (* (- (* v v)) (sqrt 2)))) (* 4 (sqrt (+ (* (* 3 v) v) 1)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (101 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (262 enodes) * * [misc]simplify: iters left: 1 (353 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (sqrt (+ (* (pow v 4) 9) (+ (* v (* 3 v)) 1))))) (sqrt (+ 16 (* (* v v) 48)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))))) (sqrt (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (sqrt 2) (* (- (* v v)) (sqrt 2)))) (* 4 (sqrt (+ (* (* 3 v) v) 1)))))) (* (sqrt (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (sqrt (+ (* (pow v 4) 9) (+ (* v (* 3 v)) 1))))) (sqrt (+ 16 (* (* v v) 48)))))) * * * * [misc]progress: [ 191 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (112 enodes) * * [misc]simplify: iters left: 4 (359 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (/ (sqrt 2) 4)) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))))) (sqrt (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (/ (sqrt 2) 4)) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))))) (sqrt (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (167 enodes) * * [misc]simplify: iters left: 2 (299 enodes) * * [misc]simplify: iters left: 1 (383 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* 9 (pow v 4)) (+ (* (* 3 v) v) 1))) (sqrt (+ 16 (* (* v v) 48)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (/ (sqrt 2) 4)) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))))) (sqrt (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2)))))) (* (sqrt (+ (* 9 (pow v 4)) (+ (* (* 3 v) v) 1))) (sqrt (+ 16 (* (* v v) 48)))))) * * * * [misc]progress: [ 192 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (378 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (+ (* (- (* v v)) (sqrt 2)) (sqrt 2))) (* 4 (sqrt (+ (* 3 (* v v)) 1))))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (+ (* (- (* v v)) (sqrt 2)) (sqrt 2))) (* 4 (sqrt (+ (* 3 (* v v)) 1))))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (151 enodes) * * [misc]simplify: iters left: 2 (264 enodes) * * [misc]simplify: iters left: 1 (386 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt (+ (* (pow v 4) 9) (+ (* v (* 3 v)) 1))))) (sqrt (+ 16 (* 48 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (+ (* (- (* v v)) (sqrt 2)) (sqrt 2))) (* 4 (sqrt (+ (* 3 (* v v)) 1))))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)))))) (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt (+ (* (pow v 4) 9) (+ (* v (* 3 v)) 1))))) (sqrt (+ 16 (* 48 (* v v))))))) * * * * [misc]progress: [ 193 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (119 enodes) * * [misc]simplify: iters left: 4 (377 enodes) * [exit]simplify: Simplified to (* (sqrt (* (+ (- (* v v)) 1) (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* -3 v)) 1))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (+ (- (* v v)) 1) (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* -3 v)) 1))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (151 enodes) * * [misc]simplify: iters left: 2 (264 enodes) * * [misc]simplify: iters left: 1 (386 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ (* (pow v 4) 9) (+ (* v (* 3 v)) 1))))) (sqrt (+ 16 (* (* v v) 48)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (+ (- (* v v)) 1) (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* -3 v)) 1))))))) (* (sqrt (* 4 (sqrt (+ (* (pow v 4) 9) (+ (* v (* 3 v)) 1))))) (sqrt (+ 16 (* (* v v) 48)))))) * * * * [misc]progress: [ 194 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (117 enodes) * * [misc]simplify: iters left: 4 (376 enodes) * [exit]simplify: Simplified to (* (sqrt (- (/ (* 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))) (/ (/ 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (sqrt 2) (sqrt (+ 1 (* (* v v) 3))))) (* v v)))) (sqrt (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (sqrt 2) (* (- (* v v)) (sqrt 2)))) (* (sqrt (+ 1 (* (* v v) 3))) 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (/ (* 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))) (/ (/ 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (sqrt 2) (sqrt (+ 1 (* (* v v) 3))))) (* v v)))) (sqrt (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (sqrt 2) (* (- (* v v)) (sqrt 2)))) (* (sqrt (+ 1 (* (* v v) 3))) 4)))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (102 enodes) * * [misc]simplify: iters left: 3 (189 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (429 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 16 (* (* v v) 48))) (sqrt (* (* (sqrt (+ (* 3 (* v v)) 1)) 4) (sqrt (+ (* (pow v 4) 9) (+ (* 3 (* v v)) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (/ (* 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))) (/ (/ 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (sqrt 2) (sqrt (+ 1 (* (* v v) 3))))) (* v v)))) (sqrt (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (sqrt 2) (* (- (* v v)) (sqrt 2)))) (* (sqrt (+ 1 (* (* v v) 3))) 4)))) (* (sqrt (+ 16 (* (* v v) 48))) (sqrt (* (* (sqrt (+ (* 3 (* v v)) 1)) 4) (sqrt (+ (* (pow v 4) 9) (+ (* 3 (* v v)) 1)))))))) * * * * [misc]progress: [ 195 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (31 enodes) * * [misc]simplify: iters left: 5 (78 enodes) * * [misc]simplify: iters left: 4 (235 enodes) * [exit]simplify: Simplified to (* (sqrt (- (/ (* (* (sqrt (+ (* (* v v) 3) 1)) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) 1) (* (* (* (sqrt (+ (* (* v v) 3) 1)) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* v v)))) (sqrt (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (* (- (* v v)) (sqrt 2)) (sqrt 2))) (* (sqrt (+ (* (* v v) 3) 1)) 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (/ (* (* (sqrt (+ (* (* v v) 3) 1)) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) 1) (* (* (* (sqrt (+ (* (* v v) 3) 1)) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* v v)))) (sqrt (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (* (- (* v v)) (sqrt 2)) (sqrt 2))) (* (sqrt (+ (* (* v v) 3) 1)) 4)))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * * [misc]simplify: iters left: 2 (51 enodes) * * [misc]simplify: iters left: 1 (76 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 4 (* v (* v 12)))) (sqrt (+ 16 (* 48 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (/ (* (* (sqrt (+ (* (* v v) 3) 1)) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) 1) (* (* (* (sqrt (+ (* (* v v) 3) 1)) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* v v)))) (sqrt (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (* (- (* v v)) (sqrt 2)) (sqrt 2))) (* (sqrt (+ (* (* v v) 3) 1)) 4)))) (* (sqrt (+ 4 (* v (* v 12)))) (sqrt (+ 16 (* 48 (* v v))))))) * * * * [misc]progress: [ 196 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (375 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ 1 (* (* v v) 3)))))) (sqrt (- (/ (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)) (/ 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ 1 (* (* v v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ 1 (* (* v v) 3)))))) (sqrt (- (/ (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)) (/ 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ 1 (* (* v v) 3)))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (151 enodes) * * [misc]simplify: iters left: 2 (264 enodes) * * [misc]simplify: iters left: 1 (386 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt (+ (* (pow v 4) 9) (+ (* v (* 3 v)) 1))))) (sqrt (+ 16 (* 48 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ 1 (* (* v v) 3)))))) (sqrt (- (/ (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)) (/ 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ 1 (* (* v v) 3)))))))) (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt (+ (* (pow v 4) 9) (+ (* v (* 3 v)) 1))))) (sqrt (+ 16 (* 48 (* v v))))))) * * * * [misc]progress: [ 197 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (82 enodes) * * [misc]simplify: iters left: 4 (256 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* (* v v) 3) 1)) 4) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (+ (sqrt 2) (* (* (- v) v) (sqrt 2)))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (* (* v v) 3) 1))) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* v v) (* (* (/ (sqrt 2) 4) (sqrt (+ (* (* v v) 3) 1))) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* (* v v) 3) 1)) 4) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (+ (sqrt 2) (* (* (- v) v) (sqrt 2)))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (* (* v v) 3) 1))) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* v v) (* (* (/ (sqrt 2) 4) (sqrt (+ (* (* v v) 3) 1))) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (74 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* (* v v) 3))) (sqrt (+ 16 (* (* (* v v) 3) 16)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* (* v v) 3) 1)) 4) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (+ (sqrt 2) (* (* (- v) v) (sqrt 2)))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (* (* v v) 3) 1))) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* v v) (* (* (/ (sqrt 2) 4) (sqrt (+ (* (* v v) 3) 1))) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))))))) (* (sqrt (+ 1 (* (* v v) 3))) (sqrt (+ 16 (* (* (* v v) 3) 16)))))) * * * * [misc]progress: [ 198 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (90 enodes) * * [misc]simplify: iters left: 4 (279 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt 2) (sqrt (- 1 (* (* v v) 3)))) (* (* v v) (sqrt (+ (* (* v v) 3) 1)))))) (sqrt (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (* (sqrt 2) (- (* v v))) (sqrt 2))) (* (sqrt (+ (* (* v v) 3) 1)) 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt 2) (sqrt (- 1 (* (* v v) 3)))) (* (* v v) (sqrt (+ (* (* v v) 3) 1)))))) (sqrt (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (* (sqrt 2) (- (* v v))) (sqrt 2))) (* (sqrt (+ (* (* v v) 3) 1)) 4)))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (50 enodes) * * [misc]simplify: iters left: 1 (75 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 4)) (sqrt (+ 16 (* 48 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt 2) (sqrt (- 1 (* (* v v) 3)))) (* (* v v) (sqrt (+ (* (* v v) 3) 1)))))) (sqrt (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (* (sqrt 2) (- (* v v))) (sqrt 2))) (* (sqrt (+ (* (* v v) 3) 1)) 4)))) (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 4)) (sqrt (+ 16 (* 48 (* v v))))))) * * * * [misc]progress: [ 199 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (383 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (sqrt 2) (- (* (* v v) (sqrt 2))))))) (sqrt (- (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* v (* -3 v)))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (sqrt 2)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (sqrt 2) (- (* (* v v) (sqrt 2))))))) (sqrt (- (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* v (* -3 v)))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (53 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (177 enodes) * * [misc]simplify: iters left: 2 (307 enodes) * * [misc]simplify: iters left: 1 (387 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* v v) 48) 16)) (sqrt (* (sqrt (+ (* (pow v 4) 9) (+ (* 3 (* v v)) 1))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (sqrt 2) (- (* (* v v) (sqrt 2))))))) (sqrt (- (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* v (* -3 v)))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (+ (* (* v v) 48) 16)) (sqrt (* (sqrt (+ (* (pow v 4) 9) (+ (* 3 (* v v)) 1))) 16))))) * * * * [misc]progress: [ 200 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (82 enodes) * * [misc]simplify: iters left: 4 (240 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* (* v v) 3) 1)) 4) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (+ (sqrt 2) (* (- v) (* v (sqrt 2))))))) (sqrt (+ (* (* (sqrt 2) (sqrt (+ 1 (* -3 (* v v))))) (* (sqrt (+ (* (* v v) 3) 1)) 4)) (* (* (* (sqrt 2) 4) (* (- v) v)) (sqrt (- 1 (* (* (* v v) (* v v)) 9))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* (* v v) 3) 1)) 4) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (+ (sqrt 2) (* (- v) (* v (sqrt 2))))))) (sqrt (+ (* (* (sqrt 2) (sqrt (+ 1 (* -3 (* v v))))) (* (sqrt (+ (* (* v v) 3) 1)) 4)) (* (* (* (sqrt 2) 4) (* (- v) v)) (sqrt (- 1 (* (* (* v v) (* v v)) 9))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * * [misc]simplify: iters left: 2 (58 enodes) * * [misc]simplify: iters left: 1 (92 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 16)) (sqrt (+ 16 (* 48 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* (* v v) 3) 1)) 4) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (+ (sqrt 2) (* (- v) (* v (sqrt 2))))))) (sqrt (+ (* (* (sqrt 2) (sqrt (+ 1 (* -3 (* v v))))) (* (sqrt (+ (* (* v v) 3) 1)) 4)) (* (* (* (sqrt 2) 4) (* (- v) v)) (sqrt (- 1 (* (* (* v v) (* v v)) 9))))))) (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 16)) (sqrt (+ 16 (* 48 (* v v))))))) * * * * [misc]progress: [ 201 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (119 enodes) * * [misc]simplify: iters left: 4 (383 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (* (- v) (* v (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ 1 (* (* v v) 3)))))) (sqrt (- (* (* (sqrt 2) (sqrt (+ (* -3 (* v v)) 1))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (* (- v) (* v (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ 1 (* (* v v) 3)))))) (sqrt (- (* (* (sqrt 2) (sqrt (+ (* -3 (* v v)) 1))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (151 enodes) * * [misc]simplify: iters left: 2 (264 enodes) * * [misc]simplify: iters left: 1 (386 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ (* (pow v 4) 9) (+ (* v (* 3 v)) 1))))) (sqrt (+ 16 (* (* v v) 48)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (* (- v) (* v (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ 1 (* (* v v) 3)))))) (sqrt (- (* (* (sqrt 2) (sqrt (+ (* -3 (* v v)) 1))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (* 4 (sqrt (+ (* (pow v 4) 9) (+ (* v (* 3 v)) 1))))) (sqrt (+ 16 (* (* v v) 48)))))) * * * * [misc]progress: [ 202 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (90 enodes) * * [misc]simplify: iters left: 4 (288 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (sqrt 2)) (sqrt (- 1 (* (* v v) 3)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (* (- (* v v)) (sqrt 2)) (sqrt 2))) (* 4 (sqrt (+ (* (* v v) 3) 1)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (sqrt 2)) (sqrt (- 1 (* (* v v) 3)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (* (- (* v v)) (sqrt 2)) (sqrt 2))) (* 4 (sqrt (+ (* (* v v) 3) 1)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (50 enodes) * * [misc]simplify: iters left: 1 (75 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 16 (* 48 (* v v)))) (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (sqrt 2)) (sqrt (- 1 (* (* v v) 3)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (* (- (* v v)) (sqrt 2)) (sqrt 2))) (* 4 (sqrt (+ (* (* v v) 3) 1)))))) (* (sqrt (+ 16 (* 48 (* v v)))) (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) 4))))) * * * * [misc]progress: [ 203 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (33 enodes) * * [misc]simplify: iters left: 5 (86 enodes) * * [misc]simplify: iters left: 4 (262 enodes) * [exit]simplify: Simplified to (* (sqrt (* (+ (- (* v v)) 1) (* (* 4 (sqrt 2)) (sqrt (+ (* (* v v) -3) 1))))) (sqrt (* (+ (- (* v v)) 1) (* (* (sqrt (+ (* v (* 3 v)) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (* (* (* v v) (* v v)) 9))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (+ (- (* v v)) 1) (* (* 4 (sqrt 2)) (sqrt (+ (* (* v v) -3) 1))))) (sqrt (* (+ (- (* v v)) 1) (* (* (sqrt (+ (* v (* 3 v)) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (* (* (* v v) (* v v)) 9))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 4))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * * [misc]simplify: iters left: 2 (51 enodes) * * [misc]simplify: iters left: 1 (76 enodes) * [exit]simplify: Simplified to (* 4 (sqrt (+ 16 (* 48 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (+ (- (* v v)) 1) (* (* 4 (sqrt 2)) (sqrt (+ (* (* v v) -3) 1))))) (sqrt (* (+ (- (* v v)) 1) (* (* (sqrt (+ (* v (* 3 v)) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (* (* (* v v) (* v v)) 9))))))) (* 4 (sqrt (+ 16 (* 48 (* v v))))))) * * * * [misc]progress: [ 204 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3)))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (95 enodes) * * [misc]simplify: iters left: 4 (343 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (- 1 (* (* v v) (* 9 (* v v))))) (+ (sqrt 2) (* (- v) (* v (sqrt 2))))) (* (sqrt (+ (* (* 3 v) v) 1)) 4))) (sqrt (- (pow (* (sqrt (+ (* -3 (* v v)) 1)) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* -3 (* v v)) 1))) 3)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* (* v v) (* 9 (* v v))))) (+ (sqrt 2) (* (- v) (* v (sqrt 2))))) (* (sqrt (+ (* (* 3 v) v) 1)) 4))) (sqrt (- (pow (* (sqrt (+ (* -3 (* v v)) 1)) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* -3 (* v v)) 1))) 3)))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (75 enodes) * * [misc]simplify: iters left: 4 (241 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* (- (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* -3 v)) 1))) (* (sqrt (+ (* v (* -3 v)) 1)) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))) (* (* (sqrt (+ (* v (* -3 v)) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* v (* -3 v)) 1)) (/ (sqrt 2) 4))))) (sqrt (* (+ 1 (* 3 (* v v))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* (* v v) (* 9 (* v v))))) (+ (sqrt 2) (* (- v) (* v (sqrt 2))))) (* (sqrt (+ (* (* 3 v) v) 1)) 4))) (sqrt (- (pow (* (sqrt (+ (* -3 (* v v)) 1)) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* -3 (* v v)) 1))) 3)))) (* (sqrt (+ (* (* (* (- (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* -3 v)) 1))) (* (sqrt (+ (* v (* -3 v)) 1)) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))) (* (* (sqrt (+ (* v (* -3 v)) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* v (* -3 v)) 1)) (/ (sqrt 2) 4))))) (sqrt (* (+ 1 (* 3 (* v v))) 16))))) * * * * [misc]progress: [ 205 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (96 enodes) * * [misc]simplify: iters left: 4 (339 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (* (sqrt (+ (* (* (* v v) -9) (* v v)) 1)) (+ (* v (* (- v) (sqrt 2))) (sqrt 2))))) (sqrt (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))) (* (sqrt (+ (* (* v -3) v) 1)) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (- (* v v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (* (sqrt (+ (* (* (* v v) -9) (* v v)) 1)) (+ (* v (* (- v) (sqrt 2))) (sqrt 2))))) (sqrt (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))) (* (sqrt (+ (* (* v -3) v) 1)) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (- (* v v)))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (56 enodes) * * [misc]simplify: iters left: 4 (143 enodes) * * [misc]simplify: iters left: 3 (433 enodes) * [exit]simplify: Simplified to (* (sqrt (* (+ 1 (* (* v v) 3)) 16)) (sqrt (* (/ (* (sqrt 2) (+ 1 (* v v))) 4) (sqrt (+ (* (* -3 v) v) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (* (sqrt (+ (* (* (* v v) -9) (* v v)) 1)) (+ (* v (* (- v) (sqrt 2))) (sqrt 2))))) (sqrt (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))) (* (sqrt (+ (* (* v -3) v) 1)) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (- (* v v)))))))) (* (sqrt (* (+ 1 (* (* v v) 3)) 16)) (sqrt (* (/ (* (sqrt 2) (+ 1 (* v v))) 4) (sqrt (+ (* (* -3 v) v) 1))))))) * * * * [misc]progress: [ 206 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (117 enodes) * * [misc]simplify: iters left: 4 (389 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* 3 (* v v)) 1)) 4) (* v v))))) (sqrt (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* 3 (* v v)) 1)) 4) (* v v))))) (sqrt (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (101 enodes) * * [misc]simplify: iters left: 3 (154 enodes) * * [misc]simplify: iters left: 2 (269 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) (* (pow v 3) (* v 9))) 1)) (* (sqrt (+ (* (* v v) 3) 1)) 4))) (sqrt (+ 16 (* 16 (+ (* (* v v) 3) (* (pow v 3) (* v 9))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* 3 (* v v)) 1)) 4) (* v v))))) (sqrt (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2)))))) (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) (* (pow v 3) (* v 9))) 1)) (* (sqrt (+ (* (* v v) 3) 1)) 4))) (sqrt (+ 16 (* 16 (+ (* (* v v) 3) (* (pow v 3) (* v 9))))))))) * * * * [misc]progress: [ 207 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (119 enodes) * * [misc]simplify: iters left: 4 (408 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* v v)) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (/ (sqrt 2) 4))))) (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (sqrt (+ (* (* 3 v) v) 1))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* v v)) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (/ (sqrt 2) 4))))) (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (sqrt (+ (* (* 3 v) v) 1))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) 4))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (106 enodes) * * [misc]simplify: iters left: 3 (161 enodes) * * [misc]simplify: iters left: 2 (248 enodes) * * [misc]simplify: iters left: 1 (288 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 4))) (sqrt (* (* (sqrt (+ (* v (* 3 v)) 1)) 16) (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* v v)) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (/ (sqrt 2) 4))))) (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (sqrt (+ (* (* 3 v) v) 1))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) 4))))) (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 4))) (sqrt (* (* (sqrt (+ (* v (* 3 v)) 1)) 16) (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1))))))) * * * * [misc]progress: [ 208 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (110 enodes) * * [misc]simplify: iters left: 4 (357 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (sqrt 2))))) (sqrt (- (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (sqrt 2))))) (sqrt (- (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3)))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (194 enodes) * * [misc]simplify: iters left: 2 (386 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (* v 9) (pow v 3))) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 4))) (sqrt (+ (* (* v v) (* 36 (* v v))) (+ (* v (* 12 v)) 4)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (sqrt 2))))) (sqrt (- (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3)))))))) (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (* v 9) (pow v 3))) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 4))) (sqrt (+ (* (* v v) (* 36 (* v v))) (+ (* v (* 12 v)) 4)))))) * * * * [misc]progress: [ 209 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (426 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* 4 (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* v v) (/ (sqrt 2) 4)))))) (sqrt (- (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* 3 v) v) 1)) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* 4 (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* v v) (/ (sqrt 2) 4)))))) (sqrt (- (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* 3 v) v) 1)) 4)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (226 enodes) * * [misc]simplify: iters left: 1 (265 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 4)) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* 4 (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* v v) (/ (sqrt 2) 4)))))) (sqrt (- (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* 3 v) v) 1)) 4)))))) (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 4)))) * * * * [misc]progress: [ 210 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (123 enodes) * * [misc]simplify: iters left: 4 (415 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (* v v) (/ (sqrt 2) 4))) (* (sqrt (+ (* v (* 3 v)) 1)) 4)))) (sqrt (+ (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt (- 1 (* v (* 3 v)))) (* (* (sqrt 2) (- (* v v))) 4))) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* 4 (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (* v v) (/ (sqrt 2) 4))) (* (sqrt (+ (* v (* 3 v)) 1)) 4)))) (sqrt (+ (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt (- 1 (* v (* 3 v)))) (* (* (sqrt 2) (- (* v v))) 4))) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* 4 (sqrt 2)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (241 enodes) * * [misc]simplify: iters left: 1 (301 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 4))) (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (* v v) (/ (sqrt 2) 4))) (* (sqrt (+ (* v (* 3 v)) 1)) 4)))) (sqrt (+ (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt (- 1 (* v (* 3 v)))) (* (* (sqrt 2) (- (* v v))) 4))) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* 4 (sqrt 2)))))) (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 4))) (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) 16))))) * * * * [misc]progress: [ 211 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (371 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* 4 (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* v v) (sqrt 2))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (/ (sqrt 2) 4) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* 4 (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* v v) (sqrt 2))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (/ (sqrt 2) 4) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (104 enodes) * * [misc]simplify: iters left: 3 (181 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * * [misc]simplify: iters left: 1 (309 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* 9 (pow v 4))) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 4))) (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* 9 (pow v 4))) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 16)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* 4 (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* v v) (sqrt 2))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (/ (sqrt 2) 4) (* v v)))))) (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* 9 (pow v 4))) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 4))) (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* 9 (pow v 4))) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 16)))))) * * * * [misc]progress: [ 212 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (111 enodes) * * [misc]simplify: iters left: 4 (373 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (/ (sqrt 2) 4) (* v v))))) (sqrt (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (sqrt 2) (- (* (* v v) (sqrt 2)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (/ (sqrt 2) 4) (* v v))))) (sqrt (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (sqrt 2) (- (* (* v v) (sqrt 2)))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (101 enodes) * * [misc]simplify: iters left: 3 (154 enodes) * * [misc]simplify: iters left: 2 (261 enodes) * * [misc]simplify: iters left: 1 (353 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* 9 (pow v 4))) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 4))) (sqrt (+ (* 48 (* v v)) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (/ (sqrt 2) 4) (* v v))))) (sqrt (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (sqrt 2) (- (* (* v v) (sqrt 2)))))))) (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* 9 (pow v 4))) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 4))) (sqrt (+ (* 48 (* v v)) 16))))) * * * * [misc]progress: [ 213 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (90 enodes) * * [misc]simplify: iters left: 4 (276 enodes) * [exit]simplify: Simplified to (- (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (/ (sqrt 2) 4)) (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* v v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (/ (sqrt 2) 4)) (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* v v)))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (135 enodes) * * [misc]simplify: iters left: 2 (224 enodes) * * [misc]simplify: iters left: 1 (260 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ (* 3 (* v v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* 3 (* v v)) 1)) 4)) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (/ (sqrt 2) 4)) (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* v v)))) (* (sqrt (+ (+ (* 3 (* v v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* 3 (* v v)) 1)) 4)))) * * * * [misc]progress: [ 214 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (113 enodes) * * [misc]simplify: iters left: 4 (401 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt 2) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (/ (sqrt 2) 4)) (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* v v))))) (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (+ (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (* (- v) v) (/ (sqrt 2) 4)) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt 2) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (/ (sqrt 2) 4)) (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* v v))))) (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (+ (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (* (- v) v) (/ (sqrt 2) 4)) 4)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (173 enodes) * * [misc]simplify: iters left: 2 (314 enodes) * * [misc]simplify: iters left: 1 (424 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* (* v v) 3) 1)) 4))) (sqrt (+ (* 12 (* v v)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt 2) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (/ (sqrt 2) 4)) (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* v v))))) (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (+ (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (* (- v) v) (/ (sqrt 2) 4)) 4)))))) (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* (* v v) 3) 1)) 4))) (sqrt (+ (* 12 (* v v)) 4))))) * * * * [misc]progress: [ 215 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (386 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (/ (sqrt 2) 4) v)) (* v (* (sqrt (+ (* (* 3 v) v) 1)) 4))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (+ (* (* 3 v) v) 1)) (* 4 (sqrt 2))) (* (sqrt (- 1 (* (* 3 v) v))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (/ (sqrt 2) 4) v)) (* v (* (sqrt (+ (* (* 3 v) v) 1)) 4))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (+ (* (* 3 v) v) 1)) (* 4 (sqrt 2))) (* (sqrt (- 1 (* (* 3 v) v))) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (163 enodes) * * [misc]simplify: iters left: 2 (263 enodes) * * [misc]simplify: iters left: 1 (293 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) (* 9 (pow v 4))) 1)) (* (sqrt (+ (* (* v v) 3) 1)) 4))) (sqrt (* (sqrt (+ (* (* v v) 3) 1)) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (/ (sqrt 2) 4) v)) (* v (* (sqrt (+ (* (* 3 v) v) 1)) 4))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (+ (* (* 3 v) v) 1)) (* 4 (sqrt 2))) (* (sqrt (- 1 (* (* 3 v) v))) (* v v)))))) (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) (* 9 (pow v 4))) 1)) (* (sqrt (+ (* (* v v) 3) 1)) 4))) (sqrt (* (sqrt (+ (* (* v v) 3) 1)) 16))))) * * * * [misc]progress: [ 216 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (383 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt 2) (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* (* (sqrt (+ (* (* 3 v) v) 1)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* v v)))) (sqrt (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (sqrt 2) (- (* v v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt 2) (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* (* (sqrt (+ (* (* 3 v) v) 1)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* v v)))) (sqrt (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (sqrt 2) (- (* v v)))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (254 enodes) * * [misc]simplify: iters left: 1 (418 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 4))) (sqrt (+ (+ 4 (* (pow v 3) (* 36 v))) (* (* v v) 12)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt 2) (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* (* (sqrt (+ (* (* 3 v) v) 1)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* v v)))) (sqrt (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (sqrt 2) (- (* v v)))))))) (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 4))) (sqrt (+ (+ 4 (* (pow v 3) (* 36 v))) (* (* v v) 12)))))) * * * * [misc]progress: [ 217 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (112 enodes) * * [misc]simplify: iters left: 4 (361 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (+ (* (* 3 v) v) 1)) 4)))) (sqrt (- (* (sqrt (+ (* (* 3 v) v) 1)) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (+ (* (* 3 v) v) 1)) 4)))) (sqrt (- (* (sqrt (+ (* (* 3 v) v) 1)) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (136 enodes) * * [misc]simplify: iters left: 2 (225 enodes) * * [misc]simplify: iters left: 1 (260 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ (* (* 3 v) v) (* 9 (pow v 4))) 1)) (* (sqrt (+ (* (* 3 v) v) 1)) 4)) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (+ (* (* 3 v) v) 1)) 4)))) (sqrt (- (* (sqrt (+ (* (* 3 v) v) 1)) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))))))) (* (sqrt (+ (+ (* (* 3 v) v) (* 9 (pow v 4))) 1)) (* (sqrt (+ (* (* 3 v) v) 1)) 4)))) * * * * [misc]progress: [ 218 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (104 enodes) * * [misc]simplify: iters left: 4 (315 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt 2) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))))) (* (* v v) (* (* (sqrt (+ (* v (* 3 v)) 1)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* v (* 3 v)) 3))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (* v (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* v (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v)))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt 2) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))))) (* (* v v) (* (* (sqrt (+ (* v (* 3 v)) 1)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* v (* 3 v)) 3))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (* v (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* v (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v)))))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (85 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (230 enodes) * * [misc]simplify: iters left: 1 (269 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* 9 (pow v 4))) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 4))) (sqrt (+ (+ (* v (* 3 v)) (* 9 (pow v 4))) 1))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt 2) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))))) (* (* v v) (* (* (sqrt (+ (* v (* 3 v)) 1)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* v (* 3 v)) 3))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (* v (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* v (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v)))))))))) (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* 9 (pow v 4))) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 4))) (sqrt (+ (+ (* v (* 3 v)) (* 9 (pow v 4))) 1))))) * * * * [misc]progress: [ 219 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (396 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* v v) (/ (sqrt 2) 4))))) (sqrt (- (* (sqrt 2) (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* 4 (sqrt (+ (* (* 3 v) v) 1))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* v v) (/ (sqrt 2) 4))))) (sqrt (- (* (sqrt 2) (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* 4 (sqrt (+ (* (* 3 v) v) 1))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (224 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* 3 v) v) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* (* 3 v) v) 1)) 4))) (sqrt (* (sqrt (+ (+ (* (* 3 v) v) (* (pow v 4) 9)) 1)) (sqrt (+ (* (* 3 v) v) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* v v) (/ (sqrt 2) 4))))) (sqrt (- (* (sqrt 2) (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* 4 (sqrt (+ (* (* 3 v) v) 1))))))) (* (sqrt (* (sqrt (+ (+ (* (* 3 v) v) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* (* 3 v) v) 1)) 4))) (sqrt (* (sqrt (+ (+ (* (* 3 v) v) (* (pow v 4) 9)) 1)) (sqrt (+ (* (* 3 v) v) 1))))))) * * * * [misc]progress: [ 220 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (383 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* 3 (* v v)))) (* (* v v) (sqrt 2))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (- (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* 3 (* v v)))) (* (* v v) (sqrt 2))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (- (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* v v))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (254 enodes) * * [misc]simplify: iters left: 1 (280 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* (* v v) 3) 1)) 4))) (sqrt (* 4 (sqrt (+ (+ (* (* v v) 3) (* (pow v 4) 9)) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* 3 (* v v)))) (* (* v v) (sqrt 2))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (- (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* v v))))) (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* (* v v) 3) 1)) 4))) (sqrt (* 4 (sqrt (+ (+ (* (* v v) 3) (* (pow v 4) 9)) 1))))))) * * * * [misc]progress: [ 221 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (375 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* v v) 3) 1)))))) (sqrt (- (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (* v v) (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* v v) 3) 1)))))) (sqrt (- (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (* v v) (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (229 enodes) * * [misc]simplify: iters left: 1 (268 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 4)) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* v v) 3) 1)))))) (sqrt (- (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (* v v) (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))))))) (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 4)))) * * * * [misc]progress: [ 222 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (386 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))))) (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt 2) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (* (sqrt 2) (* v v)) 4)) (* 4 (sqrt (+ (* 3 (* v v)) 1))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))))) (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt 2) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (* (sqrt 2) (* v v)) 4)) (* 4 (sqrt (+ (* 3 (* v v)) 1))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (277 enodes) * * [misc]simplify: iters left: 1 (344 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* (* v v) 3) 1)) 4))) (sqrt (+ 4 (* (* v v) 12)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))))) (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt 2) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (* (sqrt 2) (* v v)) 4)) (* 4 (sqrt (+ (* 3 (* v v)) 1))))))) (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* (* v v) 3) 1)) 4))) (sqrt (+ 4 (* (* v v) 12)))))) * * * * [misc]progress: [ 223 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (106 enodes) * * [misc]simplify: iters left: 4 (319 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (* (sqrt (+ (* (* v v) 3) 1)) 4))))) (sqrt (- (/ (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (/ 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ (* (* v v) 3) 1))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (* (sqrt (+ (* (* v v) 3) 1)) 4))))) (sqrt (- (/ (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (/ 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ (* (* v v) 3) 1))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (224 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* 3 v) v) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* (* 3 v) v) 1)) 4))) (sqrt (* (sqrt (+ (+ (* (* 3 v) v) (* (pow v 4) 9)) 1)) (sqrt (+ (* (* 3 v) v) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (* (sqrt (+ (* (* v v) 3) 1)) 4))))) (sqrt (- (/ (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (/ 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ (* (* v v) 3) 1))))))) (* (sqrt (* (sqrt (+ (+ (* (* 3 v) v) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* (* 3 v) v) 1)) 4))) (sqrt (* (sqrt (+ (+ (* (* 3 v) v) (* (pow v 4) 9)) 1)) (sqrt (+ (* (* 3 v) v) 1))))))) * * * * [misc]progress: [ 224 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (113 enodes) * * [misc]simplify: iters left: 4 (373 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ (* (sqrt 2) (* v v)) 4)) (* 4 (sqrt (+ (* (* v v) 3) 1))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ (* (sqrt 2) (* v v)) 4)) (* 4 (sqrt (+ (* (* v v) 3) 1))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (148 enodes) * * [misc]simplify: iters left: 2 (253 enodes) * * [misc]simplify: iters left: 1 (351 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt (* (* 4 (sqrt (+ (* v (* 3 v)) 1))) (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ (* (sqrt 2) (* v v)) 4)) (* 4 (sqrt (+ (* (* v v) 3) 1))))))) (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt (* (* 4 (sqrt (+ (* v (* 3 v)) 1))) (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1))))))) * * * * [misc]progress: [ 225 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (385 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (- 1 (* 3 (* v v)))) (sqrt (+ (* 3 (* v v)) 1))) (* (* v v) (sqrt 2))))) (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* 3 (* v v)) 1)) 4) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (- 1 (* 3 (* v v)))) (sqrt (+ (* 3 (* v v)) 1))) (* (* v v) (sqrt 2))))) (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* 3 (* v v)) 1)) 4) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (224 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* 3 v) v) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* (* 3 v) v) 1)) 4))) (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (- 1 (* 3 (* v v)))) (sqrt (+ (* 3 (* v v)) 1))) (* (* v v) (sqrt 2))))) (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* 3 (* v v)) 1)) 4) (* v v)))))) (* (sqrt (* (sqrt (+ (+ (* (* 3 v) v) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* (* 3 v) v) 1)) 4))) (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) 4))))) * * * * [misc]progress: [ 226 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (122 enodes) * * [misc]simplify: iters left: 4 (381 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (/ (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ 4 (* (sqrt 2) (* v v)))) (* (sqrt (+ (* (* v v) 3) 1)) 4)))) (sqrt (- (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (sqrt 2) (* v v)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (/ (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ 4 (* (sqrt 2) (* v v)))) (* (sqrt (+ (* (* v v) 3) 1)) 4)))) (sqrt (- (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (sqrt 2) (* v v)) 4))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (242 enodes) * * [misc]simplify: iters left: 1 (304 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 4))) (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (/ (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ 4 (* (sqrt 2) (* v v)))) (* (sqrt (+ (* (* v v) 3) 1)) 4)))) (sqrt (- (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (sqrt 2) (* v v)) 4))))) (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 4))) (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) 16))))) * * * * [misc]progress: [ 227 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (386 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (sqrt 2) (sqrt (- 1 (* (* v v) 3)))) (* (sqrt (+ (* (* v v) 3) 1)) 4)) (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* v v) 3) 1)) 4) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt 2) (sqrt (- 1 (* (* v v) 3)))) (* (sqrt (+ (* (* v v) 3) 1)) 4)) (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* v v) 3) 1)) 4) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (257 enodes) * * [misc]simplify: iters left: 1 (280 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) (* 9 (pow v 4))) 1)) (* (sqrt (+ (* (* v v) 3) 1)) 4))) (sqrt (* 16 (sqrt (+ (* (* v v) 3) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt 2) (sqrt (- 1 (* (* v v) 3)))) (* (sqrt (+ (* (* v v) 3) 1)) 4)) (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* v v) 3) 1)) 4) (* v v)))))) (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) (* 9 (pow v 4))) 1)) (* (sqrt (+ (* (* v v) 3) 1)) 4))) (sqrt (* 16 (sqrt (+ (* (* v v) 3) 1))))))) * * * * [misc]progress: [ 228 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (111 enodes) * * [misc]simplify: iters left: 4 (334 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2))) (* (* v v) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (sqrt (+ (* 3 (* v v)) 1)) (/ (* 4 (sqrt 2)) 4)))))) (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt 2) (sqrt (+ 1 (* -3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2))) (* (* v v) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (sqrt (+ (* 3 (* v v)) 1)) (/ (* 4 (sqrt 2)) 4)))))) (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt 2) (sqrt (+ 1 (* -3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (254 enodes) * * [misc]simplify: iters left: 1 (280 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* (* v v) 3) 1)) 4))) (sqrt (* 4 (sqrt (+ (+ (* (* v v) 3) (* (pow v 4) 9)) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2))) (* (* v v) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (sqrt (+ (* 3 (* v v)) 1)) (/ (* 4 (sqrt 2)) 4)))))) (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt 2) (sqrt (+ 1 (* -3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* (* v v) 3) 1)) 4))) (sqrt (* 4 (sqrt (+ (+ (* (* v v) 3) (* (pow v 4) 9)) 1))))))) * * * * [misc]progress: [ 229 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (403 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt 2)) (sqrt (- 1 (* (* 3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* (sqrt 2) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (/ (sqrt 2) 4)) (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt 2)) (sqrt (- 1 (* (* 3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* (sqrt 2) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (/ (sqrt 2) 4)) (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (262 enodes) * * [misc]simplify: iters left: 1 (285 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 4))) (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt 2)) (sqrt (- 1 (* (* 3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* (sqrt 2) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (/ (sqrt 2) 4)) (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* v v)))))) (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 4))) (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) 4))))) * * * * [misc]progress: [ 230 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (117 enodes) * * [misc]simplify: iters left: 4 (370 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt 2) (sqrt (+ 1 (* (* v -3) v)))) (+ (* (* 4 v) (- v)) 4))) (sqrt (- (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* v (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* v (* (sqrt (+ (* (* 3 v) v) 1)) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt 2) (sqrt (+ 1 (* (* v -3) v)))) (+ (* (* 4 v) (- v)) 4))) (sqrt (- (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* v (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* v (* (sqrt (+ (* (* 3 v) v) 1)) 4)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (231 enodes) * * [misc]simplify: iters left: 1 (270 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* 9 (pow v 4))) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 4))) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt 2) (sqrt (+ 1 (* (* v -3) v)))) (+ (* (* 4 v) (- v)) 4))) (sqrt (- (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* v (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* v (* (sqrt (+ (* (* 3 v) v) 1)) 4)))))) (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* 9 (pow v 4))) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 4))) 4))) * * * * [misc]progress: [ 231 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3)))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (124 enodes) * * [misc]simplify: iters left: 4 (443 enodes) * [exit]simplify: Simplified to (* (sqrt (* (+ (* (* (* v v) (* v v)) (- (* v v))) 1) (pow (* (/ (sqrt 2) 4) (sqrt (- 1 (* v (* 3 v))))) 3))) (sqrt (- (* (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (sqrt 2)) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* 9 (* v v)) (* v v))))) (* (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (/ (* (sqrt 2) (* v v)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (+ (* (* (* v v) (* v v)) (- (* v v))) 1) (pow (* (/ (sqrt 2) 4) (sqrt (- 1 (* v (* 3 v))))) 3))) (sqrt (- (* (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (sqrt 2)) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* 9 (* v v)) (* v v))))) (* (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (/ (* (sqrt 2) (* v v)) 4))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * * [misc]simplify: iters left: 6 (33 enodes) * * [misc]simplify: iters left: 5 (93 enodes) * * [misc]simplify: iters left: 4 (292 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) (* (sqrt (+ (* (* 3 v) v) 1)) 4))) (sqrt (+ (* (* (sqrt (+ (* v (* -3 v)) 1)) (- (* (/ (sqrt 2) 4) (- (* v v))) (/ (sqrt 2) 4))) (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (+ (* v (* -3 v)) 1)))) (* (* (sqrt (+ (* v (* -3 v)) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* v (* -3 v)) 1)) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (+ (* (* (* v v) (* v v)) (- (* v v))) 1) (pow (* (/ (sqrt 2) 4) (sqrt (- 1 (* v (* 3 v))))) 3))) (sqrt (- (* (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (sqrt 2)) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* 9 (* v v)) (* v v))))) (* (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (/ (* (sqrt 2) (* v v)) 4))))) (* (sqrt (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) (* (sqrt (+ (* (* 3 v) v) 1)) 4))) (sqrt (+ (* (* (sqrt (+ (* v (* -3 v)) 1)) (- (* (/ (sqrt 2) 4) (- (* v v))) (/ (sqrt 2) 4))) (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (+ (* v (* -3 v)) 1)))) (* (* (sqrt (+ (* v (* -3 v)) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* v (* -3 v)) 1)) (/ (sqrt 2) 4)))))))) * * * * [misc]progress: [ 232 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (126 enodes) * * [misc]simplify: iters left: 4 (443 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (* (+ 1 (* (- v) v)) (/ (sqrt 2) 4)) (sqrt (- 1 (* 3 (* v v))))) (* (sqrt (- 1 (* 3 (* v v)))) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (* (+ 1 (* (- v) v)) (/ (sqrt 2) 4)) (sqrt (- 1 (* 3 (* v v))))) (* (sqrt (- 1 (* 3 (* v v)))) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* v v))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (29 enodes) * * [misc]simplify: iters left: 5 (74 enodes) * * [misc]simplify: iters left: 4 (196 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ (* v (* 3 v)) 1))) (* (sqrt (+ (* v (* 3 v)) 1)) 4))) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* -3 v) v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (* (+ 1 (* (- v) v)) (/ (sqrt 2) 4)) (sqrt (- 1 (* 3 (* v v))))) (* (sqrt (- 1 (* 3 (* v v)))) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* v v))))) (* (sqrt (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ (* v (* 3 v)) 1))) (* (sqrt (+ (* v (* 3 v)) 1)) 4))) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* -3 v) v)))))))) * * * * [misc]progress: [ 233 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (410 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) 4) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (* (sqrt 2) (- (* v v))) (sqrt 2))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (+ (* (* v v) 3) 1)) 4)) (* (/ (sqrt 2) 4) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) 4) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (* (sqrt 2) (- (* v v))) (sqrt 2))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (+ (* (* v v) 3) 1)) 4)) (* (/ (sqrt 2) 4) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (98 enodes) * * [misc]simplify: iters left: 3 (167 enodes) * * [misc]simplify: iters left: 2 (321 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 4 (* (* v 12) v))) (sqrt (* (+ (* (* v 12) (* (* v v) (* 3 v))) (+ 4 (* (* v 12) v))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) 4) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (* (sqrt 2) (- (* v v))) (sqrt 2))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (+ (* (* v v) 3) 1)) 4)) (* (/ (sqrt 2) 4) (* v v)))))) (* (sqrt (+ 4 (* (* v 12) v))) (sqrt (* (+ (* (* v 12) (* (* v v) (* 3 v))) (+ 4 (* (* v 12) v))) 4))))) * * * * [misc]progress: [ 234 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (399 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* 4 (* (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* 4 (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))))))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (+ (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (* v (- v)) (/ (sqrt 2) 4)) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* 4 (* (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* 4 (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))))))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (+ (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (* v (- v)) (/ (sqrt 2) 4)) 4)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (207 enodes) * * [misc]simplify: iters left: 2 (373 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 4 (* (* v 12) v))) (sqrt (* (* (sqrt (+ (* v (* 3 v)) 1)) 16) (sqrt (+ (* (* 9 v) (pow v 3)) (+ (* v (* 3 v)) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* 4 (* (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* 4 (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))))))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (+ (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (* v (- v)) (/ (sqrt 2) 4)) 4)))))) (* (sqrt (+ 4 (* (* v 12) v))) (sqrt (* (* (sqrt (+ (* v (* 3 v)) 1)) 16) (sqrt (+ (* (* 9 v) (pow v 3)) (+ (* v (* 3 v)) 1)))))))) * * * * [misc]progress: [ 235 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (430 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt 2) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (sqrt (- 1 (pow (* (* v v) 3) 3))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (sqrt 2) 4) (* v v))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) 4)))) (sqrt (* (sqrt (+ (* (* v v) 3) 1)) (+ (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt 2) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (sqrt (- 1 (pow (* (* v v) 3) 3))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (sqrt 2) 4) (* v v))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) 4)))) (sqrt (* (sqrt (+ (* (* v v) 3) 1)) (+ (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (175 enodes) * * [misc]simplify: iters left: 2 (362 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* v v) 12) 4)) (sqrt (+ (* (* (* 9 v) (* v v)) (* v 4)) (+ (* (* v v) 12) 4)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt 2) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (sqrt (- 1 (pow (* (* v v) 3) 3))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (sqrt 2) 4) (* v v))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) 4)))) (sqrt (* (sqrt (+ (* (* v v) 3) 1)) (+ (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4)))))) (* (sqrt (+ (* (* v v) 12) 4)) (sqrt (+ (* (* (* 9 v) (* v v)) (* v 4)) (+ (* (* v v) 12) 4)))))) * * * * [misc]progress: [ 236 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (110 enodes) * * [misc]simplify: iters left: 4 (363 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* 4 (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (/ (sqrt 2) 4) (* v v)))))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (+ (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* 4 (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (/ (sqrt 2) 4) (* v v)))))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (+ (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (291 enodes) * * [misc]simplify: iters left: 1 (421 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* 12 v) v) 4)) (sqrt (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (sqrt (+ (* 9 (pow v 4)) (+ (* v (* 3 v)) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* 4 (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (/ (sqrt 2) 4) (* v v)))))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (+ (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4)))))) (* (sqrt (+ (* (* 12 v) v) 4)) (sqrt (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (sqrt (+ (* 9 (pow v 4)) (+ (* v (* 3 v)) 1)))))))) * * * * [misc]progress: [ 237 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (123 enodes) * * [misc]simplify: iters left: 4 (417 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (+ (* (* -3 v) v) 1)) (* (* (sqrt 2) (- (* v v))) 4))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (+ (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)) (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (+ (* (* -3 v) v) 1)) (* (* (sqrt 2) (- (* v v))) 4))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (+ (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)) (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * * [misc]simplify: iters left: 2 (280 enodes) * * [misc]simplify: iters left: 1 (386 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 4 (* 12 (* v v)))) (sqrt (* (sqrt (+ (* 9 (pow v 4)) (+ (* v (* 3 v)) 1))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (+ (* (* -3 v) v) 1)) (* (* (sqrt 2) (- (* v v))) 4))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (+ (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)) (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (+ 4 (* 12 (* v v)))) (sqrt (* (sqrt (+ (* 9 (pow v 4)) (+ (* v (* 3 v)) 1))) 16))))) * * * * [misc]progress: [ 238 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (414 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) 4) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2))) (* (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* v v) (sqrt 2))))) (sqrt (* (sqrt (+ 1 (* (* v v) 3))) (+ (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) 4) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2))) (* (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* v v) (sqrt 2))))) (sqrt (* (sqrt (+ 1 (* (* v v) 3))) (+ (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (207 enodes) * * [misc]simplify: iters left: 2 (371 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 4 (* (* v 12) v))) (sqrt (* (* (sqrt (+ (* v (* 3 v)) 1)) 16) (sqrt (+ (* (* 9 v) (pow v 3)) (+ (* v (* 3 v)) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) 4) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2))) (* (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* v v) (sqrt 2))))) (sqrt (* (sqrt (+ 1 (* (* v v) 3))) (+ (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4)))))) (* (sqrt (+ 4 (* (* v 12) v))) (sqrt (* (* (sqrt (+ (* v (* 3 v)) 1)) 16) (sqrt (+ (* (* 9 v) (pow v 3)) (+ (* v (* 3 v)) 1)))))))) * * * * [misc]progress: [ 239 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (31 enodes) * * [misc]simplify: iters left: 5 (82 enodes) * * [misc]simplify: iters left: 4 (290 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (sqrt 2) (* (- v) (* v (sqrt 2))))) (* (sqrt (+ (* (* 3 v) v) 1)) 4))) (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (+ (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)) (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (sqrt 2) (* (- v) (* v (sqrt 2))))) (* (sqrt (+ (* (* 3 v) v) 1)) 4))) (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (+ (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)) (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (111 enodes) * * [misc]simplify: iters left: 1 (151 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* v v) 48) 16)) (sqrt (+ (* (* v v) 12) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (sqrt 2) (* (- v) (* v (sqrt 2))))) (* (sqrt (+ (* (* 3 v) v) 1)) 4))) (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (+ (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)) (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))))))) (* (sqrt (+ (* (* v v) 48) 16)) (sqrt (+ (* (* v v) 12) 4))))) * * * * [misc]progress: [ 240 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (113 enodes) * * [misc]simplify: iters left: 4 (406 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ 1 (* (* v v) 3))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* v v))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (/ (sqrt 2) 4) (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ 1 (* (* v v) 3))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* v v))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (/ (sqrt 2) 4) (* v v))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (160 enodes) * * [misc]simplify: iters left: 2 (286 enodes) * * [misc]simplify: iters left: 1 (398 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* 3 (* v v)) 1)) 4) (sqrt (+ (* (pow v 4) 9) (+ (* 3 (* v v)) 1))))) (sqrt (+ 4 (* v (* v 12))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ 1 (* (* v v) 3))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* v v))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (/ (sqrt 2) 4) (* v v))))))) (* (sqrt (* (* (sqrt (+ (* 3 (* v v)) 1)) 4) (sqrt (+ (* (pow v 4) 9) (+ (* 3 (* v v)) 1))))) (sqrt (+ 4 (* v (* v 12))))))) * * * * [misc]progress: [ 241 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (62 enodes) * * [misc]simplify: iters left: 4 (202 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* v v) 3) 1)) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* v v) 3) 1)) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (52 enodes) * * [misc]simplify: iters left: 1 (61 enodes) * [exit]simplify: Simplified to (+ 4 (* v (* v 12))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* v v) 3) 1)) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))) (+ 4 (* v (* v 12))))) * * * * [misc]progress: [ 242 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (88 enodes) * * [misc]simplify: iters left: 4 (314 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) (+ (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (sqrt 2)) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4))))) (sqrt (+ (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* 4 (sqrt 2))) (* (* (- (* v v)) (sqrt (+ (* (* v v) -3) 1))) (* (sqrt (+ (* v (* 3 v)) 1)) (* 4 (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) (+ (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (sqrt 2)) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4))))) (sqrt (+ (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* 4 (sqrt 2))) (* (* (- (* v v)) (sqrt (+ (* (* v v) -3) 1))) (* (sqrt (+ (* v (* 3 v)) 1)) (* 4 (sqrt 2))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) 16)) (sqrt (+ 4 (* v (* 12 v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) (+ (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (sqrt 2)) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4))))) (sqrt (+ (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* 4 (sqrt 2))) (* (* (- (* v v)) (sqrt (+ (* (* v v) -3) 1))) (* (sqrt (+ (* v (* 3 v)) 1)) (* 4 (sqrt 2))))))) (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) 16)) (sqrt (+ 4 (* v (* 12 v))))))) * * * * [misc]progress: [ 243 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (428 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (sqrt 2) (* v v)))))) (sqrt (- (* (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (* 4 (sqrt (+ (* v (* 3 v)) 1))) (* v v)) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (sqrt 2) (* v v)))))) (sqrt (- (* (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (* 4 (sqrt (+ (* v (* 3 v)) 1))) (* v v)) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (/ (sqrt 2) 4)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (149 enodes) * * [misc]simplify: iters left: 2 (294 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* 12 (* v v)) 4)) (sqrt (+ (* (* (* v v) (* 3 v)) (* v 12)) (+ (* 12 (* v v)) 4)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (sqrt 2) (* v v)))))) (sqrt (- (* (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (* 4 (sqrt (+ (* v (* 3 v)) 1))) (* v v)) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (/ (sqrt 2) 4)))))) (* (sqrt (+ (* 12 (* v v)) 4)) (sqrt (+ (* (* (* v v) (* 3 v)) (* v 12)) (+ (* 12 (* v v)) 4)))))) * * * * [misc]progress: [ 244 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (394 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (sqrt 2) 4) (* 4 (sqrt (+ 1 (* (* v v) 3)))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (* (sqrt 2) (* v v)) 4)) (* 4 (sqrt (+ 1 (* (* v v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (sqrt 2) 4) (* 4 (sqrt (+ 1 (* (* v v) 3)))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (* (sqrt 2) (* v v)) 4)) (* 4 (sqrt (+ 1 (* (* v v) 3)))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (160 enodes) * * [misc]simplify: iters left: 2 (290 enodes) * * [misc]simplify: iters left: 1 (419 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (sqrt (+ (* 9 (pow v 4)) (+ (* (* 3 v) v) 1))))) (sqrt (+ (* v (* v 12)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (sqrt 2) 4) (* 4 (sqrt (+ 1 (* (* v v) 3)))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (* (sqrt 2) (* v v)) 4)) (* 4 (sqrt (+ 1 (* (* v v) 3)))))))) (* (sqrt (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (sqrt (+ (* 9 (pow v 4)) (+ (* (* 3 v) v) 1))))) (sqrt (+ (* v (* v 12)) 4))))) * * * * [misc]progress: [ 245 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (391 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* v (* 3 v)) 3))))))) (sqrt (- (* (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (* v v)) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* v (* 3 v)) 3))))))) (sqrt (- (* (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (* v v)) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (/ (sqrt 2) 4)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (276 enodes) * * [misc]simplify: iters left: 1 (384 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (pow v 4) 9) (+ (* v (* 3 v)) 1))) (sqrt (+ (* 12 (* v v)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* v (* 3 v)) 3))))))) (sqrt (- (* (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (* v v)) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (/ (sqrt 2) 4)))))) (* (sqrt (+ (* (pow v 4) 9) (+ (* v (* 3 v)) 1))) (sqrt (+ (* 12 (* v v)) 4))))) * * * * [misc]progress: [ 246 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (108 enodes) * * [misc]simplify: iters left: 4 (358 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* (* 3 v) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (/ (sqrt 2) 4) (* v v))) (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v))))))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (+ (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (* (- v) v) (/ (sqrt 2) 4)) 4)) (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* 3 v) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (/ (sqrt 2) 4) (* v v))) (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v))))))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (+ (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (* (- v) v) (/ (sqrt 2) 4)) 4)) (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (300 enodes) * * [misc]simplify: iters left: 1 (459 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (pow v 4) 9) (+ (* (* v v) 3) 1))) (sqrt (+ (* (* v v) 3) 1)))) (sqrt (+ (* (* v v) 12) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* 3 v) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (/ (sqrt 2) 4) (* v v))) (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v))))))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (+ (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (* (- v) v) (/ (sqrt 2) 4)) 4)) (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))))))) (* (sqrt (* (sqrt (+ (* (pow v 4) 9) (+ (* (* v v) 3) 1))) (sqrt (+ (* (* v v) 3) 1)))) (sqrt (+ (* (* v v) 12) 4))))) * * * * [misc]progress: [ 247 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (410 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* 4 (/ (sqrt 2) 4))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v v) 3)))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (+ 1 (* (* v v) 3))) 4)) (* (/ (sqrt 2) 4) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* 4 (/ (sqrt 2) 4))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v v) 3)))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (+ 1 (* (* v v) 3))) 4)) (* (/ (sqrt 2) 4) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (300 enodes) * * [misc]simplify: iters left: 1 (453 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ (* (pow v 4) 9) (+ (* (* v v) 3) 1))))) (sqrt (+ (* (* v v) 12) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* 4 (/ (sqrt 2) 4))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v v) 3)))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (+ 1 (* (* v v) 3))) 4)) (* (/ (sqrt 2) 4) (* v v)))))) (* (sqrt (* 4 (sqrt (+ (* (pow v 4) 9) (+ (* (* v v) 3) 1))))) (sqrt (+ (* (* v v) 12) 4))))) * * * * [misc]progress: [ 248 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (388 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* 3 v) v))))))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* 3 v) v))))))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (161 enodes) * * [misc]simplify: iters left: 2 (291 enodes) * * [misc]simplify: iters left: 1 (431 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 4 (* v (* 12 v)))) (sqrt (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (sqrt (+ (* (pow v 4) 9) (+ (* v (* 3 v)) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* 3 v) v))))))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)))))) (* (sqrt (+ 4 (* v (* 12 v)))) (sqrt (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (sqrt (+ (* (pow v 4) 9) (+ (* v (* 3 v)) 1)))))))) * * * * [misc]progress: [ 249 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (82 enodes) * * [misc]simplify: iters left: 4 (257 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (sqrt (+ (* v (* 3 v)) 1))) (* (* (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* v v)))) (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) (+ (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (sqrt 2)) (* (* 4 (* (* (- v) v) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (sqrt (+ (* v (* 3 v)) 1))) (* (* (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* v v)))) (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) (+ (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (sqrt 2)) (* (* 4 (* (* (- v) v) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (66 enodes) * [exit]simplify: Simplified to (+ (* v (* 12 v)) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (sqrt (+ (* v (* 3 v)) 1))) (* (* (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* v v)))) (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) (+ (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (sqrt 2)) (* (* 4 (* (* (- v) v) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))))))) (+ (* v (* 12 v)) 4))) * * * * [misc]progress: [ 250 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (382 enodes) * [exit]simplify: Simplified to (* (sqrt (- (/ (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (/ (/ 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* 3 (* v v)))) (* v v))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (/ (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (/ (/ 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* 3 (* v v)))) (* v v))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (300 enodes) * * [misc]simplify: iters left: 1 (459 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (pow v 4) 9) (+ (* (* v v) 3) 1))) (sqrt (+ (* (* v v) 3) 1)))) (sqrt (+ (* (* v v) 12) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (/ (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (/ (/ 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* 3 (* v v)))) (* v v))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (* v v)))))) (* (sqrt (* (sqrt (+ (* (pow v 4) 9) (+ (* (* v v) 3) 1))) (sqrt (+ (* (* v v) 3) 1)))) (sqrt (+ (* (* v v) 12) 4))))) * * * * [misc]progress: [ 251 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (31 enodes) * * [misc]simplify: iters left: 5 (74 enodes) * * [misc]simplify: iters left: 4 (220 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (sqrt (+ (* v (* 3 v)) 1)) (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* (/ (sqrt 2) 4) (sqrt (+ (* v (* 3 v)) 1))) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))))) (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (sqrt 2) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt (+ (* v (* 3 v)) 1)) (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* (/ (sqrt 2) 4) (sqrt (+ (* v (* 3 v)) 1))) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))))) (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (sqrt 2) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* (* v v) 3))) (sqrt (+ (* v (* 12 v)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt (+ (* v (* 3 v)) 1)) (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* (/ (sqrt 2) 4) (sqrt (+ (* v (* 3 v)) 1))) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))))) (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (sqrt 2) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))))))) (* (sqrt (+ 1 (* (* v v) 3))) (sqrt (+ (* v (* 12 v)) 4))))) * * * * [misc]progress: [ 252 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (89 enodes) * * [misc]simplify: iters left: 4 (290 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt 2)) (* (sqrt (+ (* (* v v) -3) 1)) (* v v))))) (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt 2)) (* (sqrt (+ (* (* v v) -3) 1)) (* v v))))) (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (53 enodes) * * [misc]simplify: iters left: 1 (62 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) 4)) (sqrt (+ 4 (* v (* 12 v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt 2)) (* (sqrt (+ (* (* v v) -3) 1)) (* v v))))) (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))))))) (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) 4)) (sqrt (+ 4 (* v (* 12 v))))))) * * * * [misc]progress: [ 253 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (123 enodes) * * [misc]simplify: iters left: 4 (409 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (+ (* v (* v -3)) 1))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (sqrt 2) (* v v)) 4)))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (* v v)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (+ (* v (* v -3)) 1))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (sqrt 2) (* v v)) 4)))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (* v v)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (152 enodes) * * [misc]simplify: iters left: 2 (281 enodes) * * [misc]simplify: iters left: 1 (383 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 4 (* v (* 12 v)))) (sqrt (* 16 (sqrt (+ (* (pow v 4) 9) (+ (* v (* 3 v)) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (+ (* v (* v -3)) 1))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (sqrt 2) (* v v)) 4)))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (* v v)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4)))))) (* (sqrt (+ 4 (* v (* 12 v)))) (sqrt (* 16 (sqrt (+ (* (pow v 4) 9) (+ (* v (* 3 v)) 1)))))))) * * * * [misc]progress: [ 254 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (91 enodes) * * [misc]simplify: iters left: 4 (297 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (- (* v v)) (* 4 (sqrt 2))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* (sqrt 2) (sqrt (- 1 (* (* 3 v) v))))))) (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (+ (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)) (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (- (* v v)) (* 4 (sqrt 2))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* (sqrt 2) (sqrt (- 1 (* (* 3 v) v))))))) (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (+ (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)) (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (67 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ 1 (* v (* 3 v)))))) (sqrt (+ 4 (* v (* 12 v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (- (* v v)) (* 4 (sqrt 2))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* (sqrt 2) (sqrt (- 1 (* (* 3 v) v))))))) (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (+ (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)) (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))))))) (* (sqrt (* 16 (sqrt (+ 1 (* v (* 3 v)))))) (sqrt (+ 4 (* v (* 12 v))))))) * * * * [misc]progress: [ 255 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (405 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* (* v v) -3) 1)) (sqrt 2)) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* v v) -3) 1)) (sqrt 2)) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (300 enodes) * * [misc]simplify: iters left: 1 (453 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ (* (pow v 4) 9) (+ (* (* v v) 3) 1))))) (sqrt (+ (* (* v v) 12) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* v v) -3) 1)) (sqrt 2)) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)))))) (* (sqrt (* 4 (sqrt (+ (* (pow v 4) 9) (+ (* (* v v) 3) 1))))) (sqrt (+ (* (* v v) 12) 4))))) * * * * [misc]progress: [ 256 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (83 enodes) * * [misc]simplify: iters left: 4 (259 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) (+ (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (sqrt 2)) (* (* (/ (* 4 (sqrt 2)) 4) (- (* v v))) (sqrt (- 1 (* (* (* v v) (* v v)) 9))))))) (sqrt (- (* (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt 2)) (sqrt (+ (* v (* v -3)) 1))) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) (+ (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (sqrt 2)) (* (* (/ (* 4 (sqrt 2)) 4) (- (* v v))) (sqrt (- 1 (* (* (* v v) (* v v)) 9))))))) (sqrt (- (* (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt 2)) (sqrt (+ (* v (* v -3)) 1))) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (53 enodes) * * [misc]simplify: iters left: 1 (63 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 4 (* (* v v) 12))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) (+ (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (sqrt 2)) (* (* (/ (* 4 (sqrt 2)) 4) (- (* v v))) (sqrt (- 1 (* (* (* v v) (* v v)) 9))))))) (sqrt (- (* (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt 2)) (sqrt (+ (* v (* v -3)) 1))) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (+ 4 (* (* v v) 12))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) 4))))) * * * * [misc]progress: [ 257 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (89 enodes) * * [misc]simplify: iters left: 4 (292 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2)) (+ (* (* 4 v) (- v)) 4))) (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (+ (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4)) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2)) (+ (* (* 4 v) (- v)) 4))) (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (+ (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4)) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 4))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (65 enodes) * [exit]simplify: Simplified to (* 4 (sqrt (+ (* v (* v 12)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2)) (+ (* (* 4 v) (- v)) 4))) (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (+ (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4)) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)))))) (* 4 (sqrt (+ (* v (* v 12)) 4))))) * * * * [misc]progress: [ 258 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3)))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (97 enodes) * * [misc]simplify: iters left: 4 (368 enodes) * [exit]simplify: Simplified to (* (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ (* (* v v) -3) 1))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1))) 3))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (* v v)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ (* (* v v) -3) 1))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1))) 3))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (* v v)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (73 enodes) * * [misc]simplify: iters left: 4 (232 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (sqrt (+ 1 (* (* v v) -3))) (- (* (* v (- v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (* v (- v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v v) -3))))) (* (* (sqrt (+ 1 (* (* v v) -3))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* (* v v) -3))) (/ (sqrt 2) 4))))) (sqrt (+ (* 4 (* (* v v) 3)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ (* (* v v) -3) 1))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1))) 3))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (* v v)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4)))))) (* (sqrt (+ (* (* (sqrt (+ 1 (* (* v v) -3))) (- (* (* v (- v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (* v (- v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v v) -3))))) (* (* (sqrt (+ 1 (* (* v v) -3))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* (* v v) -3))) (/ (sqrt 2) 4))))) (sqrt (+ (* 4 (* (* v v) 3)) 4))))) * * * * [misc]progress: [ 259 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (98 enodes) * * [misc]simplify: iters left: 4 (364 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* v (* v -3)) 1)) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (- (* v v))))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1))))) (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (+ (* (sqrt (- 1 (* (* (* v v) 9) (* v v)))) (sqrt 2)) (* (sqrt (- 1 (* (* (* v v) 9) (* v v)))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* v (* v -3)) 1)) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (- (* v v))))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1))))) (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (+ (* (sqrt (- 1 (* (* (* v v) 9) (* v v)))) (sqrt 2)) (* (sqrt (- 1 (* (* (* v v) 9) (* v v)))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (54 enodes) * * [misc]simplify: iters left: 4 (134 enodes) * * [misc]simplify: iters left: 3 (432 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 4 (* 12 (* v v)))) (sqrt (* (/ (* (+ 1 (* v v)) (sqrt 2)) 4) (sqrt (+ 1 (* (* v v) -3)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* v (* v -3)) 1)) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (- (* v v))))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1))))) (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (+ (* (sqrt (- 1 (* (* (* v v) 9) (* v v)))) (sqrt 2)) (* (sqrt (- 1 (* (* (* v v) 9) (* v v)))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4)))))) (* (sqrt (+ 4 (* 12 (* v v)))) (sqrt (* (/ (* (+ 1 (* v v)) (sqrt 2)) 4) (sqrt (+ 1 (* (* v v) -3)))))))) * * * * [misc]progress: [ 260 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (388 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (+ (sqrt 2) (- (* (* v v) (sqrt 2))))) (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v (* 3 v)) (* v (* 3 v))))) 4))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (sqrt (+ 1 (* v (* 3 v)))) (* 4 (sqrt 2))) (* (sqrt (+ 1 (* v (* -3 v)))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (+ (sqrt 2) (- (* (* v v) (sqrt 2))))) (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v (* 3 v)) (* v (* 3 v))))) 4))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (sqrt (+ 1 (* v (* 3 v)))) (* 4 (sqrt 2))) (* (sqrt (+ 1 (* v (* -3 v)))) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (96 enodes) * * [misc]simplify: iters left: 3 (154 enodes) * * [misc]simplify: iters left: 2 (275 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) 16)) (sqrt (+ (* (+ (* (pow v 3) (* v 9)) (* 3 (* v v))) 16) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (+ (sqrt 2) (- (* (* v v) (sqrt 2))))) (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v (* 3 v)) (* v (* 3 v))))) 4))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (sqrt (+ 1 (* v (* 3 v)))) (* 4 (sqrt 2))) (* (sqrt (+ 1 (* v (* -3 v)))) (* v v)))))) (* (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) 16)) (sqrt (+ (* (+ (* (pow v 3) (* v 9)) (* 3 (* v v))) 16) 16))))) * * * * [misc]progress: [ 261 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (391 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* 9 (* v v)) (* v v)))) (* 4 (sqrt 2))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (- (* v v)))) (* (* (sqrt (+ 1 (* (* v v) 3))) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* v v) 3) 3)))))) (sqrt (- (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (sqrt 2) 4)) (* (* (sqrt (+ (* (* -3 v) v) 1)) (* (* v v) (sqrt 2))) (* (sqrt (+ 1 (* (* v v) 3))) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* 9 (* v v)) (* v v)))) (* 4 (sqrt 2))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (- (* v v)))) (* (* (sqrt (+ 1 (* (* v v) 3))) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* v v) 3) 3)))))) (sqrt (- (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (sqrt 2) 4)) (* (* (sqrt (+ (* (* -3 v) v) 1)) (* (* v v) (sqrt 2))) (* (sqrt (+ 1 (* (* v v) 3))) 4))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (163 enodes) * * [misc]simplify: iters left: 2 (250 enodes) * * [misc]simplify: iters left: 1 (286 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) 16)) (sqrt (* (* (sqrt (+ (* v (* 3 v)) 1)) 16) (sqrt (+ (* 9 (pow v 4)) (+ (* v (* 3 v)) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* 9 (* v v)) (* v v)))) (* 4 (sqrt 2))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (- (* v v)))) (* (* (sqrt (+ 1 (* (* v v) 3))) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* v v) 3) 3)))))) (sqrt (- (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (sqrt 2) 4)) (* (* (sqrt (+ (* (* -3 v) v) 1)) (* (* v v) (sqrt 2))) (* (sqrt (+ 1 (* (* v v) 3))) 4))))) (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) 16)) (sqrt (* (* (sqrt (+ (* v (* 3 v)) 1)) 16) (sqrt (+ (* 9 (pow v 4)) (+ (* v (* 3 v)) 1)))))))) * * * * [misc]progress: [ 262 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (123 enodes) * * [misc]simplify: iters left: 4 (418 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v (* 3 v)) (* v (* 3 v))))) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (sqrt 2))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* -3 v) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v (* 3 v)) (* v (* 3 v))))) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (sqrt 2))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* -3 v) v)))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (340 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) 16)) (sqrt (+ (+ (* (* v v) 12) 4) (* (* v 4) (* (* 9 v) (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v (* 3 v)) (* v (* 3 v))))) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (sqrt 2))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* -3 v) v)))))))) (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) 16)) (sqrt (+ (+ (* (* v v) 12) 4) (* (* v 4) (* (* 9 v) (* v v)))))))) * * * * [misc]progress: [ 263 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (123 enodes) * * [misc]simplify: iters left: 4 (420 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v))))) (sqrt (- (* (* (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (* (sqrt (- 1 (* (* v v) 3))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v))))) (sqrt (- (* (* (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (* (sqrt (- 1 (* (* v v) 3))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (172 enodes) * * [misc]simplify: iters left: 2 (290 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) 16)) (sqrt (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (sqrt (+ (* (pow v 4) 9) (+ (* v (* 3 v)) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v))))) (sqrt (- (* (* (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (* (sqrt (- 1 (* (* v v) 3))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) 16)) (sqrt (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (sqrt (+ (* (pow v 4) 9) (+ (* v (* 3 v)) 1)))))))) * * * * [misc]progress: [ 264 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (112 enodes) * * [misc]simplify: iters left: 4 (347 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (- 1 (* (* v v) 3))) (* (* (- (* v v)) (sqrt 2)) 4))))) (sqrt (- (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt 2) 4)) (* (* (sqrt (+ 1 (* (* v v) 3))) (* 4 (sqrt 2))) (* (sqrt (- 1 (* (* v v) 3))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (- 1 (* (* v v) 3))) (* (* (- (* v v)) (sqrt 2)) 4))))) (sqrt (- (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt 2) 4)) (* (* (sqrt (+ 1 (* (* v v) 3))) (* 4 (sqrt 2))) (* (sqrt (- 1 (* (* v v) 3))) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (289 enodes) * * [misc]simplify: iters left: 1 (310 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) 16)) (sqrt (* (sqrt (+ (* (pow v 4) 9) (+ (* v (* 3 v)) 1))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (- 1 (* (* v v) 3))) (* (* (- (* v v)) (sqrt 2)) 4))))) (sqrt (- (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt 2) 4)) (* (* (sqrt (+ 1 (* (* v v) 3))) (* 4 (sqrt 2))) (* (sqrt (- 1 (* (* v v) 3))) (* v v)))))) (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) 16)) (sqrt (* (sqrt (+ (* (pow v 4) 9) (+ (* v (* 3 v)) 1))) 16))))) * * * * [misc]progress: [ 265 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (381 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (sqrt 2) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* v v)))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (- 1 (* 3 (* v v)))) (* (* v v) (sqrt 2))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (sqrt 2) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* v v)))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (- 1 (* 3 (* v v)))) (* (* v v) (sqrt 2))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (102 enodes) * * [misc]simplify: iters left: 3 (161 enodes) * * [misc]simplify: iters left: 2 (252 enodes) * * [misc]simplify: iters left: 1 (292 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) 16)) (sqrt (* (* (sqrt (+ (* (* 3 v) v) 1)) 16) (sqrt (+ (* 9 (pow v 4)) (+ (* (* 3 v) v) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (sqrt 2) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* v v)))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (- 1 (* 3 (* v v)))) (* (* v v) (sqrt 2))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) 16)) (sqrt (* (* (sqrt (+ (* (* 3 v) v) 1)) 16) (sqrt (+ (* 9 (pow v 4)) (+ (* (* 3 v) v) 1)))))))) * * * * [misc]progress: [ 266 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (84 enodes) * * [misc]simplify: iters left: 4 (275 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt 2)) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* v (* 3 v)))))))) (sqrt (* (+ (* (- v) v) 1) (* (* (sqrt (+ (* v (* 3 v)) 1)) (* (sqrt 2) 4)) (sqrt (+ (* (* (* v v) -9) (* v v)) 1)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt 2)) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* v (* 3 v)))))))) (sqrt (* (+ (* (- v) v) 1) (* (* (sqrt (+ (* v (* 3 v)) 1)) (* (sqrt 2) 4)) (sqrt (+ (* (* (* v v) -9) (* v v)) 1)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * * [misc]simplify: iters left: 2 (58 enodes) * * [misc]simplify: iters left: 1 (103 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 16 (* v (* 48 v)))) (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt 2)) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* v (* 3 v)))))))) (sqrt (* (+ (* (- v) v) 1) (* (* (sqrt (+ (* v (* 3 v)) 1)) (* (sqrt 2) 4)) (sqrt (+ (* (* (* v v) -9) (* v v)) 1)))))) (* (sqrt (+ 16 (* v (* 48 v)))) (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 16))))) * * * * [misc]progress: [ 267 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (386 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* 4 (sqrt (+ 1 (* v (* 3 v)))))) (* (/ (sqrt 2) 4) (* v v))))) (sqrt (- (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt 2) 4)) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* v (* 3 v))))) (* 4 (sqrt (+ 1 (* v (* 3 v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* 4 (sqrt (+ 1 (* v (* 3 v)))))) (* (/ (sqrt 2) 4) (* v v))))) (sqrt (- (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt 2) 4)) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* v (* 3 v))))) (* 4 (sqrt (+ 1 (* v (* 3 v))))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (253 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (sqrt (+ (* (pow v 4) 9) (+ (* (* 3 v) v) 1))))) (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* 4 (sqrt (+ 1 (* v (* 3 v)))))) (* (/ (sqrt 2) 4) (* v v))))) (sqrt (- (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt 2) 4)) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* v (* 3 v))))) (* 4 (sqrt (+ 1 (* v (* 3 v))))))))) (* (sqrt (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (sqrt (+ (* (pow v 4) 9) (+ (* (* 3 v) v) 1))))) (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) 16))))) * * * * [misc]progress: [ 268 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (88 enodes) * * [misc]simplify: iters left: 4 (314 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (sqrt (+ (* v (* 3 v)) 1)) (* 4 (sqrt 2))) (* (* v v) (sqrt (+ (* (* v v) -3) 1)))))) (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) (+ (* (sqrt 2) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (* (* (/ (sqrt 2) 4) (- (* v v))) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (sqrt (+ (* v (* 3 v)) 1)) (* 4 (sqrt 2))) (* (* v v) (sqrt (+ (* (* v v) -3) 1)))))) (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) (+ (* (sqrt 2) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (* (* (/ (sqrt 2) 4) (- (* v v))) 4)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 4 (* v (* 12 v)))) (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (sqrt (+ (* v (* 3 v)) 1)) (* 4 (sqrt 2))) (* (* v v) (sqrt (+ (* (* v v) -3) 1)))))) (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) (+ (* (sqrt 2) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (* (* (/ (sqrt 2) 4) (- (* v v))) 4)))))) (* (sqrt (+ 4 (* v (* 12 v)))) (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) 16))))) * * * * [misc]progress: [ 269 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (64 enodes) * * [misc]simplify: iters left: 4 (184 enodes) * [exit]simplify: Simplified to (- (* (* (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (- 1 (* (* v v) 3))) (* (sqrt 2) (* v v))) (* 4 (sqrt (+ (* (* v v) 3) 1))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (* (* (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (- 1 (* (* v v) 3))) (* (sqrt 2) (* v v))) (* 4 (sqrt (+ (* (* v v) 3) 1))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (27 enodes) * [exit]simplify: Simplified to (* 16 (sqrt (+ 1 (* (* 3 v) v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (* (* (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (- 1 (* (* v v) 3))) (* (sqrt 2) (* v v))) (* 4 (sqrt (+ (* (* v v) 3) 1))))) (* 16 (sqrt (+ 1 (* (* 3 v) v)))))) * * * * [misc]progress: [ 270 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (123 enodes) * * [misc]simplify: iters left: 4 (409 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (- (* (* (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (* (sqrt (- 1 (* (* v v) 3))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (- (* (* (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (* (sqrt (- 1 (* (* v v) 3))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (159 enodes) * * [misc]simplify: iters left: 2 (303 enodes) * * [misc]simplify: iters left: 1 (454 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ (* v (* 3 v)) 1)))) (sqrt (+ 4 (+ (* (pow v 4) 36) (* v (* 12 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (- (* (* (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (* (sqrt (- 1 (* (* v v) 3))) (* (* v v) (sqrt 2))))))) (* (sqrt (* 16 (sqrt (+ (* v (* 3 v)) 1)))) (sqrt (+ 4 (+ (* (pow v 4) 36) (* v (* 12 v)))))))) * * * * [misc]progress: [ 271 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (388 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (sqrt (+ (* v (* 3 v)) 1)) (* 4 (/ (sqrt 2) 4)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v)))))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* -3 v) v) 1))) (* 4 (sqrt (+ (* v (* 3 v)) 1))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (sqrt (+ (* v (* 3 v)) 1)) (* 4 (/ (sqrt 2) 4)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v)))))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* -3 v) v) 1))) (* 4 (sqrt (+ (* v (* 3 v)) 1))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (173 enodes) * * [misc]simplify: iters left: 2 (280 enodes) * * [misc]simplify: iters left: 1 (319 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* (* v v) 3) 1)) 4) (sqrt (+ (* 9 (pow v 4)) (+ (* (* v v) 3) 1))))) (sqrt (* (sqrt (+ (* (* v v) 3) 1)) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (sqrt (+ (* v (* 3 v)) 1)) (* 4 (/ (sqrt 2) 4)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v)))))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* -3 v) v) 1))) (* 4 (sqrt (+ (* v (* 3 v)) 1))))))) (* (sqrt (* (* (sqrt (+ (* (* v v) 3) 1)) 4) (sqrt (+ (* 9 (pow v 4)) (+ (* (* v v) 3) 1))))) (sqrt (* (sqrt (+ (* (* v v) 3) 1)) 16))))) * * * * [misc]progress: [ 272 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (117 enodes) * * [misc]simplify: iters left: 4 (377 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* v v))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* (* -3 v) v))) (* (* v v) (sqrt 2))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* v v))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* (* -3 v) v))) (* (* v v) (sqrt 2))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (136 enodes) * * [misc]simplify: iters left: 2 (223 enodes) * * [misc]simplify: iters left: 1 (262 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* 9 (pow v 4)) (+ (* v (* 3 v)) 1))) (sqrt (* 16 (sqrt (+ (* v (* 3 v)) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* v v))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* (* -3 v) v))) (* (* v v) (sqrt 2))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (+ (* 9 (pow v 4)) (+ (* v (* 3 v)) 1))) (sqrt (* 16 (sqrt (+ (* v (* 3 v)) 1))))))) * * * * [misc]progress: [ 273 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (407 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v v) -3)))) (* 4 (sqrt (+ (* (* v v) 3) 1)))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v v) -3)))) (* 4 (sqrt (+ (* (* v v) 3) 1)))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (248 enodes) * * [misc]simplify: iters left: 1 (337 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt (+ (* (pow v 4) 9) (+ (* (* 3 v) v) 1))))) (sqrt (* 16 (sqrt (+ (* (* 3 v) v) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v v) -3)))) (* 4 (sqrt (+ (* (* v v) 3) 1)))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))))) (* (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt (+ (* (pow v 4) 9) (+ (* (* 3 v) v) 1))))) (sqrt (* 16 (sqrt (+ (* (* 3 v) v) 1))))))) * * * * [misc]progress: [ 274 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (111 enodes) * * [misc]simplify: iters left: 4 (344 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (+ (* (* v -3) v) 1)) (* (* v v) (sqrt 2))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (+ (* (* 3 v) v) 1)) (* 4 (sqrt 2))) (* (sqrt (+ (* (* v -3) v) 1)) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (+ (* (* v -3) v) 1)) (* (* v v) (sqrt 2))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (+ (* (* 3 v) v) 1)) (* 4 (sqrt 2))) (* (sqrt (+ (* (* v -3) v) 1)) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (248 enodes) * * [misc]simplify: iters left: 1 (337 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ (* (pow v 4) 9) (+ (* (* 3 v) v) 1))))) (sqrt (* 16 (sqrt (+ (* (* 3 v) v) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (+ (* (* v -3) v) 1)) (* (* v v) (sqrt 2))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (+ (* (* 3 v) v) 1)) (* 4 (sqrt 2))) (* (sqrt (+ (* (* v -3) v) 1)) (* v v)))))) (* (sqrt (* 4 (sqrt (+ (* (pow v 4) 9) (+ (* (* 3 v) v) 1))))) (sqrt (* 16 (sqrt (+ (* (* 3 v) v) 1))))))) * * * * [misc]progress: [ 275 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (122 enodes) * * [misc]simplify: iters left: 4 (384 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* 3 v)) 1)))))) (sqrt (- (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt 2) 4)) (* (* 4 (sqrt (+ (* v (* 3 v)) 1))) (* (sqrt (+ 1 (* v (* v -3)))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* 3 v)) 1)))))) (sqrt (- (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt 2) 4)) (* (* 4 (sqrt (+ (* v (* 3 v)) 1))) (* (sqrt (+ 1 (* v (* v -3)))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (148 enodes) * * [misc]simplify: iters left: 2 (239 enodes) * * [misc]simplify: iters left: 1 (287 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ (* v (* 3 v)) 1)))) (sqrt (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (sqrt (+ (* (pow v 4) 9) (+ (* v (* 3 v)) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* 3 v)) 1)))))) (sqrt (- (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt 2) 4)) (* (* 4 (sqrt (+ (* v (* 3 v)) 1))) (* (sqrt (+ 1 (* v (* v -3)))) (* (* v v) (sqrt 2))))))) (* (sqrt (* 16 (sqrt (+ (* v (* 3 v)) 1)))) (sqrt (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (sqrt (+ (* (pow v 4) 9) (+ (* v (* 3 v)) 1)))))))) * * * * [misc]progress: [ 276 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (91 enodes) * * [misc]simplify: iters left: 4 (288 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (sqrt 2) 4)) (* (* (sqrt (+ (* (* 3 v) v) 1)) (* 4 (sqrt 2))) (* (* v v) (sqrt (- 1 (* (* 3 v) v))))))) (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (sqrt 2) 4)) (* (* (sqrt (+ (* (* 3 v) v) 1)) (* 4 (sqrt 2))) (* (* v v) (sqrt (- 1 (* (* 3 v) v))))))) (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * * [misc]simplify: iters left: 2 (42 enodes) * * [misc]simplify: iters left: 1 (59 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 4 (* (* 12 v) v))) (sqrt (* 16 (sqrt (+ 1 (* v (* 3 v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (sqrt 2) 4)) (* (* (sqrt (+ (* (* 3 v) v) 1)) (* 4 (sqrt 2))) (* (* v v) (sqrt (- 1 (* (* 3 v) v))))))) (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))))))) (* (sqrt (+ 4 (* (* 12 v) v))) (sqrt (* 16 (sqrt (+ 1 (* v (* 3 v))))))))) * * * * [misc]progress: [ 277 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (385 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (sqrt 2))) (* (sqrt (+ 1 (* v (* -3 v)))) (* v v))))) (sqrt (+ (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (sqrt 2))) (* (sqrt (+ 1 (* v (* -3 v)))) (* v v))))) (sqrt (+ (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (248 enodes) * * [misc]simplify: iters left: 1 (337 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt (+ (* (pow v 4) 9) (+ (* (* 3 v) v) 1))))) (sqrt (* 16 (sqrt (+ (* (* 3 v) v) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (sqrt 2))) (* (sqrt (+ 1 (* v (* -3 v)))) (* v v))))) (sqrt (+ (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (* (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt (+ (* (pow v 4) 9) (+ (* (* 3 v) v) 1))))) (sqrt (* 16 (sqrt (+ (* (* 3 v) v) 1))))))) * * * * [misc]progress: [ 278 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (88 enodes) * * [misc]simplify: iters left: 4 (281 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) 4) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (+ (* (* 3 v) v) 1)) (* 4 (sqrt 2))) (* (* v v) (sqrt (+ (* -3 (* v v)) 1)))))) (sqrt (+ (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (- (* v v))) (* (sqrt (+ (* (* 3 v) v) 1)) (/ (sqrt 2) 4))) (* (* (sqrt (+ (* (* 3 v) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) 4) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (+ (* (* 3 v) v) 1)) (* 4 (sqrt 2))) (* (* v v) (sqrt (+ (* -3 (* v v)) 1)))))) (sqrt (+ (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (- (* v v))) (* (sqrt (+ (* (* 3 v) v) 1)) (/ (sqrt 2) 4))) (* (* (sqrt (+ (* (* 3 v) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (38 enodes) * * [misc]simplify: iters left: 1 (39 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* (* v v) 3))) (sqrt (* 16 (sqrt (+ 1 (* (* v v) 3)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) 4) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (+ (* (* 3 v) v) 1)) (* 4 (sqrt 2))) (* (* v v) (sqrt (+ (* -3 (* v v)) 1)))))) (sqrt (+ (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (- (* v v))) (* (sqrt (+ (* (* 3 v) v) 1)) (/ (sqrt 2) 4))) (* (* (sqrt (+ (* (* 3 v) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))))) (* (sqrt (+ 1 (* (* v v) 3))) (sqrt (* 16 (sqrt (+ 1 (* (* v v) 3)))))))) * * * * [misc]progress: [ 279 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (81 enodes) * * [misc]simplify: iters left: 4 (236 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (* (* v v) (* (* v v) -9)) 1)) (* (sqrt 2) 4)) (* (* (sqrt (+ (* v (* 3 v)) 1)) (* 4 (sqrt 2))) (* (* v v) (sqrt (+ (* v (* v -3)) 1)))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) (* (* v v) -9)) 1))) (* (* (sqrt (+ (* v (* v -3)) 1)) (* (sqrt 2) (* v v))) (sqrt (+ (* v (* 3 v)) 1)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* (* v v) (* (* v v) -9)) 1)) (* (sqrt 2) 4)) (* (* (sqrt (+ (* v (* 3 v)) 1)) (* 4 (sqrt 2))) (* (* v v) (sqrt (+ (* v (* v -3)) 1)))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) (* (* v v) -9)) 1))) (* (* (sqrt (+ (* v (* v -3)) 1)) (* (sqrt 2) (* v v))) (sqrt (+ (* v (* 3 v)) 1)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) 4)) (sqrt (* 16 (sqrt (+ 1 (* v (* 3 v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* (* v v) (* (* v v) -9)) 1)) (* (sqrt 2) 4)) (* (* (sqrt (+ (* v (* 3 v)) 1)) (* 4 (sqrt 2))) (* (* v v) (sqrt (+ (* v (* v -3)) 1)))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) (* (* v v) -9)) 1))) (* (* (sqrt (+ (* v (* v -3)) 1)) (* (sqrt 2) (* v v))) (sqrt (+ (* v (* 3 v)) 1)))))) (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) 4)) (sqrt (* 16 (sqrt (+ 1 (* v (* 3 v))))))))) * * * * [misc]progress: [ 280 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (119 enodes) * * [misc]simplify: iters left: 4 (372 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* v -3) v))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v -3) v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* v -3) v))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v -3) v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (220 enodes) * * [misc]simplify: iters left: 1 (259 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ (* v (* 3 v)) 1)))) (sqrt (* 16 (sqrt (+ (* 9 (pow v 4)) (+ (* v (* 3 v)) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* v -3) v))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v -3) v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* 16 (sqrt (+ (* v (* 3 v)) 1)))) (sqrt (* 16 (sqrt (+ (* 9 (pow v 4)) (+ (* v (* 3 v)) 1)))))))) * * * * [misc]progress: [ 281 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (33 enodes) * * [misc]simplify: iters left: 5 (86 enodes) * * [misc]simplify: iters left: 4 (259 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (* (* v v) (sqrt (+ (* v (* -3 v)) 1)))))) (sqrt (+ (* (* (sqrt (+ (* (* v v) 3) 1)) 4) (* (sqrt 2) (sqrt (+ (* v (* -3 v)) 1)))) (* (* (* (sqrt 2) 4) (- (* v v))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (* (* v v) (sqrt (+ (* v (* -3 v)) 1)))))) (sqrt (+ (* (* (sqrt (+ (* (* v v) 3) 1)) 4) (* (sqrt 2) (sqrt (+ (* v (* -3 v)) 1)))) (* (* (* (sqrt 2) 4) (- (* v v))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * [exit]simplify: Simplified to (* 16 (sqrt (+ 1 (* v (* 3 v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (* (* v v) (sqrt (+ (* v (* -3 v)) 1)))))) (sqrt (+ (* (* (sqrt (+ (* (* v v) 3) 1)) 4) (* (sqrt 2) (sqrt (+ (* v (* -3 v)) 1)))) (* (* (* (sqrt 2) 4) (- (* v v))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (* 16 (sqrt (+ 1 (* v (* 3 v))))))) * * * * [misc]progress: [ 282 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (375 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (+ 1 (* (* v -3) v)))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt 2) 4)) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v -3) v)))) (* (sqrt (+ 1 (* (* v v) 3))) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (+ 1 (* (* v -3) v)))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt 2) 4)) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v -3) v)))) (* (sqrt (+ 1 (* (* v v) 3))) 4))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (248 enodes) * * [misc]simplify: iters left: 1 (337 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ (* (pow v 4) 9) (+ (* (* 3 v) v) 1))))) (sqrt (* 16 (sqrt (+ (* (* 3 v) v) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (+ 1 (* (* v -3) v)))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt 2) 4)) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v -3) v)))) (* (sqrt (+ 1 (* (* v v) 3))) 4))))) (* (sqrt (* 4 (sqrt (+ (* (pow v 4) 9) (+ (* (* 3 v) v) 1))))) (sqrt (* 16 (sqrt (+ (* (* 3 v) v) 1))))))) * * * * [misc]progress: [ 283 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (90 enodes) * * [misc]simplify: iters left: 4 (292 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 v) v))))))) (sqrt (- (* (sqrt (+ (* (* 3 v) v) 1)) (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2))) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 v) v))))))) (sqrt (- (* (sqrt (+ (* (* 3 v) v) 1)) (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2))) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ 1 (* (* 3 v) v))))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 v) v))))))) (sqrt (- (* (sqrt (+ (* (* 3 v) v) 1)) (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2))) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (* 16 (sqrt (+ 1 (* (* 3 v) v))))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) 4))))) * * * * [misc]progress: [ 284 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (78 enodes) * * [misc]simplify: iters left: 4 (220 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt 2) 4)) (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (* (* v v) (sqrt (+ 1 (* v (* -3 v)))))))) (sqrt (* (* (sqrt 2) (sqrt (+ 1 (* v (* -3 v))))) (+ 4 (* (* 4 v) (- v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt 2) 4)) (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (* (* v v) (sqrt (+ 1 (* v (* -3 v)))))))) (sqrt (* (* (sqrt 2) (sqrt (+ 1 (* v (* -3 v))))) (+ 4 (* (* 4 v) (- v)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* 4 4))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (* 4 4))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * [exit]simplify: Simplified to (* 4 (sqrt (* 16 (sqrt (+ 1 (* (* v v) 3)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt 2) 4)) (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (* (* v v) (sqrt (+ 1 (* v (* -3 v)))))))) (sqrt (* (* (sqrt 2) (sqrt (+ 1 (* v (* -3 v))))) (+ 4 (* (* 4 v) (- v)))))) (* 4 (sqrt (* 16 (sqrt (+ 1 (* (* v v) 3)))))))) * * * * [misc]progress: [ 285 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3)))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (94 enodes) * * [misc]simplify: iters left: 4 (335 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (* (sqrt (+ (* (* v v) -3) 1)) (* v v))))) (sqrt (- (pow (* (sqrt (+ (* (* v v) -3) 1)) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1))) 3)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (* (sqrt (+ (* (* v v) -3) 1)) (* v v))))) (sqrt (- (pow (* (sqrt (+ (* (* v v) -3) 1)) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1))) 3)))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (71 enodes) * * [misc]simplify: iters left: 4 (232 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* (* v -3) v))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* (* v -3) v))) (/ (sqrt 2) 4))) (* (* (sqrt (+ 1 (* (* v -3) v))) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (- (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (+ 1 (* (* v -3) v))))))) (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (* (sqrt (+ (* (* v v) -3) 1)) (* v v))))) (sqrt (- (pow (* (sqrt (+ (* (* v v) -3) 1)) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1))) 3)))) (* (sqrt (- (* (* (sqrt (+ 1 (* (* v -3) v))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* (* v -3) v))) (/ (sqrt 2) 4))) (* (* (sqrt (+ 1 (* (* v -3) v))) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (- (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (+ 1 (* (* v -3) v))))))) (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) 16))))) * * * * [misc]progress: [ 286 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (95 enodes) * * [misc]simplify: iters left: 4 (331 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) 4) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* v -3)) 1))) (* 4 (sqrt (+ (* (* 3 v) v) 1)))))) (sqrt (* (* (sqrt (+ (* v (* v -3)) 1)) (- (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4)))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) 4) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* v -3)) 1))) (* 4 (sqrt (+ (* (* 3 v) v) 1)))))) (sqrt (* (* (sqrt (+ (* v (* v -3)) 1)) (- (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4)))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * [enter]simplify: Simplifying (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (134 enodes) * * [misc]simplify: iters left: 3 (411 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ 1 (* (* v v) 3))))) (sqrt (* (sqrt (+ 1 (* v (* -3 v)))) (* (/ (sqrt 2) 4) (+ 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) 4) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* v -3)) 1))) (* 4 (sqrt (+ (* (* 3 v) v) 1)))))) (sqrt (* (* (sqrt (+ (* v (* v -3)) 1)) (- (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4)))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1)))))) (* (sqrt (* 16 (sqrt (+ 1 (* (* v v) 3))))) (sqrt (* (sqrt (+ 1 (* v (* -3 v)))) (* (/ (sqrt 2) 4) (+ 1 (* v v)))))))) * * * * [misc]progress: [ 287 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (98 enodes) * * [misc]simplify: iters left: 4 (314 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (* (* 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (sqrt 2) (- (* (* v v) (sqrt 2)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (* (* 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (sqrt 2) (- (* (* v v) (sqrt 2)))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (159 enodes) * * [misc]simplify: iters left: 2 (286 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ (* 12 (* v v)) 4) (* (* v (* 3 v)) (* 12 (* v v))))) (sqrt (* 4 (+ (+ (* 12 (* v v)) 4) (* (* v (* 3 v)) (* 12 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (* (* 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (sqrt 2) (- (* (* v v) (sqrt 2)))))))) (* (sqrt (+ (+ (* 12 (* v v)) 4) (* (* v (* 3 v)) (* 12 (* v v))))) (sqrt (* 4 (+ (+ (* 12 (* v v)) 4) (* (* v (* 3 v)) (* 12 (* v v))))))))) * * * * [misc]progress: [ 288 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (386 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (* (* v v) 3) 1)) 4)) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (* (* v v) 3) 1)) 4)) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) 4))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (282 enodes) * * [misc]simplify: iters left: 1 (437 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* 12 (* v v)) (+ 4 (* (pow v 3) (* v 36))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) (* 16 (sqrt (+ 1 (* v (* 3 v)))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (* (* v v) 3) 1)) 4)) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) 4))))) (* (sqrt (+ (* 12 (* v v)) (+ 4 (* (pow v 3) (* v 36))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) (* 16 (sqrt (+ 1 (* v (* 3 v)))))))))) * * * * [misc]progress: [ 289 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (36 enodes) * * [misc]simplify: iters left: 5 (102 enodes) * * [misc]simplify: iters left: 4 (340 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ (* 3 (* v v)) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (sqrt (- (* (* (sqrt 2) (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ (* 3 (* v v)) 1)))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ (* 3 (* v v)) 1))) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ (* 3 (* v v)) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (sqrt (- (* (* (sqrt 2) (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ (* 3 (* v v)) 1)))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ (* 3 (* v v)) 1))) 4))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (186 enodes) * * [misc]simplify: iters left: 2 (371 enodes) * [exit]simplify: Simplified to (+ (+ (* (* v v) 12) 4) (* (* (* v v) 12) (* (* v v) 3))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ (* 3 (* v v)) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (sqrt (- (* (* (sqrt 2) (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ (* 3 (* v v)) 1)))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ (* 3 (* v v)) 1))) 4))))) (+ (+ (* (* v v) 12) 4) (* (* (* v v) 12) (* (* v v) 3))))) * * * * [misc]progress: [ 290 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (385 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (174 enodes) * * [misc]simplify: iters left: 2 (309 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ (* 12 (* v v)) 4) (* (* (* v v) (* v v)) 36))) (sqrt (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ 1 (+ (* (* 3 v) v) (* (* v 9) (pow v 3)))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (+ (+ (* 12 (* v v)) 4) (* (* (* v v) (* v v)) 36))) (sqrt (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ 1 (+ (* (* 3 v) v) (* (* v 9) (pow v 3)))))))))) * * * * [misc]progress: [ 291 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (111 enodes) * * [misc]simplify: iters left: 4 (367 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v 3) v) 3))))))) (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (sqrt (+ 1 (* (* v v) -3))) (* (* (* (sqrt 2) v) (- v)) 4)) (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v 3) v) 3))))))) (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (sqrt (+ 1 (* (* v v) -3))) (* (* (* (sqrt 2) v) (- v)) 4)) (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (161 enodes) * * [misc]simplify: iters left: 2 (284 enodes) * * [misc]simplify: iters left: 1 (421 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ (* 12 (* v v)) 4) (* 36 (pow v 4)))) (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* 9 (pow v 4)))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v 3) v) 3))))))) (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (sqrt (+ 1 (* (* v v) -3))) (* (* (* (sqrt 2) v) (- v)) 4)) (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))))))) (* (sqrt (+ (+ (* 12 (* v v)) 4) (* 36 (pow v 4)))) (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* 9 (pow v 4)))) 16))))) * * * * [misc]progress: [ 292 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (112 enodes) * * [misc]simplify: iters left: 4 (366 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (sqrt (+ (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (- (* v v)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (sqrt (+ (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (- (* v v)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (sqrt 2))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * * [misc]simplify: iters left: 1 (446 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* v v) 12) (+ 4 (* (* 36 v) (pow v 3))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) (* 16 (sqrt (+ 1 (* v (* 3 v)))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (sqrt (+ (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (- (* v v)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (sqrt 2))))))) (* (sqrt (+ (* (* v v) 12) (+ 4 (* (* 36 v) (pow v 3))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) (* 16 (sqrt (+ 1 (* v (* 3 v)))))))))) * * * * [misc]progress: [ 293 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (398 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v 3) v) 3))))))) (sqrt (* (* (sqrt (+ (* (* v 3) v) 1)) 4) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (+ (* (- v) (* v (sqrt 2))) (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v 3) v) 3))))))) (sqrt (* (* (sqrt (+ (* (* v 3) v) 1)) 4) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (+ (* (- v) (* v (sqrt 2))) (sqrt 2)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (292 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* 9 (* v v)) (* (* v v) 4)) (+ (* 12 (* v v)) 4))) (sqrt (+ 16 (* (* 3 (* v v)) 16)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v 3) v) 3))))))) (sqrt (* (* (sqrt (+ (* (* v 3) v) 1)) 4) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (+ (* (- v) (* v (sqrt 2))) (sqrt 2)))))) (* (sqrt (+ (* (* 9 (* v v)) (* (* v v) 4)) (+ (* 12 (* v v)) 4))) (sqrt (+ 16 (* (* 3 (* v v)) 16)))))) * * * * [misc]progress: [ 294 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (386 enodes) * [exit]simplify: Simplified to (* (sqrt (* (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* v (* v 3)) 3))))) (sqrt (+ (* (* v (* v 3)) (* v (* v 3))) (+ (* v (* v 3)) 1))))) (sqrt (- (* (sqrt 2) (* (sqrt (+ (* (* v (* v 3)) (* v (* v 3))) (+ (* v (* v 3)) 1))) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))))) (* (/ (sqrt (- 1 (pow (* v (* v 3)) 3))) (/ 4 (* (* v v) (sqrt 2)))) (* (sqrt (+ (* v (* v 3)) 1)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* v (* v 3)) 3))))) (sqrt (+ (* (* v (* v 3)) (* v (* v 3))) (+ (* v (* v 3)) 1))))) (sqrt (- (* (sqrt 2) (* (sqrt (+ (* (* v (* v 3)) (* v (* v 3))) (+ (* v (* v 3)) 1))) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))))) (* (/ (sqrt (- 1 (pow (* v (* v 3)) 3))) (/ 4 (* (* v v) (sqrt 2)))) (* (sqrt (+ (* v (* v 3)) 1)) 4))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (180 enodes) * * [misc]simplify: iters left: 2 (338 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ (* 12 (* v v)) 4) (* 36 (* (* v v) (* v v))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 3) (* v 9))))) (* 4 (sqrt (+ 1 (* v (* 3 v)))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* v (* v 3)) 3))))) (sqrt (+ (* (* v (* v 3)) (* v (* v 3))) (+ (* v (* v 3)) 1))))) (sqrt (- (* (sqrt 2) (* (sqrt (+ (* (* v (* v 3)) (* v (* v 3))) (+ (* v (* v 3)) 1))) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))))) (* (/ (sqrt (- 1 (pow (* v (* v 3)) 3))) (/ 4 (* (* v v) (sqrt 2)))) (* (sqrt (+ (* v (* v 3)) 1)) 4))))) (* (sqrt (+ (+ (* 12 (* v v)) 4) (* 36 (* (* v v) (* v v))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 3) (* v 9))))) (* 4 (sqrt (+ 1 (* v (* 3 v)))))))))) * * * * [misc]progress: [ 295 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (422 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (sqrt 2) (* v v)))))) (sqrt (* (sqrt (+ (* (* v 3) v) 1)) (+ (* (sqrt 2) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* (- v) v) (/ (sqrt 2) 4)) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (sqrt 2) (* v v)))))) (sqrt (* (sqrt (+ (* (* v 3) v) 1)) (+ (* (sqrt 2) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* (- v) v) (/ (sqrt 2) 4)) 4)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (154 enodes) * * [misc]simplify: iters left: 2 (300 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* v (* 3 v)) (* (* 12 v) v)) (+ 4 (* (* 12 v) v)))) (sqrt (+ 4 (* (* 12 v) v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (sqrt 2) (* v v)))))) (sqrt (* (sqrt (+ (* (* v 3) v) 1)) (+ (* (sqrt 2) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* (- v) v) (/ (sqrt 2) 4)) 4)))))) (* (sqrt (+ (* (* v (* 3 v)) (* (* 12 v) v)) (+ 4 (* (* 12 v) v)))) (sqrt (+ 4 (* (* 12 v) v)))))) * * * * [misc]progress: [ 296 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (123 enodes) * * [misc]simplify: iters left: 4 (404 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (- 1 (* (* v v) 3))) (* (* v v) (sqrt 2))) (* (sqrt (+ (* (* v v) 3) 1)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (- 1 (* (* v v) 3))) (* (* v v) (sqrt 2))) (* (sqrt (+ (* (* v v) 3) 1)) 4))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * * [misc]simplify: iters left: 2 (277 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ 4 (* 12 (* v v))) (* (* 4 (* v v)) (* 9 (* v v))))) (sqrt (* 16 (sqrt (+ 1 (* v (* 3 v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (- 1 (* (* v v) 3))) (* (* v v) (sqrt 2))) (* (sqrt (+ (* (* v v) 3) 1)) 4))))) (* (sqrt (+ (+ 4 (* 12 (* v v))) (* (* 4 (* v v)) (* 9 (* v v))))) (sqrt (* 16 (sqrt (+ 1 (* v (* 3 v))))))))) * * * * [misc]progress: [ 297 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (30 enodes) * * [misc]simplify: iters left: 5 (82 enodes) * * [misc]simplify: iters left: 4 (272 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (85 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (269 enodes) * [exit]simplify: Simplified to (+ (* (* 9 (* v v)) (* (* v v) 4)) (+ 4 (* (* v v) 12))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2))))) (+ (* (* 9 (* v v)) (* (* v v) 4)) (+ 4 (* (* v v) 12))))) * * * * [misc]progress: [ 298 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (112 enodes) * * [misc]simplify: iters left: 4 (371 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (/ (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (sqrt (+ (* 3 (* v v)) 1)))) (/ 4 (sqrt 2))) (* (* (sqrt 2) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (/ (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (sqrt (+ (* 3 (* v v)) 1)))) (/ 4 (sqrt 2))) (* (* (sqrt 2) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (175 enodes) * * [misc]simplify: iters left: 2 (322 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ (* 12 (* v v)) 4) (* 36 (* (* v v) (* v v))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (* v 9) (pow v 3))))) (* 4 (sqrt (+ 1 (* v (* 3 v)))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (/ (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (sqrt (+ (* 3 (* v v)) 1)))) (/ 4 (sqrt 2))) (* (* (sqrt 2) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)))))) (* (sqrt (+ (+ (* 12 (* v v)) 4) (* 36 (* (* v v) (* v v))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (* v 9) (pow v 3))))) (* 4 (sqrt (+ 1 (* v (* 3 v)))))))))) * * * * [misc]progress: [ 299 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (98 enodes) * * [misc]simplify: iters left: 4 (337 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (+ (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (- (* (* v v) (sqrt 2)))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (- (* (/ (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ 4 (sqrt 2))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (/ (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ 4 (sqrt 2))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (+ (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (- (* (* v v) (sqrt 2)))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (- (* (/ (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ 4 (sqrt 2))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (/ (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ 4 (sqrt 2))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (148 enodes) * * [misc]simplify: iters left: 2 (261 enodes) * * [misc]simplify: iters left: 1 (419 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* 12 v) v) (+ (* (* 36 v) (pow v 3)) 4))) (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (+ (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (- (* (* v v) (sqrt 2)))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (- (* (/ (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ 4 (sqrt 2))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (/ (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ 4 (sqrt 2))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))))) (* (sqrt (+ (* (* 12 v) v) (+ (* (* 36 v) (pow v 3)) 4))) (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4)))))))) * * * * [misc]progress: [ 300 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (111 enodes) * * [misc]simplify: iters left: 4 (375 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (/ (sqrt 2) 4) (* v v))))) (sqrt (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (/ (sqrt 2) 4) (* v v))))) (sqrt (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (263 enodes) * * [misc]simplify: iters left: 1 (462 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ 4 (* 12 (* v v))) (* (* v 36) (pow v 3)))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (+ (* 3 (* v v)) (* 9 (pow v 4)))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (/ (sqrt 2) 4) (* v v))))) (sqrt (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* v v) (sqrt 2))))))) (* (sqrt (+ (+ 4 (* 12 (* v v))) (* (* v 36) (pow v 3)))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (+ (* 3 (* v v)) (* 9 (pow v 4)))))))))) * * * * [misc]progress: [ 301 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (38 enodes) * * [misc]simplify: iters left: 5 (105 enodes) * * [misc]simplify: iters left: 4 (356 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (* 4 (sqrt 2)) 4)) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* -3 v) v)))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (- (* (sqrt 2) (* v v))) (/ (* 4 (sqrt 2)) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (* 4 (sqrt 2)) 4)) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* -3 v) v)))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (- (* (sqrt 2) (* v v))) (/ (* 4 (sqrt 2)) 4)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (268 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* 3 v) (* v v)) (* (* 3 v) 4)) (+ 4 (* 12 (* v v))))) (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (* 9 v) (pow v 3)))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (* 4 (sqrt 2)) 4)) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* -3 v) v)))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (- (* (sqrt 2) (* v v))) (/ (* 4 (sqrt 2)) 4)))))) (* (sqrt (+ (* (* (* 3 v) (* v v)) (* (* 3 v) 4)) (+ 4 (* 12 (* v v))))) (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (* 9 v) (pow v 3)))) 4))))) * * * * [misc]progress: [ 302 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (110 enodes) * * [misc]simplify: iters left: 4 (358 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) 4)) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* 3 (* v v)) 1)))))) (sqrt (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) 4)) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* 3 (* v v)) 1)))))) (sqrt (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (180 enodes) * * [misc]simplify: iters left: 2 (335 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ (* (* v v) 12) 4) (* 36 (* (* v v) (* v v))))) (sqrt (* (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 3) (* 9 v))))) (* 4 (sqrt (+ 1 (* (* v v) 3))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) 4)) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* 3 (* v v)) 1)))))) (sqrt (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2))))))) (* (sqrt (+ (+ (* (* v v) 12) 4) (* 36 (* (* v v) (* v v))))) (sqrt (* (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 3) (* 9 v))))) (* 4 (sqrt (+ 1 (* (* v v) 3))))))))) * * * * [misc]progress: [ 303 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (409 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2)))))) (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2)))))) (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (279 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ 4 (* 12 (* v v))) (* (* (* v 9) (* v v)) (* v 4)))) (sqrt (+ 4 (* 12 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2)))))) (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (+ (+ 4 (* 12 (* v v))) (* (* (* v 9) (* v v)) (* v 4)))) (sqrt (+ 4 (* 12 (* v v))))))) * * * * [misc]progress: [ 304 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (377 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (/ (* (sqrt 2) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (/ 4 (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (/ (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ 4 (* (* v v) (sqrt 2)))) (sqrt (+ (* 3 (* v v)) 1)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (/ (* (sqrt 2) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (/ 4 (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (/ (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ 4 (* (* v v) (sqrt 2)))) (sqrt (+ (* 3 (* v v)) 1)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (263 enodes) * * [misc]simplify: iters left: 1 (462 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ 4 (* 12 (* v v))) (* (* v 36) (pow v 3)))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (+ (* 3 (* v v)) (* 9 (pow v 4)))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (/ (* (sqrt 2) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (/ 4 (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (/ (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ 4 (* (* v v) (sqrt 2)))) (sqrt (+ (* 3 (* v v)) 1)))))) (* (sqrt (+ (+ 4 (* 12 (* v v))) (* (* v 36) (pow v 3)))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (+ (* 3 (* v v)) (* 9 (pow v 4)))))))))) * * * * [misc]progress: [ 305 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (380 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2)))))) (sqrt (+ (* (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2)))))) (sqrt (+ (* (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (151 enodes) * * [misc]simplify: iters left: 2 (295 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* 4 (* v v)) (* v (* 9 v))) (+ (* (* v v) 12) 4))) (sqrt (+ 1 (* v (* 3 v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2)))))) (sqrt (+ (* (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))))) (* (sqrt (+ (* (* 4 (* v v)) (* v (* 9 v))) (+ (* (* v v) 12) 4))) (sqrt (+ 1 (* v (* 3 v))))))) * * * * [misc]progress: [ 306 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (396 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (sqrt 2) (* v v)))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (sqrt 2)) (* (sqrt (+ 1 (* v (* -3 v)))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (sqrt 2) (* v v)))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (sqrt 2)) (* (sqrt (+ 1 (* v (* -3 v)))) (* v v)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (263 enodes) * * [misc]simplify: iters left: 1 (462 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ 4 (* 12 (* v v))) (* (* 36 v) (pow v 3)))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (sqrt 2) (* v v)))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (sqrt 2)) (* (sqrt (+ 1 (* v (* -3 v)))) (* v v)))))) (* (sqrt (+ (+ 4 (* 12 (* v v))) (* (* 36 v) (pow v 3)))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * * * * [misc]progress: [ 307 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (38 enodes) * * [misc]simplify: iters left: 5 (105 enodes) * * [misc]simplify: iters left: 4 (348 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* -3 v) v))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* -3 v) v))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (294 enodes) * * [misc]simplify: iters left: 1 (434 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* 36 (pow v 4)) (+ (* v (* v 12)) 4))) (sqrt (* (sqrt (+ (+ 1 (* 3 (* v v))) (* 9 (pow v 4)))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* -3 v) v))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* v v) (sqrt 2))))))) (* (sqrt (+ (* 36 (pow v 4)) (+ (* v (* v 12)) 4))) (sqrt (* (sqrt (+ (+ 1 (* 3 (* v v))) (* 9 (pow v 4)))) 16))))) * * * * [misc]progress: [ 308 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (123 enodes) * * [misc]simplify: iters left: 4 (402 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) 4) (* (sqrt (+ 1 (* (* v v) -3))) (sqrt 2))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (sqrt 2)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) 4) (* (sqrt (+ 1 (* (* v v) -3))) (sqrt 2))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (253 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* 12 v) v) (+ (* (pow v 3) (* v 36)) 4))) (sqrt (* 16 (sqrt (+ 1 (* v (* 3 v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) 4) (* (sqrt (+ 1 (* (* v v) -3))) (sqrt 2))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (+ (* (* 12 v) v) (+ (* (pow v 3) (* v 36)) 4))) (sqrt (* 16 (sqrt (+ 1 (* v (* 3 v))))))))) * * * * [misc]progress: [ 309 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (109 enodes) * * [misc]simplify: iters left: 4 (361 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1)))) (* (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (sqrt 2)) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* v v))))) (sqrt (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (* (sqrt (+ 1 (* v (* v -3)))) (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1)))) (* (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (sqrt 2)) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* v v))))) (sqrt (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (* (sqrt (+ 1 (* v (* v -3)))) (sqrt 2)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (254 enodes) * * [misc]simplify: iters left: 1 (456 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) 4)) (sqrt (+ (+ (* (* v 36) (pow v 3)) 4) (* (* v 12) v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1)))) (* (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (sqrt 2)) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* v v))))) (sqrt (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (* (sqrt (+ 1 (* v (* v -3)))) (sqrt 2)))))) (* (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) 4)) (sqrt (+ (+ (* (* v 36) (pow v 3)) 4) (* (* v 12) v)))))) * * * * [misc]progress: [ 310 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (402 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (263 enodes) * * [misc]simplify: iters left: 1 (462 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ 4 (* 12 (* v v))) (* (* 36 v) (pow v 3)))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) (* (sqrt (+ (+ 4 (* 12 (* v v))) (* (* 36 v) (pow v 3)))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * * * * [misc]progress: [ 311 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (109 enodes) * * [misc]simplify: iters left: 4 (363 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* v v) (sqrt 2)))))) (sqrt (* (* (sqrt (+ 1 (* v (* v -3)))) (sqrt 2)) (+ 4 (* (* 4 v) (- v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* v v) (sqrt 2)))))) (sqrt (* (* (sqrt (+ 1 (* v (* v -3)))) (sqrt 2)) (+ 4 (* (* 4 v) (- v)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 4))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (251 enodes) * * [misc]simplify: iters left: 1 (411 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ 4 (* v (* v 12))) (* (* 36 v) (pow v 3)))) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* v v) (sqrt 2)))))) (sqrt (* (* (sqrt (+ 1 (* v (* v -3)))) (sqrt 2)) (+ 4 (* (* 4 v) (- v)))))) (* (sqrt (+ (+ 4 (* v (* v 12))) (* (* 36 v) (pow v 3)))) 4))) * * * * [misc]progress: [ 312 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3)))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (439 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v v) 3)))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) 3)))) 3)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v v) 3)))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) 3)))) 3)))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * * [misc]simplify: iters left: 6 (31 enodes) * * [misc]simplify: iters left: 5 (88 enodes) * * [misc]simplify: iters left: 4 (287 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (- (* (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (+ 1 (* v (* v -3))))) (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (+ 1 (* v (* v -3)))))) (* (* (sqrt (+ 1 (* v (* v -3)))) (- (* (/ (sqrt 2) 4) (- (* v v))) (/ (sqrt 2) 4))) (* (/ (sqrt 2) 4) (sqrt (+ 1 (* v (* v -3))))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v v) 3)))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) 3)))) 3)))) (* (sqrt (* 4 (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (- (* (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (+ 1 (* v (* v -3))))) (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (+ 1 (* v (* v -3)))))) (* (* (sqrt (+ 1 (* v (* v -3)))) (- (* (/ (sqrt 2) 4) (- (* v v))) (/ (sqrt 2) 4))) (* (/ (sqrt 2) 4) (sqrt (+ 1 (* v (* v -3))))))))))) * * * * [misc]progress: [ 313 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (438 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* v v) (sqrt 2)))))) (sqrt (* (* (sqrt (+ (* v (* v -3)) 1)) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* v (- v))))) (* (* (+ (* v (- v)) 1) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* v v) (sqrt 2)))))) (sqrt (* (* (sqrt (+ (* v (* v -3)) 1)) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* v (- v))))) (* (* (+ (* v (- v)) 1) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (69 enodes) * * [misc]simplify: iters left: 4 (189 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v)))))) (sqrt (* (* (+ (* v v) 1) (/ (sqrt 2) 4)) (sqrt (+ (* (* -3 v) v) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* v v) (sqrt 2)))))) (sqrt (* (* (sqrt (+ (* v (* v -3)) 1)) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* v (- v))))) (* (* (+ (* v (- v)) 1) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1)))))) (* (sqrt (* 4 (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v)))))) (sqrt (* (* (+ (* v v) 1) (/ (sqrt 2) 4)) (sqrt (+ (* (* -3 v) v) 1))))))) * * * * [misc]progress: [ 314 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (117 enodes) * * [misc]simplify: iters left: 4 (377 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ 1 (* (* v v) 3))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3))))) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* v v) (sqrt 2))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (sqrt 2) (* (- v) (* v (sqrt 2))))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ 1 (* (* v v) 3))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3))))) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* v v) (sqrt 2))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (sqrt 2) (* (- v) (* v (sqrt 2))))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) 4)))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (102 enodes) * * [misc]simplify: iters left: 3 (181 enodes) * * [misc]simplify: iters left: 2 (328 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9)))))) (sqrt (+ (* (+ (* (* v v) 3) (* (pow v 4) 9)) 16) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ 1 (* (* v v) 3))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3))))) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* v v) (sqrt 2))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (sqrt 2) (* (- v) (* v (sqrt 2))))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) 4)))) (* (sqrt (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9)))))) (sqrt (+ (* (+ (* (* v v) 3) (* (pow v 4) 9)) 16) 16))))) * * * * [misc]progress: [ 315 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (110 enodes) * * [misc]simplify: iters left: 4 (335 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2))) (* (* 4 (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* v v) 3) 3))))) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2))) (* (* 4 (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* v v) 3) 3))))) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (106 enodes) * * [misc]simplify: iters left: 3 (199 enodes) * * [misc]simplify: iters left: 2 (312 enodes) * * [misc]simplify: iters left: 1 (361 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))))) (sqrt (* (* (sqrt (+ 1 (* v (* 3 v)))) 16) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2))) (* (* 4 (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* v v) 3) 3))))) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))))) (sqrt (* (* (sqrt (+ 1 (* v (* 3 v)))) 16) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9))))))))) * * * * [misc]progress: [ 316 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (387 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (/ (sqrt 2) 4))) (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* v v)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2))))) (sqrt (- (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* 4 (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (/ (sqrt 2) 4))) (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* v v)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2))))) (sqrt (- (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* 4 (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (184 enodes) * * [misc]simplify: iters left: 2 (366 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 3) (* v 9))))))) (sqrt (+ (+ (* (* v v) 12) 4) (* (* v v) (* (* v 9) (* v 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (/ (sqrt 2) 4))) (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* v v)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2))))) (sqrt (- (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* 4 (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 3) (* v 9))))))) (sqrt (+ (+ (* (* v v) 12) 4) (* (* v v) (* (* v 9) (* v 4)))))))) * * * * [misc]progress: [ 317 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (375 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) (sqrt 2)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* 4 (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) 4) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* v 3) v) 3))))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (sqrt 2)) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) (sqrt 2)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* 4 (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) 4) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* v 3) v) 3))))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (sqrt 2)) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (152 enodes) * * [misc]simplify: iters left: 2 (253 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) (sqrt 2)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* 4 (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) 4) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* v 3) v) 3))))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (sqrt 2)) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))))))) (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9))))))) * * * * [misc]progress: [ 318 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (122 enodes) * * [misc]simplify: iters left: 4 (383 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v))))) (sqrt (+ (* (* (* 4 (* (sqrt 2) (- (* v v)))) (sqrt (+ 1 (* v (* -3 v))))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* 4 (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v))))) (sqrt (+ (* (* (* 4 (* (sqrt 2) (- (* v v)))) (sqrt (+ 1 (* v (* -3 v))))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* 4 (sqrt 2)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (185 enodes) * * [misc]simplify: iters left: 2 (298 enodes) * * [misc]simplify: iters left: 1 (360 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v))))) (sqrt (+ (* (* (* 4 (* (sqrt 2) (- (* v v)))) (sqrt (+ 1 (* v (* -3 v))))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* 4 (sqrt 2)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) 16))))) * * * * [misc]progress: [ 319 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (119 enodes) * * [misc]simplify: iters left: 4 (395 enodes) * [exit]simplify: Simplified to (* (sqrt (- (/ (* (sqrt 2) (* 4 (sqrt (+ 1 (* (* v v) 3))))) (/ 4 (sqrt (- 1 (pow (* (* v v) 3) 3))))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) 4) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2))) (* (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt 2)) (* (* v v) (sqrt (- 1 (pow (* (* v v) 3) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (/ (* (sqrt 2) (* 4 (sqrt (+ 1 (* (* v v) 3))))) (/ 4 (sqrt (- 1 (pow (* (* v v) 3) 3))))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) 4) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2))) (* (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt 2)) (* (* v v) (sqrt (- 1 (pow (* (* v v) 3) 3)))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (104 enodes) * * [misc]simplify: iters left: 3 (193 enodes) * * [misc]simplify: iters left: 2 (305 enodes) * * [misc]simplify: iters left: 1 (360 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) (* (sqrt (+ 1 (* v (* 3 v)))) 16)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (/ (* (sqrt 2) (* 4 (sqrt (+ 1 (* (* v v) 3))))) (/ 4 (sqrt (- 1 (pow (* (* v v) 3) 3))))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) 4) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2))) (* (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt 2)) (* (* v v) (sqrt (- 1 (pow (* (* v v) 3) 3)))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) (* (sqrt (+ 1 (* v (* 3 v)))) 16)))))) * * * * [misc]progress: [ 320 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (108 enodes) * * [misc]simplify: iters left: 4 (340 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (sqrt (+ 1 (* (* v 3) v)))) (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* 9 (* v v)) (* v v)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 9 (* v v)) (* v v)))))))) (sqrt (* (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (+ (sqrt 2) (* v (* (- v) (sqrt 2))))) (* 4 (sqrt (+ 1 (* (* v 3) v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (sqrt (+ 1 (* (* v 3) v)))) (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* 9 (* v v)) (* v v)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 9 (* v v)) (* v v)))))))) (sqrt (* (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (+ (sqrt 2) (* v (* (- v) (sqrt 2))))) (* 4 (sqrt (+ 1 (* (* v 3) v))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (261 enodes) * * [misc]simplify: iters left: 1 (347 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))))) (sqrt (+ (* 48 (* v v)) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (sqrt (+ 1 (* (* v 3) v)))) (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* 9 (* v v)) (* v v)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 9 (* v v)) (* v v)))))))) (sqrt (* (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (+ (sqrt 2) (* v (* (- v) (sqrt 2))))) (* 4 (sqrt (+ 1 (* (* v 3) v))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))))) (sqrt (+ (* 48 (* v v)) 16))))) * * * * [misc]progress: [ 321 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (112 enodes) * * [misc]simplify: iters left: 4 (363 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (/ (sqrt 2) 4) (* 4 (sqrt (+ 1 (* (* v v) 3))))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ (sqrt 2) 4)) (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (* 4 (sqrt (+ 1 (* (* v v) 3))))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ (sqrt 2) 4)) (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (* v v)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (171 enodes) * * [misc]simplify: iters left: 2 (282 enodes) * * [misc]simplify: iters left: 1 (326 enodes) * [exit]simplify: Simplified to (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (+ (* 3 (* v v)) (* (pow v 4) 9))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (* 4 (sqrt (+ 1 (* (* v v) 3))))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ (sqrt 2) 4)) (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (+ (* 3 (* v v)) (* (pow v 4) 9))))))) * * * * [misc]progress: [ 322 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (390 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) (+ (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* 4 (* (/ (sqrt 2) 4) (- (* v v)))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* 4 (* (* (sqrt (+ 1 (* (* v v) 3))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3))))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) (+ (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* 4 (* (/ (sqrt 2) 4) (- (* v v)))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* 4 (* (* (sqrt (+ 1 (* (* v v) 3))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3))))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (161 enodes) * * [misc]simplify: iters left: 2 (296 enodes) * * [misc]simplify: iters left: 1 (434 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9)))))) (sqrt (+ 4 (* (* v v) 12)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) (+ (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* 4 (* (/ (sqrt 2) 4) (- (* v v)))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* 4 (* (* (sqrt (+ 1 (* (* v v) 3))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3))))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9)))))) (sqrt (+ 4 (* (* v v) 12)))))) * * * * [misc]progress: [ 323 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (386 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (* (* (sqrt (+ (* -3 (* v v)) 1)) (- (* v v))) (* (sqrt (+ 1 (* (* v 3) v))) (* 4 (sqrt 2)))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* 9 (* v v)) (* v v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (* (* (sqrt (+ (* -3 (* v v)) 1)) (- (* v v))) (* (sqrt (+ 1 (* (* v 3) v))) (* 4 (sqrt 2)))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* 9 (* v v)) (* v v)))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (96 enodes) * * [misc]simplify: iters left: 3 (181 enodes) * * [misc]simplify: iters left: 2 (304 enodes) * * [misc]simplify: iters left: 1 (353 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9)))))) (sqrt (* 16 (sqrt (+ 1 (* (* v v) 3)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (* (* (sqrt (+ (* -3 (* v v)) 1)) (- (* v v))) (* (sqrt (+ 1 (* (* v 3) v))) (* 4 (sqrt 2)))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* 9 (* v v)) (* v v)))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9)))))) (sqrt (* 16 (sqrt (+ 1 (* (* v v) 3)))))))) * * * * [misc]progress: [ 324 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (112 enodes) * * [misc]simplify: iters left: 4 (371 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (/ (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (sqrt 2)) (/ 4 (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (/ (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (sqrt 2)) (/ 4 (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (176 enodes) * * [misc]simplify: iters left: 2 (322 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (* 9 v) (pow v 3))))))) (sqrt (+ (* 36 (* (* v v) (* v v))) (+ (* 12 (* v v)) 4)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (/ (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (sqrt 2)) (/ 4 (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (* 9 v) (pow v 3))))))) (sqrt (+ (* 36 (* (* v v) (* v v))) (+ (* 12 (* v v)) 4)))))) * * * * [misc]progress: [ 325 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (90 enodes) * * [misc]simplify: iters left: 4 (277 enodes) * [exit]simplify: Simplified to (- (* (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (* (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (153 enodes) * * [misc]simplify: iters left: 2 (255 enodes) * * [misc]simplify: iters left: 1 (268 enodes) * [exit]simplify: Simplified to (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (+ (* 3 (* v v)) (* 9 (pow v 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (* (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (+ (* 3 (* v v)) (* 9 (pow v 4)))))))) * * * * [misc]progress: [ 326 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (107 enodes) * * [misc]simplify: iters left: 4 (354 enodes) * [exit]simplify: Simplified to (* (sqrt (- (/ (* (* (sqrt (+ 1 (* (* v 3) v))) 4) (sqrt 2)) (/ 4 (sqrt (- 1 (pow (* (* v 3) v) 3))))) (* (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (sqrt 2)) (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* v v))))) (sqrt (- (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* v 3) v) 3))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (/ (* (* (sqrt (+ 1 (* (* v 3) v))) 4) (sqrt 2)) (/ 4 (sqrt (- 1 (pow (* (* v 3) v) 3))))) (* (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (sqrt 2)) (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* v v))))) (sqrt (- (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* v 3) v) 3))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (154 enodes) * * [misc]simplify: iters left: 2 (256 enodes) * * [misc]simplify: iters left: 1 (339 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (/ (* (* (sqrt (+ 1 (* (* v 3) v))) 4) (sqrt 2)) (/ 4 (sqrt (- 1 (pow (* (* v 3) v) 3))))) (* (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (sqrt 2)) (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* v v))))) (sqrt (- (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* v 3) v) 3))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9))))))) * * * * [misc]progress: [ 327 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (110 enodes) * * [misc]simplify: iters left: 4 (349 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (/ (sqrt 2) 4))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (/ (sqrt 2) 4))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (239 enodes) * * [misc]simplify: iters left: 1 (298 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))))) (sqrt (* (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))) (sqrt (+ 1 (* (* 3 v) v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (/ (sqrt 2) 4))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))))) (sqrt (* (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))) (sqrt (+ 1 (* (* 3 v) v)))))))) * * * * [misc]progress: [ 328 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (113 enodes) * * [misc]simplify: iters left: 4 (358 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt (+ 1 (* v (* -3 v)))) (* (* v v) (sqrt 2))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt (+ 1 (* v (* -3 v)))) (* (* v v) (sqrt 2))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (240 enodes) * * [misc]simplify: iters left: 1 (291 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (+ (* 3 (* v v)) (* 9 (pow v 4))))))) (sqrt (* (sqrt (+ 1 (+ (* 3 (* v v)) (* 9 (pow v 4))))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt (+ 1 (* v (* -3 v)))) (* (* v v) (sqrt 2))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (+ (* 3 (* v v)) (* 9 (pow v 4))))))) (sqrt (* (sqrt (+ 1 (+ (* 3 (* v v)) (* 9 (pow v 4))))) 4))))) * * * * [misc]progress: [ 329 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (401 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) 4) (/ (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ 4 (sqrt 2)))) (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* v v))))) (sqrt (- (/ (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (/ 4 (* 4 (sqrt (+ 1 (* (* v v) 3)))))) (* (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) 4) (/ (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ 4 (sqrt 2)))) (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* v v))))) (sqrt (- (/ (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (/ 4 (* 4 (sqrt (+ 1 (* (* v v) 3)))))) (* (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (169 enodes) * * [misc]simplify: iters left: 2 (276 enodes) * * [misc]simplify: iters left: 1 (297 enodes) * [exit]simplify: Simplified to (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) 4) (/ (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ 4 (sqrt 2)))) (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* v v))))) (sqrt (- (/ (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (/ 4 (* 4 (sqrt (+ 1 (* (* v v) 3)))))) (* (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))))) (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4)))))))) * * * * [misc]progress: [ 330 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (110 enodes) * * [misc]simplify: iters left: 4 (360 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* 4 (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt 2) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* 4 (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt 2) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (149 enodes) * * [misc]simplify: iters left: 2 (254 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ 1 (+ (* (* 3 v) v) (* 9 (pow v 4))))))) (sqrt (+ 4 (* v (* v 12))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* 4 (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt 2) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ 1 (+ (* (* 3 v) v) (* 9 (pow v 4))))))) (sqrt (+ 4 (* v (* v 12))))))) * * * * [misc]progress: [ 331 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (383 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ 1 (* v (* v 3))) (* (* v (* v 3)) (* v (* v 3))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))))) (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* v (* v 3))))) (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (* v v))))) (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (sqrt (+ 1 (* v (* v 3))))) (* (* (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))) (* (sqrt 2) (* v v))) (sqrt (+ (+ 1 (* v (* v 3))) (* (* v (* v 3)) (* v (* v 3))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ 1 (* v (* v 3))) (* (* v (* v 3)) (* v (* v 3))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))))) (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* v (* v 3))))) (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (* v v))))) (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (sqrt (+ 1 (* v (* v 3))))) (* (* (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))) (* (sqrt 2) (* v v))) (sqrt (+ (+ 1 (* v (* v 3))) (* (* v (* v 3)) (* v (* v 3))))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (239 enodes) * * [misc]simplify: iters left: 1 (298 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))))) (sqrt (* (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))) (sqrt (+ 1 (* (* 3 v) v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ 1 (* v (* v 3))) (* (* v (* v 3)) (* v (* v 3))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))))) (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* v (* v 3))))) (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (* v v))))) (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (sqrt (+ 1 (* v (* v 3))))) (* (* (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))) (* (sqrt 2) (* v v))) (sqrt (+ (+ 1 (* v (* v 3))) (* (* v (* v 3)) (* v (* v 3))))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))))) (sqrt (* (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))) (sqrt (+ 1 (* (* 3 v) v)))))))) * * * * [misc]progress: [ 332 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (113 enodes) * * [misc]simplify: iters left: 4 (364 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (* (* v v) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))))) (sqrt (- (* 4 (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt 2) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* v v) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (* (* v v) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))))) (sqrt (- (* 4 (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt 2) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* v v) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (149 enodes) * * [misc]simplify: iters left: 2 (255 enodes) * * [misc]simplify: iters left: 1 (348 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (* (* v v) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))))) (sqrt (- (* 4 (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt 2) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* v v) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9))))))))) * * * * [misc]progress: [ 333 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (392 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt (+ 1 (* v (* v -3)))) (sqrt 2)) (* (sqrt (+ 1 (* (* v 3) v))) (* v v))))) (sqrt (- (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (sqrt (+ 1 (* (* v 3) v))) (* 4 (/ (sqrt 2) 4)))) (* (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (sqrt 2)) (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt (+ 1 (* v (* v -3)))) (sqrt 2)) (* (sqrt (+ 1 (* (* v 3) v))) (* v v))))) (sqrt (- (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (sqrt (+ 1 (* (* v 3) v))) (* 4 (/ (sqrt 2) 4)))) (* (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (sqrt 2)) (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* v v)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (228 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))) (* 4 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (* 4 (sqrt (+ 1 (* (* 3 v) v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt (+ 1 (* v (* v -3)))) (sqrt 2)) (* (sqrt (+ 1 (* (* v 3) v))) (* v v))))) (sqrt (- (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (sqrt (+ 1 (* (* v 3) v))) (* 4 (/ (sqrt 2) 4)))) (* (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (sqrt 2)) (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* v v)))))) (* (sqrt (* (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))) (* 4 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (* 4 (sqrt (+ 1 (* (* 3 v) v)))))))) * * * * [misc]progress: [ 334 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (123 enodes) * * [misc]simplify: iters left: 4 (397 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt (+ 1 (* (* v 3) v)))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ (sqrt 2) 4))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))))) (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* v 3) v)))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (* v v) (sqrt 2)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ 1 (* (* v 3) v)))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ (sqrt 2) 4))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))))) (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* v 3) v)))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (149 enodes) * * [misc]simplify: iters left: 2 (240 enodes) * * [misc]simplify: iters left: 1 (290 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ 1 (* (* v 3) v)))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ (sqrt 2) 4))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))))) (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* v 3) v)))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) 16))))) * * * * [misc]progress: [ 335 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (113 enodes) * * [misc]simplify: iters left: 4 (348 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (/ (sqrt 2) 4))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (- (* (* (sqrt (+ 1 (* v (* -3 v)))) (sqrt 2)) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (/ (sqrt 2) 4))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (- (* (* (sqrt (+ 1 (* v (* -3 v)))) (sqrt 2)) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * * [misc]simplify: iters left: 2 (238 enodes) * * [misc]simplify: iters left: 1 (269 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ 1 (+ (* (* 3 v) v) (* 9 (pow v 4))))))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (/ (sqrt 2) 4))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (- (* (* (sqrt (+ 1 (* v (* -3 v)))) (sqrt 2)) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ 1 (+ (* (* 3 v) v) (* 9 (pow v 4))))))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) 16))))) * * * * [misc]progress: [ 336 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (380 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt (+ 1 (* (* v v) -3))) (sqrt 2))) (* (* 4 (* (* (- v) v) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v 3) v) 3)))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (* 4 (sqrt 2)) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (sqrt 2) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt (+ 1 (* (* v v) -3))) (sqrt 2))) (* (* 4 (* (* (- v) v) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v 3) v) 3)))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (* 4 (sqrt 2)) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (sqrt 2) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* v v)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (238 enodes) * * [misc]simplify: iters left: 1 (292 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))))) (sqrt (* (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt (+ 1 (* (* v v) -3))) (sqrt 2))) (* (* 4 (* (* (- v) v) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v 3) v) 3)))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (* 4 (sqrt 2)) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (sqrt 2) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))))) (sqrt (* (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))) 4))))) * * * * [misc]progress: [ 337 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (377 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* -3 (* v v)) 1)) (sqrt 2)) (sqrt (+ 1 (* (* v 3) v)))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* 4 (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* 9 (* v v)) (* v v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* -3 (* v v)) 1)) (sqrt 2)) (sqrt (+ 1 (* (* v 3) v)))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* 4 (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* 9 (* v v)) (* v v)))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (172 enodes) * * [misc]simplify: iters left: 2 (293 enodes) * * [misc]simplify: iters left: 1 (350 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))))) (sqrt (* 4 (sqrt (+ 1 (* v (* 3 v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* -3 (* v v)) 1)) (sqrt 2)) (sqrt (+ 1 (* (* v 3) v)))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* 4 (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* 9 (* v v)) (* v v)))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))))) (sqrt (* 4 (sqrt (+ 1 (* v (* 3 v))))))))) * * * * [misc]progress: [ 338 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (117 enodes) * * [misc]simplify: iters left: 4 (365 enodes) * [exit]simplify: Simplified to (* (sqrt (* (+ (* (- v) v) 1) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* -3 v) v)))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (+ (* (- v) v) 1) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* -3 v) v)))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (231 enodes) * * [misc]simplify: iters left: 1 (262 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))))) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (+ (* (- v) v) 1) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* -3 v) v)))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))))) 4))) * * * * [misc]progress: [ 339 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3)))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (124 enodes) * * [misc]simplify: iters left: 4 (441 enodes) * [exit]simplify: Simplified to (* (sqrt (* (+ (* (* (* v v) (* v v)) (- (* v v))) 1) (pow (* (/ (sqrt 2) 4) (sqrt (+ (* v (* -3 v)) 1))) 3))) (sqrt (- (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (+ (* (* (* v v) (* v v)) (- (* v v))) 1) (pow (* (/ (sqrt 2) 4) (sqrt (+ (* v (* -3 v)) 1))) 3))) (sqrt (- (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * * [misc]simplify: iters left: 6 (33 enodes) * * [misc]simplify: iters left: 5 (93 enodes) * * [misc]simplify: iters left: 4 (291 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))))) (sqrt (+ (* (* (sqrt (- 1 (* (* v v) 3))) (- (* (/ (sqrt 2) 4) (* v (- v))) (/ (sqrt 2) 4))) (* (* (/ (sqrt 2) 4) (* v (- v))) (sqrt (- 1 (* (* v v) 3))))) (* (* (sqrt (- 1 (* (* v v) 3))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* v v) 3))) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (+ (* (* (* v v) (* v v)) (- (* v v))) 1) (pow (* (/ (sqrt 2) 4) (sqrt (+ (* v (* -3 v)) 1))) 3))) (sqrt (- (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))))) (sqrt (+ (* (* (sqrt (- 1 (* (* v v) 3))) (- (* (/ (sqrt 2) 4) (* v (- v))) (/ (sqrt 2) 4))) (* (* (/ (sqrt 2) 4) (* v (- v))) (sqrt (- 1 (* (* v v) 3))))) (* (* (sqrt (- 1 (* (* v v) 3))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* v v) 3))) (/ (sqrt 2) 4)))))))) * * * * [misc]progress: [ 340 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (126 enodes) * * [misc]simplify: iters left: 4 (441 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (* (+ 1 (* (- v) v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* -3 v)) 1))) (* (sqrt (+ (* v (* -3 v)) 1)) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* (- v) v)))))) (sqrt (- (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (/ (sqrt 2) 4))) (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* v v)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (* (+ 1 (* (- v) v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* -3 v)) 1))) (* (sqrt (+ (* v (* -3 v)) 1)) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* (- v) v)))))) (sqrt (- (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (/ (sqrt 2) 4))) (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* v v)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (29 enodes) * * [misc]simplify: iters left: 5 (74 enodes) * * [misc]simplify: iters left: 4 (195 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v (* 3 v)) (* v (* 3 v))))))) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (* (+ 1 (* (- v) v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* -3 v)) 1))) (* (sqrt (+ (* v (* -3 v)) 1)) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* (- v) v)))))) (sqrt (- (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (/ (sqrt 2) 4))) (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* v v)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v (* 3 v)) (* v (* 3 v))))))) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v)))))))) * * * * [misc]progress: [ 341 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (36 enodes) * * [misc]simplify: iters left: 5 (102 enodes) * * [misc]simplify: iters left: 4 (335 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3)))))) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (* (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3))))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* v 3)) 3))))))) (sqrt (* (* (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3))))) 4) (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (+ (* (- v) (* v (sqrt 2))) (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3)))))) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (* (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3))))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* v 3)) 3))))))) (sqrt (* (* (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3))))) 4) (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (+ (* (- v) (* v (sqrt 2))) (sqrt 2)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (96 enodes) * * [misc]simplify: iters left: 3 (190 enodes) * * [misc]simplify: iters left: 2 (337 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (+ (* 3 (* v v)) (* (pow v 3) (* 9 v))))) (sqrt (* (+ (* 36 (* (* v v) (* v v))) (+ (* (* v v) 12) 4)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3)))))) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (* (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3))))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* v 3)) 3))))))) (sqrt (* (* (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3))))) 4) (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (+ (* (- v) (* v (sqrt 2))) (sqrt 2)))))) (* (sqrt (+ 1 (+ (* 3 (* v v)) (* (pow v 3) (* 9 v))))) (sqrt (* (+ (* 36 (* (* v v) (* v v))) (+ (* (* v v) 12) 4)) 4))))) * * * * [misc]progress: [ 342 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (377 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (* (sqrt 2) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))))) (sqrt (- (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (* (sqrt 2) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))))) (sqrt (- (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (105 enodes) * * [misc]simplify: iters left: 3 (203 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (401 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9)))) (sqrt (* (* (sqrt (+ 1 (* (* v v) 3))) 16) (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (* (sqrt 2) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))))) (sqrt (- (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))))))) (* (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9)))) (sqrt (* (* (sqrt (+ 1 (* (* v v) 3))) 16) (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9))))))))) * * * * [misc]progress: [ 343 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (94 enodes) * * [misc]simplify: iters left: 4 (298 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ (* (* v 3) v) 1)))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ (* (* v 3) v) 1))) (* v v))))) (sqrt (* (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ (* (* v 3) v) 1))) (+ (* (sqrt 2) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* 4 (* (/ (sqrt 2) 4) (- (* v v)))) (sqrt (- 1 (pow (* (* v 3) v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ (* (* v 3) v) 1)))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ (* (* v 3) v) 1))) (* v v))))) (sqrt (* (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ (* (* v 3) v) 1))) (+ (* (sqrt 2) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* 4 (* (/ (sqrt 2) 4) (- (* v v)))) (sqrt (- 1 (pow (* (* v 3) v) 3)))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (164 enodes) * * [misc]simplify: iters left: 2 (326 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 3) (* v 9))))) (sqrt (+ (+ (* 12 (* v v)) 4) (* (* 4 (* v v)) (* (* v v) 9))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ (* (* v 3) v) 1)))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ (* (* v 3) v) 1))) (* v v))))) (sqrt (* (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ (* (* v 3) v) 1))) (+ (* (sqrt 2) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* 4 (* (/ (sqrt 2) 4) (- (* v v)))) (sqrt (- 1 (pow (* (* v 3) v) 3)))))))) (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 3) (* v 9))))) (sqrt (+ (+ (* 12 (* v v)) 4) (* (* 4 (* v v)) (* (* v v) 9))))))) * * * * [misc]progress: [ 344 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (113 enodes) * * [misc]simplify: iters left: 4 (372 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) (sqrt 2)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* 4 (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))))) (sqrt (- (* (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ (sqrt 2) 4)) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1)))) (* (* (* v (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* v (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) (sqrt 2)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* 4 (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))))) (sqrt (- (* (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ (sqrt 2) 4)) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1)))) (* (* (* v (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* v (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1)))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (154 enodes) * * [misc]simplify: iters left: 2 (261 enodes) * * [misc]simplify: iters left: 1 (358 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) (* 4 (sqrt (+ 1 (* v (* 3 v))))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) (sqrt 2)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* 4 (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))))) (sqrt (- (* (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ (sqrt 2) 4)) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1)))) (* (* (* v (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* v (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1)))))))) (* (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) (* 4 (sqrt (+ 1 (* v (* 3 v))))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9))))))) * * * * [misc]progress: [ 345 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (108 enodes) * * [misc]simplify: iters left: 4 (361 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (+ (* v (* -3 v)) 1))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* 4 (sqrt 2))))) (sqrt (- (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (+ (* v (* -3 v)) 1))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* 4 (sqrt 2))))) (sqrt (- (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (233 enodes) * * [misc]simplify: iters left: 1 (267 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) (sqrt (* 16 (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4)))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (+ (* v (* -3 v)) 1))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* 4 (sqrt 2))))) (sqrt (- (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))))))) (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) (sqrt (* 16 (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4)))))))))) * * * * [misc]progress: [ 346 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (371 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (* (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3))))) 4)) (* (* (* (sqrt (+ (* v (* v 3)) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (* v v)))) (sqrt (- (/ (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (sqrt 2)) (/ 4 (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3))))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (* (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3))))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (* (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3))))) 4)) (* (* (* (sqrt (+ (* v (* v 3)) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (* v v)))) (sqrt (- (/ (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (sqrt 2)) (/ 4 (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3))))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (* (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3))))) (* v v)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (172 enodes) * * [misc]simplify: iters left: 2 (272 enodes) * * [misc]simplify: iters left: 1 (338 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) (sqrt (* (* (sqrt (+ 1 (* v (* 3 v)))) 16) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (* (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3))))) 4)) (* (* (* (sqrt (+ (* v (* v 3)) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (* v v)))) (sqrt (- (/ (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (sqrt 2)) (/ 4 (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3))))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (* (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3))))) (* v v)))))) (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) (sqrt (* (* (sqrt (+ 1 (* v (* 3 v)))) 16) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9))))))))) * * * * [misc]progress: [ 347 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (112 enodes) * * [misc]simplify: iters left: 4 (362 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (sqrt 2) (* (sqrt 2) (* (- v) v)))) (* (sqrt (+ (* (* v v) 3) 1)) 4))) (sqrt (- (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4)) (* (* v v) (sqrt (- 1 (pow (* (* v v) 3) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (sqrt 2) (* (sqrt 2) (* (- v) v)))) (* (sqrt (+ (* (* v v) 3) 1)) 4))) (sqrt (- (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4)) (* (* v v) (sqrt (- 1 (pow (* (* v v) 3) 3)))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * * [misc]simplify: iters left: 2 (262 enodes) * * [misc]simplify: iters left: 1 (368 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* 48 (* v v)) 16)) (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (sqrt 2) (* (sqrt 2) (* (- v) v)))) (* (sqrt (+ (* (* v v) 3) 1)) 4))) (sqrt (- (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4)) (* (* v v) (sqrt (- 1 (pow (* (* v v) 3) 3)))))))) (* (sqrt (+ (* 48 (* v v)) 16)) (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9))))))) * * * * [misc]progress: [ 348 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (104 enodes) * * [misc]simplify: iters left: 4 (320 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3))))) (* (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))) (sqrt 2))) (* (* (* (sqrt (+ (* v (* v 3)) 1)) 4) (/ (sqrt 2) 4)) (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (* v v))))) (sqrt (- (* (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3))))) (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (/ (sqrt 2) 4))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3))))) (* (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))) (sqrt 2))) (* (* (* (sqrt (+ (* v (* v 3)) 1)) 4) (/ (sqrt 2) 4)) (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (* v v))))) (sqrt (- (* (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3))))) (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (/ (sqrt 2) 4))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3))))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (151 enodes) * * [misc]simplify: iters left: 2 (254 enodes) * * [misc]simplify: iters left: 1 (343 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) (* 4 (sqrt (+ 1 (* v (* 3 v))))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3))))) (* (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))) (sqrt 2))) (* (* (* (sqrt (+ (* v (* v 3)) 1)) 4) (/ (sqrt 2) 4)) (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (* v v))))) (sqrt (- (* (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3))))) (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (/ (sqrt 2) 4))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3))))))))) (* (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) (* 4 (sqrt (+ 1 (* v (* 3 v))))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9))))))) * * * * [misc]progress: [ 349 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (387 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* v 3) v) 1)) (+ (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (sqrt 2)) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4))))) (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* v 3) v) 1)) (+ (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (sqrt 2)) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4))))) (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (85 enodes) * * [misc]simplify: iters left: 3 (184 enodes) * * [misc]simplify: iters left: 2 (358 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* v (* v 12)) 4)) (sqrt (+ 1 (+ (* v (* 3 v)) (* (* 9 v) (pow v 3)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* v 3) v) 1)) (+ (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (sqrt 2)) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4))))) (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))))))) (* (sqrt (+ (* v (* v 12)) 4)) (sqrt (+ 1 (+ (* v (* 3 v)) (* (* 9 v) (pow v 3)))))))) * * * * [misc]progress: [ 350 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (117 enodes) * * [misc]simplify: iters left: 4 (373 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4)) (* (* v v) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (* (* v v) 3) 1)) 4) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* -3 v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4)) (* (* v v) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (* (* v v) 3) 1)) 4) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* -3 v))))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (171 enodes) * * [misc]simplify: iters left: 2 (287 enodes) * * [misc]simplify: iters left: 1 (368 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) 16)) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4)) (* (* v v) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (* (* v v) 3) 1)) 4) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* -3 v))))))))) (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) 16)) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9))))))) * * * * [misc]progress: [ 351 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (98 enodes) * * [misc]simplify: iters left: 4 (335 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (/ (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ 4 (sqrt 2)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v))))))) (sqrt (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (+ (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (- (* (* v v) (sqrt 2)))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (/ (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ 4 (sqrt 2)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v))))))) (sqrt (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (+ (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (- (* (* v v) (sqrt 2)))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (149 enodes) * * [misc]simplify: iters left: 2 (263 enodes) * * [misc]simplify: iters left: 1 (419 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) (sqrt (+ (+ (* (* 36 v) (pow v 3)) 4) (* 12 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (/ (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ 4 (sqrt 2)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v))))))) (sqrt (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (+ (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (- (* (* v v) (sqrt 2)))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))))))) (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) (sqrt (+ (+ (* (* 36 v) (pow v 3)) 4) (* 12 (* v v))))))) * * * * [misc]progress: [ 352 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (107 enodes) * * [misc]simplify: iters left: 4 (354 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt (+ (* (* v 3) v) 1))) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* v 3) v) 3))))) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (* (* v 3) v) 1))) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* v 3) v) 3))))) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (230 enodes) * * [misc]simplify: iters left: 1 (262 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) (* 4 (sqrt (+ 1 (* v (* 3 v))))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (* (* v 3) v) 1))) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* v 3) v) 3))))) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))))))) (* (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) (* 4 (sqrt (+ 1 (* v (* 3 v))))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4)))))))) * * * * [misc]progress: [ 353 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (28 enodes) * * [misc]simplify: iters left: 5 (76 enodes) * * [misc]simplify: iters left: 4 (237 enodes) * [exit]simplify: Simplified to (- (/ (* (sqrt 2) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (/ 4 (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (/ (* (sqrt 2) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (/ 4 (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (132 enodes) * * [misc]simplify: iters left: 2 (212 enodes) * * [misc]simplify: iters left: 1 (251 enodes) * [exit]simplify: Simplified to (+ 1 (+ (* 3 (* v v)) (* 9 (pow v 4)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (/ (* (sqrt 2) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (/ 4 (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))))) (+ 1 (+ (* 3 (* v v)) (* 9 (pow v 4)))))) * * * * [misc]progress: [ 354 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (38 enodes) * * [misc]simplify: iters left: 5 (105 enodes) * * [misc]simplify: iters left: 4 (349 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ (sqrt 2) 4)) (sqrt (+ (+ (* (* v 3) v) 1) (* (* 9 (* v v)) (* v v))))) (* (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ (sqrt 2) 4)) (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* 9 (* v v)) (* v v)))) (* v v))))) (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (sqrt (+ (+ (* (* v 3) v) 1) (* (* 9 (* v v)) (* v v))))) (* (/ (sqrt 2) 4) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ (sqrt 2) 4)) (sqrt (+ (+ (* (* v 3) v) 1) (* (* 9 (* v v)) (* v v))))) (* (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ (sqrt 2) 4)) (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* 9 (* v v)) (* v v)))) (* v v))))) (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (sqrt (+ (+ (* (* v 3) v) 1) (* (* 9 (* v v)) (* v v))))) (* (/ (sqrt 2) 4) (* v v)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (79 enodes) * * [misc]simplify: iters left: 3 (154 enodes) * * [misc]simplify: iters left: 2 (265 enodes) * * [misc]simplify: iters left: 1 (280 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4)))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ (sqrt 2) 4)) (sqrt (+ (+ (* (* v 3) v) 1) (* (* 9 (* v v)) (* v v))))) (* (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ (sqrt 2) 4)) (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* 9 (* v v)) (* v v)))) (* v v))))) (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (sqrt (+ (+ (* (* v 3) v) 1) (* (* 9 (* v v)) (* v v))))) (* (/ (sqrt 2) 4) (* v v)))))) (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4)))))))))) * * * * [misc]progress: [ 355 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (36 enodes) * * [misc]simplify: iters left: 5 (100 enodes) * * [misc]simplify: iters left: 4 (337 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (+ (* v (* v -3)) 1)) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (+ (* v (* v -3)) 1)) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (136 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (253 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ (+ 1 (* (* v v) 3)) (* (pow v 4) 9))))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (pow v 4) 9)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (+ (* v (* v -3)) 1)) (* (* v v) (sqrt 2))))))) (* (sqrt (* 4 (sqrt (+ (+ 1 (* (* v v) 3)) (* (pow v 4) 9))))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (pow v 4) 9)))))) * * * * [misc]progress: [ 356 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (113 enodes) * * [misc]simplify: iters left: 4 (364 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* v 3) v) 1)))))) (sqrt (- (/ (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (sqrt 2)) (/ 4 (sqrt (- 1 (pow (* (* v 3) v) 3))))) (* (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (* v v)) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* v 3) v) 1)))))) (sqrt (- (/ (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (sqrt 2)) (/ 4 (sqrt (- 1 (pow (* (* v 3) v) 3))))) (* (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (* v v)) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ (sqrt 2) 4)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (235 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* v 3) v) 1)))))) (sqrt (- (/ (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (sqrt 2)) (/ 4 (sqrt (- 1 (pow (* (* v 3) v) 3))))) (* (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (* v v)) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ (sqrt 2) 4)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9))))))) * * * * [misc]progress: [ 357 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (380 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* v v) 3) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* v v) 3) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (85 enodes) * * [misc]simplify: iters left: 3 (160 enodes) * * [misc]simplify: iters left: 2 (301 enodes) * * [misc]simplify: iters left: 1 (372 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 4 (* v (* 12 v)))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* v v) 3) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))))))) (* (sqrt (+ 4 (* v (* 12 v)))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9))))))) * * * * [misc]progress: [ 358 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (38 enodes) * * [misc]simplify: iters left: 5 (102 enodes) * * [misc]simplify: iters left: 4 (311 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3)))))) (* (* (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3))))) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* v (* v 3)) 3))))))) (sqrt (- (/ (* (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3))))) (sqrt 2)) (/ 4 (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (sqrt (+ (* v (* v 3)) 1)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3)))))) (* (* (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3))))) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* v (* v 3)) 3))))))) (sqrt (- (/ (* (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3))))) (sqrt 2)) (/ 4 (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (sqrt (+ (* v (* v 3)) 1)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (79 enodes) * * [misc]simplify: iters left: 3 (154 enodes) * * [misc]simplify: iters left: 2 (265 enodes) * * [misc]simplify: iters left: 1 (280 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) (sqrt (+ 1 (* v (* 3 v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3)))))) (* (* (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3))))) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* v (* v 3)) 3))))))) (sqrt (- (/ (* (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3))))) (sqrt 2)) (/ 4 (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (sqrt (+ (* v (* v 3)) 1)))))) (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) (sqrt (+ 1 (* v (* 3 v))))))))) * * * * [misc]progress: [ 359 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (108 enodes) * * [misc]simplify: iters left: 4 (343 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (* (- (* v v)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ (sqrt 2) 4))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (* (- (* v v)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ (sqrt 2) 4))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (153 enodes) * * [misc]simplify: iters left: 2 (278 enodes) * * [misc]simplify: iters left: 1 (335 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (+ (* (* 3 v) v) (* 9 (pow v 4))))) (sqrt (+ 1 (* (* 3 v) v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (* (- (* v v)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ (sqrt 2) 4))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))))))) (* (sqrt (+ 1 (+ (* (* 3 v) v) (* 9 (pow v 4))))) (sqrt (+ 1 (* (* 3 v) v)))))) * * * * [misc]progress: [ 360 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (366 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (+ (* v (* v 3)) 1)) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* v (* v 3)))))))) (sqrt (- (/ (* (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ (* v (* v 3)) 1))) (sqrt 2)) (/ 4 (sqrt (- 1 (pow (* v (* v 3)) 3))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ (* v (* v 3)) 1))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (+ (* v (* v 3)) 1)) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* v (* v 3)))))))) (sqrt (- (/ (* (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ (* v (* v 3)) 1))) (sqrt 2)) (/ 4 (sqrt (- 1 (pow (* v (* v 3)) 3))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ (* v (* v 3)) 1))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (79 enodes) * * [misc]simplify: iters left: 3 (152 enodes) * * [misc]simplify: iters left: 2 (255 enodes) * * [misc]simplify: iters left: 1 (293 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))) (sqrt (* 4 (sqrt (+ 1 (* (* 3 v) v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (+ (* v (* v 3)) 1)) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* v (* v 3)))))))) (sqrt (- (/ (* (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ (* v (* v 3)) 1))) (sqrt 2)) (/ 4 (sqrt (- 1 (pow (* v (* v 3)) 3))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ (* v (* v 3)) 1))))))) (* (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))) (sqrt (* 4 (sqrt (+ 1 (* (* 3 v) v)))))))) * * * * [misc]progress: [ 361 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (108 enodes) * * [misc]simplify: iters left: 4 (351 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (+ (* (* v v) -3) 1)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (/ (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ 4 (* (* v v) (sqrt 2)))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (+ (* (* v v) -3) 1)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (/ (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ 4 (* (* v v) (sqrt 2)))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (233 enodes) * * [misc]simplify: iters left: 1 (266 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) (sqrt (* 16 (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (+ (* (* v v) -3) 1)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (/ (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ 4 (* (* v v) (sqrt 2)))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))))))) (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) (sqrt (* 16 (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9))))))))) * * * * [misc]progress: [ 362 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (117 enodes) * * [misc]simplify: iters left: 4 (368 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (+ (* (* v 3) v) 1) (* (* 9 (* v v)) (* v v))))) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (sqrt (+ (+ (* (* v 3) v) 1) (* (* 9 (* v v)) (* v v))))))) (sqrt (- (* (* 4 (sqrt (+ (* (* v 3) v) 1))) (* (sqrt (+ 1 (* (* v v) -3))) (sqrt 2))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (* (* v v) (sqrt 2)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (+ (* (* v 3) v) 1) (* (* 9 (* v v)) (* v v))))) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (sqrt (+ (+ (* (* v 3) v) 1) (* (* 9 (* v v)) (* v v))))))) (sqrt (- (* (* 4 (sqrt (+ (* (* v 3) v) 1))) (* (sqrt (+ 1 (* (* v v) -3))) (sqrt 2))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (138 enodes) * * [misc]simplify: iters left: 2 (233 enodes) * * [misc]simplify: iters left: 1 (284 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) 16)) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (+ (* (* v 3) v) 1) (* (* 9 (* v v)) (* v v))))) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (sqrt (+ (+ (* (* v 3) v) 1) (* (* 9 (* v v)) (* v v))))))) (sqrt (- (* (* 4 (sqrt (+ (* (* v 3) v) 1))) (* (sqrt (+ 1 (* (* v v) -3))) (sqrt 2))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) 16)) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9))))))) * * * * [misc]progress: [ 363 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (36 enodes) * * [misc]simplify: iters left: 5 (97 enodes) * * [misc]simplify: iters left: 4 (300 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (- (* v v))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (/ (sqrt 2) 4))))) (sqrt (+ (* (* (* 4 (/ (sqrt 2) 4)) (* (- v) v)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt 2) (sqrt (+ (* v (* v -3)) 1))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (- (* v v))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (/ (sqrt 2) 4))))) (sqrt (+ (* (* (* 4 (/ (sqrt 2) 4)) (* (- v) v)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt 2) (sqrt (+ (* v (* v -3)) 1))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (136 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (253 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ (+ 1 (* (* v v) 3)) (* (pow v 4) 9))))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (pow v 4) 9)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (- (* v v))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (/ (sqrt 2) 4))))) (sqrt (+ (* (* (* 4 (/ (sqrt 2) 4)) (* (- v) v)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt 2) (sqrt (+ (* v (* v -3)) 1))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))))))) (* (sqrt (* 4 (sqrt (+ (+ 1 (* (* v v) 3)) (* (pow v 4) 9))))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (pow v 4) 9)))))) * * * * [misc]progress: [ 364 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (366 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt 2) (* (sqrt (+ (* v (* -3 v)) 1)) (sqrt (+ (* 3 (* v v)) 1)))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 9 (* v v)) (* v v)))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (sqrt 2) 4)) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 9 (* v v)) (* v v)))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt 2) (* (sqrt (+ (* v (* -3 v)) 1)) (sqrt (+ (* 3 (* v v)) 1)))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 9 (* v v)) (* v v)))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (sqrt 2) 4)) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 9 (* v v)) (* v v)))) (* v v)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (77 enodes) * * [misc]simplify: iters left: 3 (127 enodes) * * [misc]simplify: iters left: 2 (213 enodes) * * [misc]simplify: iters left: 1 (252 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9)))) (sqrt (* 4 (sqrt (+ 1 (* (* v v) 3)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt 2) (* (sqrt (+ (* v (* -3 v)) 1)) (sqrt (+ (* 3 (* v v)) 1)))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 9 (* v v)) (* v v)))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (sqrt 2) 4)) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 9 (* v v)) (* v v)))) (* v v)))))) (* (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9)))) (sqrt (* 4 (sqrt (+ 1 (* (* v v) 3)))))))) * * * * [misc]progress: [ 365 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (37 enodes) * * [misc]simplify: iters left: 5 (103 enodes) * * [misc]simplify: iters left: 4 (332 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ 1 (* (* v -3) v))) (sqrt 2)) (+ (* (* 4 v) (- v)) 4))) (sqrt (- (/ (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)) (/ 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ 1 (* (* v -3) v))) (sqrt 2)) (+ (* (* 4 v) (- v)) 4))) (sqrt (- (/ (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)) (/ 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (* v v)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 4))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (164 enodes) * * [misc]simplify: iters left: 2 (282 enodes) * * [misc]simplify: iters left: 1 (353 enodes) * [exit]simplify: Simplified to (* 4 (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ 1 (* (* v -3) v))) (sqrt 2)) (+ (* (* 4 v) (- v)) 4))) (sqrt (- (/ (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2)) (/ 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (* v v)))))) (* 4 (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9))))))) * * * * [misc]progress: [ 366 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3)))) * * [misc]simplify: iters left: 6 (37 enodes) * * [misc]simplify: iters left: 5 (110 enodes) * * [misc]simplify: iters left: 4 (400 enodes) * [exit]simplify: Simplified to (* (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ 1 (* -3 (* v v))))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* -3 (* v v))))) 3))) (sqrt (- (* (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ (sqrt 2) 4)) (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ 1 (* -3 (* v v))))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* -3 (* v v))))) 3))) (sqrt (- (* (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ (sqrt 2) 4)) (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * * [misc]simplify: iters left: 6 (30 enodes) * * [misc]simplify: iters left: 5 (87 enodes) * * [misc]simplify: iters left: 4 (283 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (sqrt (+ (* (* (* (- (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* -3 v)) 1))) (* (sqrt (+ (* v (* -3 v)) 1)) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))) (* (* (/ (sqrt 2) 4) (sqrt (+ (* v (* -3 v)) 1))) (* (/ (sqrt 2) 4) (sqrt (+ (* v (* -3 v)) 1))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ 1 (* -3 (* v v))))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* -3 (* v v))))) 3))) (sqrt (- (* (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ (sqrt 2) 4)) (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))))))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (sqrt (+ (* (* (* (- (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* -3 v)) 1))) (* (sqrt (+ (* v (* -3 v)) 1)) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))) (* (* (/ (sqrt 2) 4) (sqrt (+ (* v (* -3 v)) 1))) (* (/ (sqrt 2) 4) (sqrt (+ (* v (* -3 v)) 1))))))))) * * * * [misc]progress: [ 367 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (37 enodes) * * [misc]simplify: iters left: 5 (112 enodes) * * [misc]simplify: iters left: 4 (400 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* (* v -3) v) 1)) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* (- v) v)))) (* (sqrt (+ (* (* v -3) v) 1)) (+ (* (/ (sqrt 2) 4) (* (- v) v)) (/ (sqrt 2) 4))))) (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* (* v -3) v) 1)) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* (- v) v)))) (* (sqrt (+ (* (* v -3) v) 1)) (+ (* (/ (sqrt 2) 4) (* (- v) v)) (/ (sqrt 2) 4))))) (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (68 enodes) * * [misc]simplify: iters left: 4 (183 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* -3 v) v) 1)))) (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* (* v -3) v) 1)) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* (- v) v)))) (* (sqrt (+ (* (* v -3) v) 1)) (+ (* (/ (sqrt 2) 4) (* (- v) v)) (/ (sqrt 2) 4))))) (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)))))) (* (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* -3 v) v) 1)))) (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v)))))))) * * * * [misc]progress: [ 368 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (377 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (* (sqrt 2) (- (* v v))) (sqrt 2))))) (sqrt (+ (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (/ (sqrt 2) 4) (- (* v v))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (* (sqrt 2) (- (* v v))) (sqrt 2))))) (sqrt (+ (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (/ (sqrt 2) 4) (- (* v v))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (183 enodes) * * [misc]simplify: iters left: 2 (337 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))))) (sqrt (+ (* (+ (* v (* 3 v)) (* (pow v 4) 9)) 16) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (* (sqrt 2) (- (* v v))) (sqrt 2))))) (sqrt (+ (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (/ (sqrt 2) 4) (- (* v v))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))))) (sqrt (+ (* (+ (* v (* 3 v)) (* (pow v 4) 9)) 16) 16))))) * * * * [misc]progress: [ 369 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (371 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v))))) (sqrt (- (* (sqrt 2) (* (* (sqrt (+ (* 3 (* v v)) 1)) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v))))) (sqrt (- (* (sqrt 2) (* (* (sqrt (+ (* 3 (* v v)) 1)) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (164 enodes) * * [misc]simplify: iters left: 2 (262 enodes) * * [misc]simplify: iters left: 1 (319 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) (* (sqrt (+ 1 (* v (* 3 v)))) 16)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v))))) (sqrt (- (* (sqrt 2) (* (* (sqrt (+ (* 3 (* v v)) 1)) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) (* (sqrt (+ 1 (* v (* 3 v)))) 16)))))) * * * * [misc]progress: [ 370 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (382 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (sqrt 2))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) 4)))) (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (sqrt 2))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) 4)))) (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1)))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (85 enodes) * * [misc]simplify: iters left: 3 (162 enodes) * * [misc]simplify: iters left: 2 (329 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt (+ 1 (+ (* (* 3 v) v) (* (* v 9) (pow v 3))))))) (sqrt (+ (+ 4 (* (* v v) 12)) (* (* (* v 9) (* v v)) (* 4 v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (sqrt 2))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) 4)))) (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1)))))))) (* (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt (+ 1 (+ (* (* 3 v) v) (* (* v 9) (pow v 3))))))) (sqrt (+ (+ 4 (* (* v v) 12)) (* (* (* v 9) (* v v)) (* 4 v))))))) * * * * [misc]progress: [ 371 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (106 enodes) * * [misc]simplify: iters left: 4 (325 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (/ (sqrt 2) 4))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) 4)))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (/ (sqrt 2) 4))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) 4)))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (233 enodes) * * [misc]simplify: iters left: 1 (291 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9)))))) (sqrt (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (/ (sqrt 2) 4))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) 4)))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)))))) (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9)))))) (sqrt (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9))))))))) * * * * [misc]progress: [ 372 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (385 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* 4 (* (sqrt 2) (* (- v) v))) (sqrt (- 1 (* (* v v) 3)))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (* v v) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (* 4 (* (sqrt 2) (* (- v) v))) (sqrt (- 1 (* (* v v) 3)))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (* v v) (/ (sqrt 2) 4)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (225 enodes) * * [misc]simplify: iters left: 1 (258 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt (+ 1 (+ (* (* 3 v) v) (* 9 (pow v 4))))))) (sqrt (* 16 (sqrt (+ 1 (+ (* (* 3 v) v) (* 9 (pow v 4)))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (* 4 (* (sqrt 2) (* (- v) v))) (sqrt (- 1 (* (* v v) 3)))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (* v v) (/ (sqrt 2) 4)))))) (* (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt (+ 1 (+ (* (* 3 v) v) (* 9 (pow v 4))))))) (sqrt (* 16 (sqrt (+ 1 (+ (* (* 3 v) v) (* 9 (pow v 4)))))))))) * * * * [misc]progress: [ 373 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (416 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (/ (sqrt 2) 4) (* v v)) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))))))) (sqrt (- (* (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) 4) (* (sqrt 2) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))) (* (* (sqrt (+ (* (* v 3) v) 1)) 4) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (/ (sqrt 2) 4) (* v v)) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))))))) (sqrt (- (* (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) 4) (* (sqrt 2) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))) (* (* (sqrt (+ (* (* v 3) v) 1)) 4) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (164 enodes) * * [misc]simplify: iters left: 2 (262 enodes) * * [misc]simplify: iters left: 1 (319 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) (* (sqrt (+ 1 (* v (* 3 v)))) 16)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (/ (sqrt 2) 4) (* v v)) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))))))) (sqrt (- (* (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) 4) (* (sqrt 2) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))) (* (* (sqrt (+ (* (* v 3) v) 1)) 4) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) (* (sqrt (+ 1 (* v (* 3 v)))) 16)))))) * * * * [misc]progress: [ 374 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (385 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (+ (sqrt 2) (* v (* (- v) (sqrt 2))))) (* (sqrt (+ (* 3 (* v v)) 1)) 4))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (/ (sqrt 2) 4))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (+ (sqrt 2) (* v (* (- v) (sqrt 2))))) (* (sqrt (+ (* 3 (* v v)) 1)) 4))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (/ (sqrt 2) 4))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (183 enodes) * * [misc]simplify: iters left: 2 (328 enodes) * * [misc]simplify: iters left: 1 (433 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))))) (sqrt (+ (* 48 (* v v)) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (+ (sqrt 2) (* v (* (- v) (sqrt 2))))) (* (sqrt (+ (* 3 (* v v)) 1)) 4))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (/ (sqrt 2) 4))))))) (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))))) (sqrt (+ (* 48 (* v v)) 16))))) * * * * [misc]progress: [ 375 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (397 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1)))) (* (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ (sqrt 2) 4)) (* (* (sqrt (+ (* (* v 3) v) 1)) 4) (* v v))))) (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1)))) (* (/ (sqrt 2) 4) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1)))) (* (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ (sqrt 2) 4)) (* (* (sqrt (+ (* (* v 3) v) 1)) 4) (* v v))))) (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1)))) (* (/ (sqrt 2) 4) (* v v)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (232 enodes) * * [misc]simplify: iters left: 1 (280 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9)))))) (sqrt (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1)))) (* (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ (sqrt 2) 4)) (* (* (sqrt (+ (* (* v 3) v) 1)) 4) (* v v))))) (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1)))) (* (/ (sqrt 2) 4) (* v v)))))) (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9)))))) (sqrt (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9))))))))) * * * * [misc]progress: [ 376 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (108 enodes) * * [misc]simplify: iters left: 4 (357 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) (sqrt 2)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* (* 4 (sqrt (+ (* (* v 3) v) 1))) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))))) (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) (sqrt 2)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* (* 4 (sqrt (+ (* (* v 3) v) 1))) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))))) (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (* v v)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (85 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (272 enodes) * * [misc]simplify: iters left: 1 (374 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))))) (sqrt (+ (* v (* 12 v)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) (sqrt 2)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* (* 4 (sqrt (+ (* (* v 3) v) 1))) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))))) (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (* v v)))))) (* (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))))) (sqrt (+ (* v (* 12 v)) 4))))) * * * * [misc]progress: [ 377 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (407 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (sqrt 2))) (* (sqrt (- 1 (* 3 (* v v)))) (* v v))))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (/ (sqrt 2) 4) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (sqrt 2))) (* (sqrt (- 1 (* 3 (* v v)))) (* v v))))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (/ (sqrt 2) 4) (* v v)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (225 enodes) * * [misc]simplify: iters left: 1 (258 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt (+ 1 (+ (* (* 3 v) v) (* 9 (pow v 4))))))) (sqrt (* 16 (sqrt (+ 1 (* (* 3 v) v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (sqrt 2))) (* (sqrt (- 1 (* 3 (* v v)))) (* v v))))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (/ (sqrt 2) 4) (* v v)))))) (* (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt (+ 1 (+ (* (* 3 v) v) (* 9 (pow v 4))))))) (sqrt (* 16 (sqrt (+ 1 (* (* 3 v) v)))))))) * * * * [misc]progress: [ 378 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (111 enodes) * * [misc]simplify: iters left: 4 (378 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (* (sqrt 2) (* v v)) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (* (sqrt 2) (* v v)) 4)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (281 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt (+ 1 (+ (* (* 3 v) v) (* (* v 9) (pow v 3))))))) (sqrt (+ (+ 4 (* (* v v) 12)) (* (* 4 (* v v)) (* (* v v) 9))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (* (sqrt 2) (* v v)) 4)))))) (* (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt (+ 1 (+ (* (* 3 v) v) (* (* v 9) (pow v 3))))))) (sqrt (+ (+ 4 (* (* v v) 12)) (* (* 4 (* v v)) (* (* v v) 9))))))) * * * * [misc]progress: [ 379 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (110 enodes) * * [misc]simplify: iters left: 4 (349 enodes) * [exit]simplify: Simplified to (* (sqrt (- (/ (* (* (sqrt (+ (* (* v v) 3) 1)) 4) (sqrt 2)) (/ 4 (sqrt (- 1 (pow (* (* v v) 3) 3))))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (* v v)) (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (/ (* (* (sqrt (+ (* (* v v) 3) 1)) 4) (sqrt 2)) (/ 4 (sqrt (- 1 (pow (* (* v v) 3) 3))))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (* v v)) (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * * [misc]simplify: iters left: 2 (253 enodes) * * [misc]simplify: iters left: 1 (323 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))))) (sqrt (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (/ (* (* (sqrt (+ (* (* v v) 3) 1)) 4) (sqrt 2)) (/ 4 (sqrt (- 1 (pow (* (* v v) 3) 3))))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (* v v)) (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))))))) (* (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))))) (sqrt (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9))))))))) * * * * [misc]progress: [ 380 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (38 enodes) * * [misc]simplify: iters left: 5 (105 enodes) * * [misc]simplify: iters left: 4 (351 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1)))) (* (/ (sqrt 2) 4) (* v v))))) (sqrt (- (/ (* (sqrt 2) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (/ 4 (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))))) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1)))) (* (/ (sqrt 2) 4) (* v v))))) (sqrt (- (/ (* (sqrt 2) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (/ 4 (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))))) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (77 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (218 enodes) * * [misc]simplify: iters left: 1 (252 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9)))))) (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1)))) (* (/ (sqrt 2) 4) (* v v))))) (sqrt (- (/ (* (sqrt 2) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (/ 4 (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))))) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))))))) (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9)))))) (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9))))))) * * * * [misc]progress: [ 381 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (33 enodes) * * [misc]simplify: iters left: 5 (88 enodes) * * [misc]simplify: iters left: 4 (267 enodes) * [exit]simplify: Simplified to (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (270 enodes) * * [misc]simplify: iters left: 1 (343 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt (+ 1 (+ (* (* 3 v) v) (* 9 (pow v 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))) (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt (+ 1 (+ (* (* 3 v) v) (* 9 (pow v 4)))))))) * * * * [misc]progress: [ 382 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (112 enodes) * * [misc]simplify: iters left: 4 (363 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v -3)))))))) (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* v v) (/ (sqrt 2) 4))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v -3)))))))) (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* v v) (/ (sqrt 2) 4))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (241 enodes) * * [misc]simplify: iters left: 1 (315 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v -3)))))))) (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* v v) (/ (sqrt 2) 4))))))) (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) 4))))) * * * * [misc]progress: [ 383 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (387 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* v v) 3) 1)))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* v v) 3) 1)))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * * [misc]simplify: iters left: 2 (253 enodes) * * [misc]simplify: iters left: 1 (323 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))))) (sqrt (* (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))) (* 4 (sqrt (+ 1 (* (* 3 v) v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* v v) 3) 1)))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))))))) (* (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))))) (sqrt (* (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))) (* 4 (sqrt (+ 1 (* (* 3 v) v))))))))) * * * * [misc]progress: [ 384 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (377 enodes) * [exit]simplify: Simplified to (* (sqrt (- (/ (* (* 4 (sqrt (+ (* v (* v 3)) 1))) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (/ 4 (sqrt 2))) (* (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* v 3)) 1)))))) (sqrt (+ (* (* (sqrt (+ (* (* v (* v 3)) (* v (* v 3))) (+ (* v (* v 3)) 1))) (- v)) (* (* v (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))))) (* (* (sqrt (+ (* v (* v 3)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* v 3)) 3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (/ (* (* 4 (sqrt (+ (* v (* v 3)) 1))) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (/ 4 (sqrt 2))) (* (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* v 3)) 1)))))) (sqrt (+ (* (* (sqrt (+ (* (* v (* v 3)) (* v (* v 3))) (+ (* v (* v 3)) 1))) (- v)) (* (* v (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))))) (* (* (sqrt (+ (* v (* v 3)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* v 3)) 3))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (271 enodes) * * [misc]simplify: iters left: 1 (393 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))))) (sqrt (+ 4 (* (* v 12) v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (/ (* (* 4 (sqrt (+ (* v (* v 3)) 1))) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (/ 4 (sqrt 2))) (* (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* v 3)) 1)))))) (sqrt (+ (* (* (sqrt (+ (* (* v (* v 3)) (* v (* v 3))) (+ (* v (* v 3)) 1))) (- v)) (* (* v (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))))) (* (* (sqrt (+ (* v (* v 3)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* v 3)) 3))))))) (* (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))))) (sqrt (+ 4 (* (* v 12) v)))))) * * * * [misc]progress: [ 385 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (108 enodes) * * [misc]simplify: iters left: 4 (345 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (* (* v v) 3) 1))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (sqrt (+ (* (* v v) 3) 1)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (* (* v v) 3) 1))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (sqrt (+ (* (* v v) 3) 1)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (241 enodes) * * [misc]simplify: iters left: 1 (320 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (* (* v v) 3) 1))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (sqrt (+ (* (* v v) 3) 1)))))) (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9))))))) * * * * [misc]progress: [ 386 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (38 enodes) * * [misc]simplify: iters left: 5 (102 enodes) * * [misc]simplify: iters left: 4 (307 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (* v (* v 3)) 1))) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (sqrt (+ (* (* v (* v 3)) (* v (* v 3))) (+ (* v (* v 3)) 1)))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (* v (* v 3)) 1))) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (* (* (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))) (/ (sqrt 2) 4)) (* (sqrt (+ (* v (* v 3)) 1)) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (* v (* v 3)) 1))) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (sqrt (+ (* (* v (* v 3)) (* v (* v 3))) (+ (* v (* v 3)) 1)))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (* v (* v 3)) 1))) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (* (* (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))) (/ (sqrt 2) 4)) (* (sqrt (+ (* v (* v 3)) 1)) (* v v)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (261 enodes) * * [misc]simplify: iters left: 1 (385 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))))) (sqrt (+ 1 (* v (* 3 v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (* v (* v 3)) 1))) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (sqrt (+ (* (* v (* v 3)) (* v (* v 3))) (+ (* v (* v 3)) 1)))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (* v (* v 3)) 1))) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (* (* (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))) (/ (sqrt 2) 4)) (* (sqrt (+ (* v (* v 3)) 1)) (* v v)))))) (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))))) (sqrt (+ 1 (* v (* 3 v))))))) * * * * [misc]progress: [ 387 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (377 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (sqrt (- 1 (* (* v v) 3)))) (* (* v v) (sqrt 2))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (sqrt (- 1 (* (* v v) 3)))) (* (* v v) (sqrt 2))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (241 enodes) * * [misc]simplify: iters left: 1 (315 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))))) (sqrt (* 4 (sqrt (+ 1 (* v (* 3 v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (sqrt (- 1 (* (* v v) 3)))) (* (* v v) (sqrt 2))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))))) (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))))) (sqrt (* 4 (sqrt (+ 1 (* v (* 3 v))))))))) * * * * [misc]progress: [ 388 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (396 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* v 3) v)))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1)))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* v 3) v)))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1)))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * * [misc]simplify: iters left: 2 (248 enodes) * * [misc]simplify: iters left: 1 (316 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))))) (sqrt (* 16 (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* v 3) v)))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1)))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))))))) (* (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))))) (sqrt (* 16 (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9))))))))) * * * * [misc]progress: [ 389 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (375 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (* 3 (* v v)) 1)) (* (* 4 (sqrt 2)) (sqrt (- 1 (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ (* 3 (* v v)) 1)))) (/ (* (sqrt 2) (* v v)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* 3 (* v v)) 1)) (* (* 4 (sqrt 2)) (sqrt (- 1 (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ (* 3 (* v v)) 1)))) (/ (* (sqrt 2) (* v v)) 4))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * * [misc]simplify: iters left: 2 (248 enodes) * * [misc]simplify: iters left: 1 (316 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))))) (sqrt (* 16 (sqrt (+ 1 (* (* 3 v) v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* 3 (* v v)) 1)) (* (* 4 (sqrt 2)) (sqrt (- 1 (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ (* 3 (* v v)) 1)))) (/ (* (sqrt 2) (* v v)) 4))))) (* (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))))) (sqrt (* 16 (sqrt (+ 1 (* (* 3 v) v)))))))) * * * * [misc]progress: [ 390 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (377 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (sqrt (- 1 (* (* v v) 3))) (sqrt 2)) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (* (- (* v v)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (/ (sqrt 2) 4) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt (- 1 (* (* v v) 3))) (sqrt 2)) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (* (- (* v v)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (/ (sqrt 2) 4) (* v v)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (241 enodes) * * [misc]simplify: iters left: 1 (315 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt (- 1 (* (* v v) 3))) (sqrt 2)) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (* (- (* v v)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (/ (sqrt 2) 4) (* v v)))))) (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) 4))))) * * * * [misc]progress: [ 391 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (109 enodes) * * [misc]simplify: iters left: 4 (332 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt 2) (* (sqrt (- 1 (* (* v v) 3))) (sqrt (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt 2) (* (sqrt (- 1 (* (* v v) 3))) (sqrt (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (241 enodes) * * [misc]simplify: iters left: 1 (315 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))))) (sqrt (* 4 (sqrt (+ 1 (* v (* 3 v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt 2) (* (sqrt (- 1 (* (* v v) 3))) (sqrt (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))))))) (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))))) (sqrt (* 4 (sqrt (+ 1 (* v (* 3 v))))))))) * * * * [misc]progress: [ 392 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (364 enodes) * [exit]simplify: Simplified to (* (sqrt (* (+ (- (* v v)) 1) (* (sqrt (- 1 (* 3 (* v v)))) (* 4 (sqrt 2))))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (* (* v v) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (+ (- (* v v)) 1) (* (sqrt (- 1 (* 3 (* v v)))) (* 4 (sqrt 2))))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (* (* v v) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 4))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (135 enodes) * * [misc]simplify: iters left: 2 (226 enodes) * * [misc]simplify: iters left: 1 (279 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9)))))) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (+ (- (* v v)) 1) (* (sqrt (- 1 (* 3 (* v v)))) (* 4 (sqrt 2))))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (* (* v v) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9)))))) 4))) * * * * [misc]progress: [ 393 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3)))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (122 enodes) * * [misc]simplify: iters left: 4 (436 enodes) * [exit]simplify: Simplified to (* (sqrt (* (pow (* (sqrt (- 1 (* v (* v 3)))) (/ (sqrt 2) 4)) 3) (+ 1 (* (- (* v v)) (* (* v v) (* v v)))))) (sqrt (- (* (* (sqrt (+ (* v (* v 3)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ (* v (* v 3)) 1))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (pow (* (sqrt (- 1 (* v (* v 3)))) (/ (sqrt 2) 4)) 3) (+ 1 (* (- (* v v)) (* (* v v) (* v v)))))) (sqrt (- (* (* (sqrt (+ (* v (* v 3)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ (* v (* v 3)) 1))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (89 enodes) * * [misc]simplify: iters left: 4 (282 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* (* (- v) v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* -3 v))))) (* (* (* (- v) v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* -3 v)))))) (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* v (* -3 v))))) (* (sqrt (+ 1 (* v (* -3 v)))) (- (* (* (- v) v) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))))) (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v)))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (pow (* (sqrt (- 1 (* v (* v 3)))) (/ (sqrt 2) 4)) 3) (+ 1 (* (- (* v v)) (* (* v v) (* v v)))))) (sqrt (- (* (* (sqrt (+ (* v (* v 3)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ (* v (* v 3)) 1))))))) (* (sqrt (- (* (* (* (* (- v) v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* -3 v))))) (* (* (* (- v) v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* -3 v)))))) (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* v (* -3 v))))) (* (sqrt (+ 1 (* v (* -3 v)))) (- (* (* (- v) v) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))))) (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v)))))))))) * * * * [misc]progress: [ 394 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (124 enodes) * * [misc]simplify: iters left: 4 (433 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (- 1 (* 3 (* v v)))) (- (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4)))) (* (sqrt (- 1 (* 3 (* v v)))) (+ (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4)))))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* 3 (* v v)))) (- (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4)))) (* (sqrt (- 1 (* 3 (* v v)))) (+ (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4)))))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (28 enodes) * * [misc]simplify: iters left: 5 (70 enodes) * * [misc]simplify: iters left: 4 (184 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (+ (* v v) 1) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1)))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* 3 (* v v)))) (- (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4)))) (* (sqrt (- 1 (* 3 (* v v)))) (+ (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4)))))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (* (* (+ (* v v) 1) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1)))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))))))) * * * * [misc]progress: [ 395 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (110 enodes) * * [misc]simplify: iters left: 4 (358 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (sqrt (- 1 (* (* v 3) v))) (* (* v v) (sqrt 2))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ 1 (* (* v 3) v))))))) (sqrt (* (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (+ (* (- (* v v)) (sqrt 2)) (sqrt 2))) (* 4 (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ 1 (* (* v 3) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (sqrt (- 1 (* (* v 3) v))) (* (* v v) (sqrt 2))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ 1 (* (* v 3) v))))))) (sqrt (* (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (+ (* (- (* v v)) (sqrt 2)) (sqrt 2))) (* 4 (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ 1 (* (* v 3) v)))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (106 enodes) * * [misc]simplify: iters left: 3 (170 enodes) * * [misc]simplify: iters left: 2 (291 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (* v 9) (pow v 3))))) 4)) (sqrt (+ (* (+ (* v (* 3 v)) (* (* v 9) (pow v 3))) 16) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (sqrt (- 1 (* (* v 3) v))) (* (* v v) (sqrt 2))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ 1 (* (* v 3) v))))))) (sqrt (* (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (+ (* (- (* v v)) (sqrt 2)) (sqrt 2))) (* 4 (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ 1 (* (* v 3) v)))))))) (* (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (* v 9) (pow v 3))))) 4)) (sqrt (+ (* (+ (* v (* 3 v)) (* (* v 9) (pow v 3))) 16) 16))))) * * * * [misc]progress: [ 396 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (122 enodes) * * [misc]simplify: iters left: 4 (383 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v v) 3)))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (sqrt (+ 1 (* (* v v) 3))) (* 4 (sqrt 2)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* 4 (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v v) 3)))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (sqrt (+ 1 (* (* v v) 3))) (* 4 (sqrt 2)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* 4 (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (173 enodes) * * [misc]simplify: iters left: 2 (265 enodes) * * [misc]simplify: iters left: 1 (314 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) 4)) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) (* 16 (sqrt (+ 1 (* v (* 3 v)))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v v) 3)))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (sqrt (+ 1 (* (* v v) 3))) (* 4 (sqrt 2)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* 4 (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))))) (* (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) 4)) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) (* 16 (sqrt (+ 1 (* v (* 3 v)))))))))) * * * * [misc]progress: [ 397 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (109 enodes) * * [misc]simplify: iters left: 4 (369 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* 3 (* v v)))))))) (sqrt (- (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt 2)) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v)))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* 4 (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v)))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* 3 (* v v)))))))) (sqrt (- (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt 2)) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v)))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* 4 (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v)))))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (172 enodes) * * [misc]simplify: iters left: 2 (350 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* 9 v) (pow v 3)))) 4)) (sqrt (+ (+ (* v (* v 12)) 4) (* (* v 4) (* (* v v) (* 9 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* 3 (* v v)))))))) (sqrt (- (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt 2)) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v)))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* 4 (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v)))))))))) (* (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* 9 v) (pow v 3)))) 4)) (sqrt (+ (+ (* v (* v 12)) 4) (* (* v 4) (* (* v v) (* 9 v)))))))) * * * * [misc]progress: [ 398 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (385 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* 3 (* v v)))) (* (* v v) (sqrt 2))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* 4 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* 3 (* v v)))) (* (* v v) (sqrt 2))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* 4 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (143 enodes) * * [misc]simplify: iters left: 2 (238 enodes) * * [misc]simplify: iters left: 1 (295 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))) (* 4 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (* (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* 3 (* v v)))) (* (* v v) (sqrt 2))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* 4 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (* (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))) (* 4 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (* (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))) 4))))) * * * * [misc]progress: [ 399 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (38 enodes) * * [misc]simplify: iters left: 5 (101 enodes) * * [misc]simplify: iters left: 4 (318 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v -3))))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (+ (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (+ 1 (* v (* v -3)))) (* (- (* (sqrt 2) (* v v))) 4))) (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v -3))))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (+ (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (+ 1 (* v (* v -3)))) (* (- (* (sqrt 2) (* v v))) 4))) (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (148 enodes) * * [misc]simplify: iters left: 2 (240 enodes) * * [misc]simplify: iters left: 1 (313 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* 3 (* v v))) (* 9 (pow v 4)))) 4)) (sqrt (* (sqrt (+ (+ 1 (* 3 (* v v))) (* 9 (pow v 4)))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v -3))))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (+ (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (+ 1 (* v (* v -3)))) (* (- (* (sqrt 2) (* v v))) 4))) (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (* (sqrt (* (sqrt (+ (+ 1 (* 3 (* v v))) (* 9 (pow v 4)))) 4)) (sqrt (* (sqrt (+ (+ 1 (* 3 (* v v))) (* 9 (pow v 4)))) 16))))) * * * * [misc]progress: [ 400 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (123 enodes) * * [misc]simplify: iters left: 4 (399 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* 3 (* v v)))))))) (sqrt (- (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* 3 (* v v)))))))) (sqrt (- (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (261 enodes) * * [misc]simplify: iters left: 1 (313 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) 4)) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) (* (sqrt (+ 1 (* v (* 3 v)))) 16)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* 3 (* v v)))))))) (sqrt (- (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))))) (* (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) 4)) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) (* (sqrt (+ 1 (* v (* 3 v)))) 16)))))) * * * * [misc]progress: [ 401 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (119 enodes) * * [misc]simplify: iters left: 4 (379 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt (+ (* -3 (* v v)) 1)) (* (* v v) (sqrt 2))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (sqrt 2) (- (* (* v v) (sqrt 2)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt (+ (* -3 (* v v)) 1)) (* (* v v) (sqrt 2))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (sqrt 2) (- (* (* v v) (sqrt 2)))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (183 enodes) * * [misc]simplify: iters left: 2 (328 enodes) * * [misc]simplify: iters left: 1 (433 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* v v) 48) 16)) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt (+ (* -3 (* v v)) 1)) (* (* v v) (sqrt 2))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (sqrt 2) (- (* (* v v) (sqrt 2)))))))) (* (sqrt (+ (* (* v v) 48) 16)) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) 4))))) * * * * [misc]progress: [ 402 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (383 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* 3 (* v v)))) (* (* v v) (sqrt 2))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v)))))))) (sqrt (- (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* 3 (* v v)))) (* (* v v) (sqrt 2))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v)))))))) (sqrt (- (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* v v)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (236 enodes) * * [misc]simplify: iters left: 1 (284 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))))) (sqrt (* (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* 3 (* v v)))) (* (* v v) (sqrt 2))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v)))))))) (sqrt (- (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))))) (sqrt (* (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))) 4))))) * * * * [misc]progress: [ 403 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (407 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* v (* v 3))))) (sqrt (+ (+ 1 (* v (* v 3))) (* (* v (* v 3)) (* v (* v 3)))))))) (sqrt (- (* (* (sqrt (+ 1 (* v (* v 3)))) (sqrt 2)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (* (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))) (* (* (* v v) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* v (* v 3)))) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* v (* v 3))))) (sqrt (+ (+ 1 (* v (* v 3))) (* (* v (* v 3)) (* v (* v 3)))))))) (sqrt (- (* (* (sqrt (+ 1 (* v (* v 3)))) (sqrt 2)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (* (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))) (* (* (* v v) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* v (* v 3)))) 4)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (173 enodes) * * [misc]simplify: iters left: 2 (330 enodes) * * [misc]simplify: iters left: 1 (425 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* 12 v) v) 4)) (sqrt (* (sqrt (+ 1 (+ (* 3 (* v v)) (* (pow v 4) 9)))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* v 3)) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* v (* v 3))))) (sqrt (+ (+ 1 (* v (* v 3))) (* (* v (* v 3)) (* v (* v 3)))))))) (sqrt (- (* (* (sqrt (+ 1 (* v (* v 3)))) (sqrt 2)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (* (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))) (* (* (* v v) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* v (* v 3)))) 4)))))) (* (sqrt (+ (* (* 12 v) v) 4)) (sqrt (* (sqrt (+ 1 (+ (* 3 (* v v)) (* (pow v 4) 9)))) 4))))) * * * * [misc]progress: [ 404 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (111 enodes) * * [misc]simplify: iters left: 4 (344 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* 4 (sqrt 2))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* v -3)) 1))) (* 4 (sqrt (+ 1 (* (* v 3) v))))))) (sqrt (- (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* 4 (/ (sqrt 2) 4))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* v -3)) 1))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ 1 (* (* v 3) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* 4 (sqrt 2))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* v -3)) 1))) (* 4 (sqrt (+ 1 (* (* v 3) v))))))) (sqrt (- (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* 4 (/ (sqrt 2) 4))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* v -3)) 1))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ 1 (* (* v 3) v)))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (162 enodes) * * [misc]simplify: iters left: 2 (277 enodes) * * [misc]simplify: iters left: 1 (300 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 16)) (sqrt (* (sqrt (+ 1 (+ (* 3 (* v v)) (* (pow v 4) 9)))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* 4 (sqrt 2))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* v -3)) 1))) (* 4 (sqrt (+ 1 (* (* v 3) v))))))) (sqrt (- (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* 4 (/ (sqrt 2) 4))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* v -3)) 1))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ 1 (* (* v 3) v)))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 16)) (sqrt (* (sqrt (+ 1 (+ (* 3 (* v v)) (* (pow v 4) 9)))) 4))))) * * * * [misc]progress: [ 405 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (38 enodes) * * [misc]simplify: iters left: 5 (105 enodes) * * [misc]simplify: iters left: 4 (355 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (* 4 (/ (sqrt 2) 4))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* v -3)) 1))) (sqrt (+ (+ 1 (* v (* v 3))) (* (* v (* v 3)) (* v (* v 3)))))))) (sqrt (* (sqrt (+ (+ 1 (* v (* v 3))) (* (* v (* v 3)) (* v (* v 3))))) (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (+ (- (* (sqrt 2) (* v v))) (* 4 (/ (sqrt 2) 4))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (* 4 (/ (sqrt 2) 4))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* v -3)) 1))) (sqrt (+ (+ 1 (* v (* v 3))) (* (* v (* v 3)) (* v (* v 3)))))))) (sqrt (* (sqrt (+ (+ 1 (* v (* v 3))) (* (* v (* v 3)) (* v (* v 3))))) (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (+ (- (* (sqrt 2) (* v v))) (* 4 (/ (sqrt 2) 4))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (251 enodes) * * [misc]simplify: iters left: 1 (382 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (pow v 4) 9))) 4)) (sqrt (+ (* v (* v 12)) (+ (* (* 36 v) (pow v 3)) 4)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (* 4 (/ (sqrt 2) 4))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* v -3)) 1))) (sqrt (+ (+ 1 (* v (* v 3))) (* (* v (* v 3)) (* v (* v 3)))))))) (sqrt (* (sqrt (+ (+ 1 (* v (* v 3))) (* (* v (* v 3)) (* v (* v 3))))) (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (+ (- (* (sqrt 2) (* v v))) (* 4 (/ (sqrt 2) 4))))))) (* (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (pow v 4) 9))) 4)) (sqrt (+ (* v (* v 12)) (+ (* (* 36 v) (pow v 3)) 4)))))) * * * * [misc]progress: [ 406 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (113 enodes) * * [misc]simplify: iters left: 4 (358 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* v v))))) (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt (+ 1 (* (* -3 v) v))) (* (* v v) (sqrt 2))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* v v))))) (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt (+ 1 (* (* -3 v) v))) (* (* v v) (sqrt 2))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * * [misc]simplify: iters left: 2 (251 enodes) * * [misc]simplify: iters left: 1 (317 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* v v))))) (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt (+ 1 (* (* -3 v) v))) (* (* v v) (sqrt 2))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) 4))))) * * * * [misc]progress: [ 407 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (36 enodes) * * [misc]simplify: iters left: 5 (100 enodes) * * [misc]simplify: iters left: 4 (338 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ 1 (* (* v 3) v)))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ (sqrt 2) 4))) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ 1 (* (* v 3) v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3))))))) (sqrt (- (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ 1 (* (* v 3) v)))) (* (sqrt (+ 1 (* (* v -3) v))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ 1 (* (* v 3) v)))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ (sqrt 2) 4))) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ 1 (* (* v 3) v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3))))))) (sqrt (- (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ 1 (* (* v 3) v)))) (* (sqrt (+ 1 (* (* v -3) v))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (220 enodes) * * [misc]simplify: iters left: 1 (252 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (pow v 4) 9))) 4)) (sqrt (+ (+ 1 (* (* v v) 3)) (* (pow v 4) 9)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ 1 (* (* v 3) v)))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ (sqrt 2) 4))) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ 1 (* (* v 3) v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3))))))) (sqrt (- (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ 1 (* (* v 3) v)))) (* (sqrt (+ 1 (* (* v -3) v))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (pow v 4) 9))) 4)) (sqrt (+ (+ 1 (* (* v v) 3)) (* (pow v 4) 9)))))) * * * * [misc]progress: [ 408 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (112 enodes) * * [misc]simplify: iters left: 4 (361 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (/ (* 4 (sqrt 2)) 4) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v 3) v)))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (/ (* 4 (sqrt 2)) 4) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v 3) v)))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (241 enodes) * * [misc]simplify: iters left: 1 (314 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) (sqrt (+ 1 (* v (* 3 v)))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (/ (* 4 (sqrt 2)) 4) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v 3) v)))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))))))) (* (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) (sqrt (+ 1 (* v (* 3 v)))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) 4))))) * * * * [misc]progress: [ 409 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (31 enodes) * * [misc]simplify: iters left: 5 (83 enodes) * * [misc]simplify: iters left: 4 (257 enodes) * [exit]simplify: Simplified to (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v -3))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v -3))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (79 enodes) * * [misc]simplify: iters left: 3 (133 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * * [misc]simplify: iters left: 1 (267 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v -3))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))))) (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) 4))) * * * * [misc]progress: [ 410 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (392 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (sqrt (- 1 (* (* v v) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (sqrt (- 1 (* (* v v) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v v) 3)))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (226 enodes) * * [misc]simplify: iters left: 1 (257 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (+ (* (* 3 v) v) (* 9 (pow v 4))))) (* 4 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (* (sqrt (+ 1 (+ (* (* 3 v) v) (* 9 (pow v 4))))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (sqrt (- 1 (* (* v v) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v v) 3)))))))) (* (sqrt (* (sqrt (+ 1 (+ (* (* 3 v) v) (* 9 (pow v 4))))) (* 4 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (* (sqrt (+ 1 (+ (* (* 3 v) v) (* 9 (pow v 4))))) 4))))) * * * * [misc]progress: [ 411 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (396 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v 3) v)))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))))) (sqrt (- (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt (+ 1 (* (* v 3) v))) (* 4 (/ (sqrt 2) 4)))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v 3) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v 3) v)))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))))) (sqrt (- (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt (+ 1 (* (* v 3) v))) (* 4 (/ (sqrt 2) 4)))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v 3) v)))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (262 enodes) * * [misc]simplify: iters left: 1 (381 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* v (* 12 v)) 4)) (sqrt (* (sqrt (+ 1 (+ (* (* v v) 3) (* 9 (pow v 4))))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v 3) v)))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))))) (sqrt (- (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt (+ 1 (* (* v 3) v))) (* 4 (/ (sqrt 2) 4)))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v 3) v)))))))) (* (sqrt (+ (* v (* 12 v)) 4)) (sqrt (* (sqrt (+ 1 (+ (* (* v v) 3) (* 9 (pow v 4))))) 4))))) * * * * [misc]progress: [ 412 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (375 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* v v) (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (* 4 (sqrt 2)) 4)) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* v -3) v) 1))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* v v) (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (* 4 (sqrt 2)) 4)) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* v -3) v) 1))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (241 enodes) * * [misc]simplify: iters left: 1 (314 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) (sqrt (+ 1 (* v (* 3 v)))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* v v) (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (* 4 (sqrt 2)) 4)) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* v -3) v) 1))))))) (* (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) (sqrt (+ 1 (* v (* 3 v)))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) 4))))) * * * * [misc]progress: [ 413 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (365 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))))) (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt (+ (* v (* v -3)) 1)) (* (* v v) (sqrt 2))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))))) (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt (+ (* v (* v -3)) 1)) (* (* v v) (sqrt 2))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (247 enodes) * * [misc]simplify: iters left: 1 (342 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (* (sqrt (+ 1 (+ (* 3 (* v v)) (* 9 (pow v 4))))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))))) (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt (+ (* v (* v -3)) 1)) (* (* v v) (sqrt 2))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (* (sqrt (+ 1 (+ (* 3 (* v v)) (* 9 (pow v 4))))) 4))))) * * * * [misc]progress: [ 414 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (109 enodes) * * [misc]simplify: iters left: 4 (333 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (/ (* 4 (sqrt 2)) 4) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v v) 3))))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (+ 1 (* (* v v) 3))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (/ (* 4 (sqrt 2)) 4) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v v) 3))))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (+ 1 (* (* v v) 3))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v v) 3)))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (241 enodes) * * [misc]simplify: iters left: 1 (314 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ 1 (* v (* 3 v)))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (/ (* 4 (sqrt 2)) 4) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v v) 3))))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (+ 1 (* (* v v) 3))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v v) 3)))))))) (* (sqrt (* 4 (sqrt (+ 1 (* v (* 3 v)))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) 4))))) * * * * [misc]progress: [ 415 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (110 enodes) * * [misc]simplify: iters left: 4 (357 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* 4 (/ (sqrt 2) 4))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v -3))))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))))) (sqrt (- (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* v (* v -3)))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (sqrt 2)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* 4 (/ (sqrt 2) 4))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v -3))))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))))) (sqrt (- (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* v (* v -3)))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (239 enodes) * * [misc]simplify: iters left: 1 (311 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (pow v 4) 9))) 4)) (sqrt (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (pow v 4) 9))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* 4 (/ (sqrt 2) 4))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v -3))))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))))) (sqrt (- (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* v (* v -3)))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (pow v 4) 9))) 4)) (sqrt (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (pow v 4) 9))) 16))))) * * * * [misc]progress: [ 416 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (365 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* -3 v) v) 1))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ 1 (* (* v 3) v))))))) (sqrt (- (* (sqrt (+ (* (* -3 v) v) 1)) (* (sqrt (+ 1 (* (* v 3) v))) (* 4 (sqrt 2)))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (sqrt 2)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* -3 v) v) 1))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ 1 (* (* v 3) v))))))) (sqrt (- (* (sqrt (+ (* (* -3 v) v) 1)) (* (sqrt (+ 1 (* (* v 3) v))) (* 4 (sqrt 2)))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (245 enodes) * * [misc]simplify: iters left: 1 (314 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 16)) (sqrt (* (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9)))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* -3 v) v) 1))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ 1 (* (* v 3) v))))))) (sqrt (- (* (sqrt (+ (* (* -3 v) v) 1)) (* (sqrt (+ 1 (* (* v 3) v))) (* 4 (sqrt 2)))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 16)) (sqrt (* (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9)))) 4))))) * * * * [misc]progress: [ 417 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (37 enodes) * * [misc]simplify: iters left: 5 (103 enodes) * * [misc]simplify: iters left: 4 (333 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ 1 (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v v) 3))))))) (sqrt (+ (* (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ 1 (* (* v v) 3)))) (* (sqrt 2) (sqrt (- 1 (* (* v v) 3))))) (* (* (* 4 (/ (sqrt 2) 4)) (* v (- v))) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ 1 (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v v) 3))))))) (sqrt (+ (* (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ 1 (* (* v v) 3)))) (* (sqrt 2) (sqrt (- 1 (* (* v v) 3))))) (* (* (* 4 (/ (sqrt 2) 4)) (* v (- v))) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (135 enodes) * * [misc]simplify: iters left: 2 (222 enodes) * * [misc]simplify: iters left: 1 (282 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ 1 (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v v) 3))))))) (sqrt (+ (* (sqrt (+ (* (* 9 (* v v)) (* v v)) (+ 1 (* (* v v) 3)))) (* (sqrt 2) (sqrt (- 1 (* (* v v) 3))))) (* (* (* 4 (/ (sqrt 2) 4)) (* v (- v))) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) 4))) * * * * [misc]progress: [ 418 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (365 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (- 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (241 enodes) * * [misc]simplify: iters left: 1 (314 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ 1 (* v (* 3 v)))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))))) (* (sqrt (* 4 (sqrt (+ 1 (* v (* 3 v)))))) (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* 9 (pow v 4))))) 4))))) * * * * [misc]progress: [ 419 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (36 enodes) * * [misc]simplify: iters left: 5 (97 enodes) * * [misc]simplify: iters left: 4 (299 enodes) * [exit]simplify: Simplified to (* (sqrt (* (+ (- (* v v)) 1) (* (* 4 (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))))) (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (/ (sqrt 2) 4))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (+ (- (* v v)) 1) (* (* 4 (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))))) (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (/ (sqrt 2) 4))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* 4 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (* 4 4))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (85 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (242 enodes) * * [misc]simplify: iters left: 1 (316 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* 3 (* v v))) (* 9 (pow v 4)))) 4)) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (+ (- (* v v)) 1) (* (* 4 (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))))) (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (/ (sqrt 2) 4))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ (+ 1 (* 3 (* v v))) (* 9 (pow v 4)))) 4)) 4))) * * * * [misc]progress: [ 420 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3)))) * * [misc]simplify: iters left: 6 (38 enodes) * * [misc]simplify: iters left: 5 (111 enodes) * * [misc]simplify: iters left: 4 (404 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (/ (* 4 (sqrt 2)) 4) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (- 1 (* (* v v) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v v) 3)))) 3) (pow (/ (sqrt (- 1 (* (* v v) 3))) (/ 4 (* (* v v) (sqrt 2)))) 3)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (/ (* 4 (sqrt 2)) 4) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (- 1 (* (* v v) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v v) 3)))) 3) (pow (/ (sqrt (- 1 (* (* v v) 3))) (/ 4 (* (* v v) (sqrt 2)))) 3)))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * * [misc]simplify: iters left: 6 (30 enodes) * * [misc]simplify: iters left: 5 (86 enodes) * * [misc]simplify: iters left: 4 (283 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (+ 1 (* (* -3 v) v)))) (* (sqrt (+ 1 (* (* -3 v) v))) (- (* (/ (sqrt 2) 4) (- (* v v))) (/ (sqrt 2) 4)))) (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* -3 v) v)))) (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* -3 v) v))))))) (sqrt (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (/ (* 4 (sqrt 2)) 4) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (- 1 (* (* v v) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v v) 3)))) 3) (pow (/ (sqrt (- 1 (* (* v v) 3))) (/ 4 (* (* v v) (sqrt 2)))) 3)))) (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (+ 1 (* (* -3 v) v)))) (* (sqrt (+ 1 (* (* -3 v) v))) (- (* (/ (sqrt 2) 4) (- (* v v))) (/ (sqrt 2) 4)))) (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* -3 v) v)))) (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* -3 v) v))))))) (sqrt (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) 4))))) * * * * [misc]progress: [ 421 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (38 enodes) * * [misc]simplify: iters left: 5 (113 enodes) * * [misc]simplify: iters left: 4 (401 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* 4 (/ (sqrt 2) 4))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v 3) v)))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ 1 (* (* v 3) v))))))) (sqrt (* (* (sqrt (- 1 (* (* v 3) v))) (+ (* (/ (sqrt 2) 4) (- (* v v))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (* (* v 3) v))) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (- (* v v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* 4 (/ (sqrt 2) 4))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v 3) v)))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ 1 (* (* v 3) v))))))) (sqrt (* (* (sqrt (- 1 (* (* v 3) v))) (+ (* (/ (sqrt 2) 4) (- (* v v))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (* (* v 3) v))) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (- (* v v)))))))) (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (67 enodes) * * [misc]simplify: iters left: 4 (185 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) 4)) (sqrt (* (* (+ (* v v) 1) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* 4 (/ (sqrt 2) 4))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v 3) v)))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ 1 (* (* v 3) v))))))) (sqrt (* (* (sqrt (- 1 (* (* v 3) v))) (+ (* (/ (sqrt 2) 4) (- (* v v))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (* (* v 3) v))) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (- (* v v)))))))) (* (sqrt (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) 4)) (sqrt (* (* (+ (* v v) 1) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))))))) * * * * [misc]progress: [ 422 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (108 enodes) * * [misc]simplify: iters left: 4 (330 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (/ (sqrt 2) 4)) (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) 4)) (* (* (* v (sqrt 2)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* v (sqrt (+ 1 (* (* v 3) v))))))) (sqrt (* (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (/ (sqrt 2) 4)) (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) 4)) (* (* (* v (sqrt 2)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* v (sqrt (+ 1 (* (* v 3) v))))))) (sqrt (* (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (153 enodes) * * [misc]simplify: iters left: 2 (269 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (+ (* 3 (* v v)) (* (* 9 v) (pow v 3))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (+ (* (* 12 (* v v)) (* 3 (* v v))) (+ 4 (* 12 (* v v)))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (/ (sqrt 2) 4)) (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) 4)) (* (* (* v (sqrt 2)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* v (sqrt (+ 1 (* (* v 3) v))))))) (sqrt (* (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))))))) (* (sqrt (* (sqrt (+ 1 (+ (* 3 (* v v)) (* (* 9 v) (pow v 3))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (+ (* (* 12 (* v v)) (* 3 (* v v))) (+ 4 (* 12 (* v v)))) 4))))) * * * * [misc]progress: [ 423 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (119 enodes) * * [misc]simplify: iters left: 4 (386 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))) (* (* (sqrt (+ 1 (* (* v 3) v))) (* v v)) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (sqrt 2))))) (sqrt (- (* (sqrt 2) (* (* (sqrt (+ 1 (* (* v 3) v))) 4) (sqrt (- 1 (pow (* (* v 3) v) 3))))) (* (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* v v) (sqrt 2))) (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))) (* (* (sqrt (+ 1 (* (* v 3) v))) (* v v)) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (sqrt 2))))) (sqrt (- (* (sqrt 2) (* (* (sqrt (+ 1 (* (* v 3) v))) 4) (sqrt (- 1 (pow (* (* v 3) v) 3))))) (* (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* v v) (sqrt 2))) (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) 4))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (105 enodes) * * [misc]simplify: iters left: 3 (164 enodes) * * [misc]simplify: iters left: 2 (254 enodes) * * [misc]simplify: iters left: 1 (309 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* v 3))))) (sqrt (+ 1 (+ (* v (* v 3)) (* 9 (pow v 4))))))) (sqrt (* (* (sqrt (+ 1 (* v (* v 3)))) 16) (sqrt (+ 1 (+ (* v (* v 3)) (* 9 (pow v 4)))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))) (* (* (sqrt (+ 1 (* (* v 3) v))) (* v v)) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (sqrt 2))))) (sqrt (- (* (sqrt 2) (* (* (sqrt (+ 1 (* (* v 3) v))) 4) (sqrt (- 1 (pow (* (* v 3) v) 3))))) (* (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* v v) (sqrt 2))) (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) 4))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* v 3))))) (sqrt (+ 1 (+ (* v (* v 3)) (* 9 (pow v 4))))))) (sqrt (* (* (sqrt (+ 1 (* v (* v 3)))) 16) (sqrt (+ 1 (+ (* v (* v 3)) (* 9 (pow v 4)))))))))) * * * * [misc]progress: [ 424 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (381 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2))) (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) 4) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (sqrt 2) 4) (* v v)))))) (sqrt (- (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (* (sqrt 2) (sqrt (+ 1 (* (* v v) 3)))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2))) (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) 4) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (sqrt 2) 4) (* v v)))))) (sqrt (- (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (* (sqrt 2) (sqrt (+ 1 (* (* v v) 3)))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* v v))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (96 enodes) * * [misc]simplify: iters left: 3 (171 enodes) * * [misc]simplify: iters left: 2 (342 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (+ (* (* v 3) v) (* (* 9 v) (pow v 3))))) (* 4 (sqrt (+ 1 (* (* v 3) v)))))) (sqrt (+ (* (* 4 (* v v)) (* (* v 3) (* v 3))) (+ (* (* v v) 12) 4)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2))) (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) 4) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (sqrt 2) 4) (* v v)))))) (sqrt (- (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (* (sqrt 2) (sqrt (+ 1 (* (* v v) 3)))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* v v))))) (* (sqrt (* (sqrt (+ 1 (+ (* (* v 3) v) (* (* 9 v) (pow v 3))))) (* 4 (sqrt (+ 1 (* (* v 3) v)))))) (sqrt (+ (* (* 4 (* v v)) (* (* v 3) (* v 3))) (+ (* (* v v) 12) 4)))))) * * * * [misc]progress: [ 425 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (112 enodes) * * [misc]simplify: iters left: 4 (351 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4)) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) 4)) (* (* (sqrt (+ 1 (* (* v v) 3))) (* v v)) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4)) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) 4)) (* (* (sqrt (+ 1 (* (* v v) 3))) (* v v)) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) 4))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (227 enodes) * * [misc]simplify: iters left: 1 (255 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (+ (* (* v 3) v) (* 9 (pow v 4))))) (* 4 (sqrt (+ 1 (* (* v 3) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4)) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) 4)) (* (* (sqrt (+ 1 (* (* v v) 3))) (* v v)) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt 2))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) 4))))) (* (sqrt (+ 1 (+ (* (* v 3) v) (* 9 (pow v 4))))) (* 4 (sqrt (+ 1 (* (* v 3) v))))))) * * * * [misc]progress: [ 426 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (376 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* 4 (sqrt 2))) (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt (+ (* (* v -3) v) 1)) (* (- (* (sqrt 2) (* v v))) 4))))) (sqrt (- (* (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* v v) (* (* (sqrt 2) (sqrt (+ 1 (* (* v 3) v)))) (sqrt (- 1 (pow (* (* v 3) v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* 4 (sqrt 2))) (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt (+ (* (* v -3) v) 1)) (* (- (* (sqrt 2) (* v v))) 4))))) (sqrt (- (* (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* v v) (* (* (sqrt 2) (sqrt (+ 1 (* (* v 3) v)))) (sqrt (- 1 (pow (* (* v 3) v) 3)))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (98 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (231 enodes) * * [misc]simplify: iters left: 1 (262 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (+ (* (* v 3) v) (* 9 (pow v 4))))) (* 4 (sqrt (+ 1 (* (* v 3) v)))))) (sqrt (* 16 (sqrt (+ 1 (+ (* (* v 3) v) (* 9 (pow v 4)))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* 4 (sqrt 2))) (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt (+ (* (* v -3) v) 1)) (* (- (* (sqrt 2) (* v v))) 4))))) (sqrt (- (* (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* v v) (* (* (sqrt 2) (sqrt (+ 1 (* (* v 3) v)))) (sqrt (- 1 (pow (* (* v 3) v) 3)))))))) (* (sqrt (* (sqrt (+ 1 (+ (* (* v 3) v) (* 9 (pow v 4))))) (* 4 (sqrt (+ 1 (* (* v 3) v)))))) (sqrt (* 16 (sqrt (+ 1 (+ (* (* v 3) v) (* 9 (pow v 4)))))))))) * * * * [misc]progress: [ 427 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (110 enodes) * * [misc]simplify: iters left: 4 (325 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) 4)) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) 4)) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (167 enodes) * * [misc]simplify: iters left: 2 (249 enodes) * * [misc]simplify: iters left: 1 (277 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9)))))) (sqrt (* (* 16 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) 4)) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9)))))) (sqrt (* (* 16 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9))))))))) * * * * [misc]progress: [ 428 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (117 enodes) * * [misc]simplify: iters left: 4 (368 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (+ (sqrt 2) (* (- v) (* v (sqrt 2))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (+ (sqrt 2) (* (- v) (* v (sqrt 2))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (161 enodes) * * [misc]simplify: iters left: 2 (275 enodes) * * [misc]simplify: iters left: 1 (394 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* v 3))))) (sqrt (+ 1 (+ (* v (* v 3)) (* (pow v 4) 9)))))) (sqrt (+ (* 48 (* v v)) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (+ (sqrt 2) (* (- v) (* v (sqrt 2))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* v 3))))) (sqrt (+ 1 (+ (* v (* v 3)) (* (pow v 4) 9)))))) (sqrt (+ (* 48 (* v v)) 16))))) * * * * [misc]progress: [ 429 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (365 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt 2) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))) (* (* 4 (sqrt (+ 1 (* (* v 3) v)))) (/ (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ 4 (* (* v v) (sqrt 2))))))) (sqrt (- (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v 3) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt 2) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))) (* (* 4 (sqrt (+ 1 (* (* v 3) v)))) (/ (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ 4 (* (* v v) (sqrt 2))))))) (sqrt (- (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v 3) v)))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (246 enodes) * * [misc]simplify: iters left: 1 (291 enodes) * [exit]simplify: Simplified to (* (* 4 (sqrt (+ 1 (* v (* v 3))))) (sqrt (+ 1 (+ (* v (* v 3)) (* 9 (pow v 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt 2) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))) (* (* 4 (sqrt (+ 1 (* (* v 3) v)))) (/ (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ 4 (* (* v v) (sqrt 2))))))) (sqrt (- (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v 3) v)))))))) (* (* 4 (sqrt (+ 1 (* v (* v 3))))) (sqrt (+ 1 (+ (* v (* v 3)) (* 9 (pow v 4)))))))) * * * * [misc]progress: [ 430 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (378 enodes) * [exit]simplify: Simplified to (* (sqrt (- (/ (* (sqrt (+ (+ 1 (* v (* v 3))) (* (* v (* v 3)) (* v (* v 3))))) 4) (/ (/ 4 (sqrt 2)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))))) (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v 3)))))))) (sqrt (* (sqrt (+ 1 (* v (* v 3)))) (+ (* (* 4 (* (/ (sqrt 2) 4) (* v (- v)))) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (* (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))) (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (/ (* (sqrt (+ (+ 1 (* v (* v 3))) (* (* v (* v 3)) (* v (* v 3))))) 4) (/ (/ 4 (sqrt 2)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))))) (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v 3)))))))) (sqrt (* (sqrt (+ 1 (* v (* v 3)))) (+ (* (* 4 (* (/ (sqrt 2) 4) (* v (- v)))) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (* (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))) (sqrt 2)))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (96 enodes) * * [misc]simplify: iters left: 3 (167 enodes) * * [misc]simplify: iters left: 2 (297 enodes) * * [misc]simplify: iters left: 1 (423 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9)))))) (sqrt (+ (* (* v 12) v) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (/ (* (sqrt (+ (+ 1 (* v (* v 3))) (* (* v (* v 3)) (* v (* v 3))))) 4) (/ (/ 4 (sqrt 2)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))))) (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v 3)))))))) (sqrt (* (sqrt (+ 1 (* v (* v 3)))) (+ (* (* 4 (* (/ (sqrt 2) 4) (* v (- v)))) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (* (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))) (sqrt 2)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9)))))) (sqrt (+ (* (* v 12) v) 4))))) * * * * [misc]progress: [ 431 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (122 enodes) * * [misc]simplify: iters left: 4 (375 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* v (* v -3)))) (* (* v v) (sqrt 2))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* v (* v -3)))) (* (* v v) (sqrt 2))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (96 enodes) * * [misc]simplify: iters left: 3 (143 enodes) * * [misc]simplify: iters left: 2 (230 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* v 3))))) (sqrt (+ 1 (+ (* v (* v 3)) (* 9 (pow v 4))))))) (sqrt (* 16 (sqrt (+ 1 (* v (* v 3))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* v (* v -3)))) (* (* v v) (sqrt 2))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* v 3))))) (sqrt (+ 1 (+ (* v (* v 3)) (* 9 (pow v 4))))))) (sqrt (* 16 (sqrt (+ 1 (* v (* v 3))))))))) * * * * [misc]progress: [ 432 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (110 enodes) * * [misc]simplify: iters left: 4 (348 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v v) 3))))))) (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v v) 3))))))) (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (96 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (257 enodes) * * [misc]simplify: iters left: 1 (391 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* v 3))))) (sqrt (+ 1 (+ (* v (* v 3)) (* (pow v 4) 9)))))) (sqrt (+ (+ (* v (* v 12)) (* (pow v 3) (* v 36))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v v) 3))))))) (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* v 3))))) (sqrt (+ 1 (+ (* v (* v 3)) (* (pow v 4) 9)))))) (sqrt (+ (+ (* v (* v 12)) (* (pow v 3) (* v 36))) 4))))) * * * * [misc]progress: [ 433 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (391 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ (sqrt 2) 4))) (* (* (sqrt 2) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v))))) (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ (sqrt 2) 4))) (* (* (sqrt 2) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v))))) (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v v) 3)))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (138 enodes) * * [misc]simplify: iters left: 2 (226 enodes) * * [misc]simplify: iters left: 1 (256 enodes) * [exit]simplify: Simplified to (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (+ 1 (+ (* (* v v) 3) (* 9 (pow v 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (/ (sqrt 2) 4))) (* (* (sqrt 2) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v))))) (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v v) 3)))))))) (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (+ 1 (+ (* (* v v) 3) (* 9 (pow v 4)))))))) * * * * [misc]progress: [ 434 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (113 enodes) * * [misc]simplify: iters left: 4 (355 enodes) * [exit]simplify: Simplified to (* (sqrt (- (/ (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)) (/ 4 (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (/ (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)) (/ 4 (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (227 enodes) * * [misc]simplify: iters left: 1 (265 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (+ 1 (+ (* (* v v) 3) (* 9 (pow v 4))))))) (sqrt (+ 1 (+ (* (* v v) 3) (* 9 (pow v 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (/ (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)) (/ 4 (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (+ 1 (+ (* (* v v) 3) (* 9 (pow v 4))))))) (sqrt (+ 1 (+ (* (* v v) 3) (* 9 (pow v 4)))))))) * * * * [misc]progress: [ 435 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (374 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (/ (sqrt 2) 4) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* 4 (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (/ (sqrt 2) 4) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* 4 (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (136 enodes) * * [misc]simplify: iters left: 2 (220 enodes) * * [misc]simplify: iters left: 1 (251 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (+ (* (* v 3) v) (* 9 (pow v 4))))) (* 4 (sqrt (+ 1 (* (* v 3) v)))))) (sqrt (* (sqrt (+ 1 (+ (* (* v 3) v) (* 9 (pow v 4))))) (sqrt (+ 1 (* (* v 3) v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (/ (sqrt 2) 4) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* 4 (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ 1 (+ (* (* v 3) v) (* 9 (pow v 4))))) (* 4 (sqrt (+ 1 (* (* v 3) v)))))) (sqrt (* (sqrt (+ 1 (+ (* (* v 3) v) (* 9 (pow v 4))))) (sqrt (+ 1 (* (* v 3) v)))))))) * * * * [misc]progress: [ 436 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (382 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ (* 4 (sqrt 2)) 4)) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* -3 v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))))) (sqrt (- (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* 4 (/ (sqrt 2) 4)))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v 3) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ (* 4 (sqrt 2)) 4)) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* -3 v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))))) (sqrt (- (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* 4 (/ (sqrt 2) 4)))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v 3) v)))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (224 enodes) * * [misc]simplify: iters left: 1 (258 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (+ (* (* v 3) v) (* 9 (pow v 4))))) (* 4 (sqrt (+ 1 (* (* v 3) v)))))) (sqrt (* 4 (sqrt (+ 1 (+ (* (* v 3) v) (* 9 (pow v 4)))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ (* 4 (sqrt 2)) 4)) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* -3 v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))))) (sqrt (- (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* 4 (/ (sqrt 2) 4)))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v 3) v)))))))) (* (sqrt (* (sqrt (+ 1 (+ (* (* v 3) v) (* 9 (pow v 4))))) (* 4 (sqrt (+ 1 (* (* v 3) v)))))) (sqrt (* 4 (sqrt (+ 1 (+ (* (* v 3) v) (* 9 (pow v 4)))))))))) * * * * [misc]progress: [ 437 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (90 enodes) * * [misc]simplify: iters left: 4 (265 enodes) * [exit]simplify: Simplified to (- (* (* (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))) (/ (sqrt 2) 4)) (* (sqrt (+ (+ 1 (* v (* v 3))) (* (* v (* v 3)) (* v (* v 3))))) 4)) (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v 3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (* (* (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))) (/ (sqrt 2) 4)) (* (sqrt (+ (+ 1 (* v (* v 3))) (* (* v (* v 3)) (* v (* v 3))))) 4)) (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v 3))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (229 enodes) * * [misc]simplify: iters left: 1 (279 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9)))) (* 4 (sqrt (+ 1 (* (* v v) 3))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (* (* (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))) (/ (sqrt 2) 4)) (* (sqrt (+ (+ 1 (* v (* v 3))) (* (* v (* v 3)) (* v (* v 3))))) 4)) (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v 3))))))) (* (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9)))) (* 4 (sqrt (+ 1 (* (* v v) 3))))))) * * * * [misc]progress: [ 438 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (112 enodes) * * [misc]simplify: iters left: 4 (362 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (95 enodes) * * [misc]simplify: iters left: 3 (149 enodes) * * [misc]simplify: iters left: 2 (249 enodes) * * [misc]simplify: iters left: 1 (324 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* v 3))))) (sqrt (+ 1 (+ (* v (* v 3)) (* (pow v 4) 9)))))) (sqrt (+ (* 12 (* v v)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* v 3))))) (sqrt (+ 1 (+ (* v (* v 3)) (* (pow v 4) 9)))))) (sqrt (+ (* 12 (* v v)) 4))))) * * * * [misc]progress: [ 439 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (110 enodes) * * [misc]simplify: iters left: 4 (337 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (136 enodes) * * [misc]simplify: iters left: 2 (220 enodes) * * [misc]simplify: iters left: 1 (251 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (+ (* (* v 3) v) (* 9 (pow v 4))))) (* 4 (sqrt (+ 1 (* (* v 3) v)))))) (sqrt (* (sqrt (+ 1 (+ (* (* v 3) v) (* 9 (pow v 4))))) (sqrt (+ 1 (* (* v 3) v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ 1 (+ (* (* v 3) v) (* 9 (pow v 4))))) (* 4 (sqrt (+ 1 (* (* v 3) v)))))) (sqrt (* (sqrt (+ 1 (+ (* (* v 3) v) (* 9 (pow v 4))))) (sqrt (+ 1 (* (* v 3) v)))))))) * * * * [misc]progress: [ 440 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (107 enodes) * * [misc]simplify: iters left: 4 (344 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) 4) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v 3) v))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* v 3) v)))) (- (* v v))) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* v 3) v)))) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) 4) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v 3) v))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* v 3) v)))) (- (* v v))) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* v 3) v)))) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (95 enodes) * * [misc]simplify: iters left: 3 (152 enodes) * * [misc]simplify: iters left: 2 (254 enodes) * * [misc]simplify: iters left: 1 (338 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* v 3))))) (sqrt (+ 1 (+ (* v (* v 3)) (* 9 (pow v 4))))))) (sqrt (+ 1 (* v (* v 3))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) 4) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v 3) v))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* v 3) v)))) (- (* v v))) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* v 3) v)))) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* v 3))))) (sqrt (+ 1 (+ (* v (* v 3)) (* 9 (pow v 4))))))) (sqrt (+ 1 (* v (* v 3))))))) * * * * [misc]progress: [ 441 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (113 enodes) * * [misc]simplify: iters left: 4 (349 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (- (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* v (* v -3))))) (* (sqrt 2) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (- (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* v (* v -3))))) (* (sqrt 2) (* v v)))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (138 enodes) * * [misc]simplify: iters left: 2 (224 enodes) * * [misc]simplify: iters left: 1 (256 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* (* v 3) v)))) (sqrt (+ 1 (+ (* (* v 3) v) (* 9 (pow v 4))))))) (sqrt (* 4 (sqrt (+ 1 (* (* v 3) v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (- (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* v (* v -3))))) (* (sqrt 2) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* (* v 3) v)))) (sqrt (+ 1 (+ (* (* v 3) v) (* 9 (pow v 4))))))) (sqrt (* 4 (sqrt (+ 1 (* (* v 3) v)))))))) * * * * [misc]progress: [ 442 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (113 enodes) * * [misc]simplify: iters left: 4 (338 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* v -3) v))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* v -3) v))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (96 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (230 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* v 3))))) (sqrt (+ 1 (+ (* v (* v 3)) (* (pow v 4) 9)))))) (sqrt (* (sqrt (+ 1 (+ (* v (* v 3)) (* (pow v 4) 9)))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* v -3) v))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* v 3))))) (sqrt (+ 1 (+ (* v (* v 3)) (* (pow v 4) 9)))))) (sqrt (* (sqrt (+ 1 (+ (* v (* v 3)) (* (pow v 4) 9)))) 16))))) * * * * [misc]progress: [ 443 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (123 enodes) * * [misc]simplify: iters left: 4 (388 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))) (* (* (sqrt (+ 1 (* (* v 3) v))) (* v v)) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (sqrt 2))))) (sqrt (- (* (* (sqrt (- 1 (* (* v 3) v))) (sqrt 2)) (* (sqrt (+ 1 (* (* v 3) v))) 4)) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (sqrt 2)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))) (* (* (sqrt (+ 1 (* (* v 3) v))) (* v v)) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (sqrt 2))))) (sqrt (- (* (* (sqrt (- 1 (* (* v 3) v))) (sqrt 2)) (* (sqrt (+ 1 (* (* v 3) v))) 4)) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (95 enodes) * * [misc]simplify: iters left: 3 (148 enodes) * * [misc]simplify: iters left: 2 (228 enodes) * * [misc]simplify: iters left: 1 (255 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* v 3))))) (sqrt (+ 1 (+ (* v (* v 3)) (* (pow v 4) 9)))))) (sqrt (* 16 (sqrt (+ 1 (* v (* v 3))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))) (* (* (sqrt (+ 1 (* (* v 3) v))) (* v v)) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (sqrt 2))))) (sqrt (- (* (* (sqrt (- 1 (* (* v 3) v))) (sqrt 2)) (* (sqrt (+ 1 (* (* v 3) v))) 4)) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* v 3))))) (sqrt (+ 1 (+ (* v (* v 3)) (* (pow v 4) 9)))))) (sqrt (* 16 (sqrt (+ 1 (* v (* v 3))))))))) * * * * [misc]progress: [ 444 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (367 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* (* v -3) v) 1)) (sqrt 2)) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* (* 4 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* v -3) v) 1)) (sqrt 2)) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* (* 4 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (226 enodes) * * [misc]simplify: iters left: 1 (254 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (+ (* 3 (* v v)) (* (pow v 4) 9)))))) (sqrt (* 4 (sqrt (+ 1 (+ (* 3 (* v v)) (* (pow v 4) 9))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* v -3) v) 1)) (sqrt 2)) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* (* 4 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (+ (* 3 (* v v)) (* (pow v 4) 9)))))) (sqrt (* 4 (sqrt (+ 1 (+ (* 3 (* v v)) (* (pow v 4) 9))))))))) * * * * [misc]progress: [ 445 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (370 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (sqrt 2) (* (sqrt (+ 1 (* (* -3 v) v))) (sqrt (+ 1 (* (* v v) 3))))) (* (* (* (* 4 v) (- v)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (* (/ (* 4 (sqrt 2)) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (sqrt 2) (* (sqrt (+ 1 (* (* -3 v) v))) (sqrt (+ 1 (* (* v v) 3))))) (* (* (* (* 4 v) (- v)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (* (/ (* 4 (sqrt 2)) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v v) 3)))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (221 enodes) * * [misc]simplify: iters left: 1 (253 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* (* v 3) v)))) (sqrt (+ 1 (+ (* (* v 3) v) (* 9 (pow v 4))))))) (sqrt (* 4 (sqrt (+ 1 (* (* v 3) v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (sqrt 2) (* (sqrt (+ 1 (* (* -3 v) v))) (sqrt (+ 1 (* (* v v) 3))))) (* (* (* (* 4 v) (- v)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (- (* (* (/ (* 4 (sqrt 2)) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v v) 3)))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* (* v 3) v)))) (sqrt (+ 1 (+ (* (* v 3) v) (* 9 (pow v 4))))))) (sqrt (* 4 (sqrt (+ 1 (* (* v 3) v)))))))) * * * * [misc]progress: [ 446 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (117 enodes) * * [misc]simplify: iters left: 4 (355 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt 2) (sqrt (+ 1 (* (* v -3) v)))) (+ (* (* 4 v) (- v)) 4))) (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v 3) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt 2) (sqrt (+ 1 (* (* v -3) v)))) (+ (* (* 4 v) (- v)) 4))) (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v 3) v)))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (148 enodes) * * [misc]simplify: iters left: 2 (230 enodes) * * [misc]simplify: iters left: 1 (260 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* v 3))))) (sqrt (+ 1 (+ (* v (* v 3)) (* 9 (pow v 4))))))) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt 2) (sqrt (+ 1 (* (* v -3) v)))) (+ (* (* 4 v) (- v)) 4))) (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v 3) v)))))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* v (* v 3))))) (sqrt (+ 1 (+ (* v (* v 3)) (* 9 (pow v 4))))))) 4))) * * * * [misc]progress: [ 447 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3)))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (124 enodes) * * [misc]simplify: iters left: 4 (433 enodes) * [exit]simplify: Simplified to (* (sqrt (* (pow (* (/ (sqrt 2) 4) (sqrt (+ (* -3 (* v v)) 1))) 3) (+ (* (* (* v v) (* v v)) (- (* v v))) 1))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* 9 (* v v)) (* v v)))) 4)) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (pow (* (/ (sqrt 2) 4) (sqrt (+ (* -3 (* v v)) 1))) 3) (+ (* (* (* v v) (* v v)) (- (* v v))) 1))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* 9 (* v v)) (* v v)))) 4)) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v v) 3)))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * * [misc]simplify: iters left: 6 (33 enodes) * * [misc]simplify: iters left: 5 (93 enodes) * * [misc]simplify: iters left: 4 (292 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* 4 (sqrt (+ 1 (* (* v 3) v)))))) (sqrt (+ (* (* (sqrt (- 1 (* (* v 3) v))) (- (* (* (- v) v) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (* (- v) v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v 3) v))))) (* (* (sqrt (- 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* v 3) v))) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (pow (* (/ (sqrt 2) 4) (sqrt (+ (* -3 (* v v)) 1))) 3) (+ (* (* (* v v) (* v v)) (- (* v v))) 1))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* 9 (* v v)) (* v v)))) 4)) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v v) 3)))))))) (* (sqrt (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* 4 (sqrt (+ 1 (* (* v 3) v)))))) (sqrt (+ (* (* (sqrt (- 1 (* (* v 3) v))) (- (* (* (- v) v) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (* (- v) v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v 3) v))))) (* (* (sqrt (- 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* v 3) v))) (/ (sqrt 2) 4)))))))) * * * * [misc]progress: [ 448 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (126 enodes) * * [misc]simplify: iters left: 4 (432 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* (* v -3) v) 1)) (+ (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))) (* (sqrt (+ (* (* v -3) v) 1)) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))))) (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (sqrt (+ (+ 1 (* v (* v 3))) (* (* v (* v 3)) (* v (* v 3)))))) (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v 3))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* (* v -3) v) 1)) (+ (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))) (* (sqrt (+ (* (* v -3) v) 1)) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))))) (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (sqrt (+ (+ 1 (* v (* v 3))) (* (* v (* v 3)) (* v (* v 3)))))) (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v 3))))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (29 enodes) * * [misc]simplify: iters left: 5 (74 enodes) * * [misc]simplify: iters left: 4 (193 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* v (* v 3))) (* (* v (* v 3)) (* v (* v 3))))) (* 4 (sqrt (+ 1 (* v (* v 3))))))) (sqrt (* (* (+ (* v v) 1) (/ (sqrt 2) 4)) (sqrt (- 1 (* v (* v 3))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* (* v -3) v) 1)) (+ (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))) (* (sqrt (+ (* (* v -3) v) 1)) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))))) (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (sqrt (+ (+ 1 (* v (* v 3))) (* (* v (* v 3)) (* v (* v 3)))))) (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v 3))))))))) (* (sqrt (* (sqrt (+ (+ 1 (* v (* v 3))) (* (* v (* v 3)) (* v (* v 3))))) (* 4 (sqrt (+ 1 (* v (* v 3))))))) (sqrt (* (* (+ (* v v) 1) (/ (sqrt 2) 4)) (sqrt (- 1 (* v (* v 3))))))))) * * * * [misc]progress: [ 449 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (388 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (+ (* (- v) (* v (sqrt 2))) (sqrt 2))))) (sqrt (* (sqrt (+ (* (* v 3) v) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* 4 (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (+ (* (- v) (* v (sqrt 2))) (sqrt 2))))) (sqrt (* (sqrt (+ (* (* v 3) v) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (151 enodes) * * [misc]simplify: iters left: 2 (279 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* v v) 12) 4)) (sqrt (* 4 (+ (+ (* (* v v) 12) 4) (* (* (* v 3) (* v v)) (* (* v 3) 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* 4 (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (+ (* (- v) (* v (sqrt 2))) (sqrt 2))))) (sqrt (* (sqrt (+ (* (* v 3) v) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* v v) (sqrt 2))))))) (* (sqrt (+ (* (* v v) 12) 4)) (sqrt (* 4 (+ (+ (* (* v v) 12) 4) (* (* (* v 3) (* v v)) (* (* v 3) 4)))))))) * * * * [misc]progress: [ 450 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (112 enodes) * * [misc]simplify: iters left: 4 (362 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) 4) (* (sqrt 2) (sqrt (- 1 (pow (* (* v 3) v) 3))))) (* (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) 4) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* v v) (sqrt 2)))))) (sqrt (* (sqrt (+ 1 (* (* v 3) v))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) 4) (* (sqrt 2) (sqrt (- 1 (pow (* (* v 3) v) 3))))) (* (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) 4) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* v v) (sqrt 2)))))) (sqrt (* (sqrt (+ 1 (* (* v 3) v))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (106 enodes) * * [misc]simplify: iters left: 3 (166 enodes) * * [misc]simplify: iters left: 2 (275 enodes) * * [misc]simplify: iters left: 1 (357 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* v (* 12 v)) 4)) (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) (* v (* v 3))) 1)) (* (sqrt (+ (* v (* v 3)) 1)) 16)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) 4) (* (sqrt 2) (sqrt (- 1 (pow (* (* v 3) v) 3))))) (* (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) 4) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* v v) (sqrt 2)))))) (sqrt (* (sqrt (+ 1 (* (* v 3) v))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* v v) (sqrt 2))))))) (* (sqrt (+ (* v (* 12 v)) 4)) (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) (* v (* v 3))) 1)) (* (sqrt (+ (* v (* v 3)) 1)) 16)))))) * * * * [misc]progress: [ 451 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (418 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (sqrt 2) 4) (* v v))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4)))) (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (sqrt 2) 4) (* v v))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4)))) (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (173 enodes) * * [misc]simplify: iters left: 2 (359 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 4 (* 12 (* v v)))) (sqrt (+ (+ 4 (* 12 (* v v))) (* (* (* v v) 3) (* 12 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (sqrt 2) 4) (* v v))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4)))) (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))))))) (* (sqrt (+ 4 (* 12 (* v v)))) (sqrt (+ (+ 4 (* 12 (* v v))) (* (* (* v v) 3) (* 12 (* v v)))))))) * * * * [misc]progress: [ 452 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (385 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (+ 1 (* 3 (* v v))))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (/ (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ 4 (* (* v v) (sqrt 2)))) (* 4 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (+ 1 (* 3 (* v v))))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (/ (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ 4 (* (* v v) (sqrt 2)))) (* 4 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (148 enodes) * * [misc]simplify: iters left: 2 (264 enodes) * * [misc]simplify: iters left: 1 (376 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* 12 (* v v)) 4)) (sqrt (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (sqrt (+ (+ (* (pow v 4) 9) (* (* v v) 3)) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (+ 1 (* 3 (* v v))))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (/ (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ 4 (* (* v v) (sqrt 2)))) (* 4 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))))))) (* (sqrt (+ (* 12 (* v v)) 4)) (sqrt (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (sqrt (+ (+ (* (pow v 4) 9) (* (* v v) 3)) 1))))))) * * * * [misc]progress: [ 453 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (123 enodes) * * [misc]simplify: iters left: 4 (400 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* 4 (sqrt 2))) (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (- 1 (* (* v 3) v))))))) (sqrt (- (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt (+ 1 (* (* v 3) v))) (* 4 (/ (sqrt 2) 4)))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v 3) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* 4 (sqrt 2))) (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (- 1 (* (* v 3) v))))))) (sqrt (- (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt (+ 1 (* (* v 3) v))) (* 4 (/ (sqrt 2) 4)))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v 3) v)))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (161 enodes) * * [misc]simplify: iters left: 2 (281 enodes) * * [misc]simplify: iters left: 1 (356 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* v (* 12 v)) 4)) (sqrt (* 16 (sqrt (+ (+ (* 9 (pow v 4)) (* v (* v 3))) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* 4 (sqrt 2))) (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (- 1 (* (* v 3) v))))))) (sqrt (- (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt (+ 1 (* (* v 3) v))) (* 4 (/ (sqrt 2) 4)))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v 3) v)))))))) (* (sqrt (+ (* v (* 12 v)) 4)) (sqrt (* 16 (sqrt (+ (+ (* 9 (pow v 4)) (* v (* v 3))) 1))))))) * * * * [misc]progress: [ 454 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (377 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt 2) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))) (* (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* 4 (sqrt (+ (* (* v 3) v) 1)))) (* (* v v) (sqrt 2))))) (sqrt (* (sqrt (+ (* (* v 3) v) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt 2) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))) (* (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* 4 (sqrt (+ (* (* v 3) v) 1)))) (* (* v v) (sqrt 2))))) (sqrt (* (sqrt (+ (* (* v 3) v) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (106 enodes) * * [misc]simplify: iters left: 3 (166 enodes) * * [misc]simplify: iters left: 2 (274 enodes) * * [misc]simplify: iters left: 1 (354 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* v v) 12) 4)) (sqrt (* (sqrt (+ (+ (* 9 (pow v 4)) (* v (* v 3))) 1)) (* (sqrt (+ (* v (* v 3)) 1)) 16)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt 2) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))) (* (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* 4 (sqrt (+ (* (* v 3) v) 1)))) (* (* v v) (sqrt 2))))) (sqrt (* (sqrt (+ (* (* v 3) v) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))))))) (* (sqrt (+ (* (* v v) 12) 4)) (sqrt (* (sqrt (+ (+ (* 9 (pow v 4)) (* v (* v 3))) 1)) (* (sqrt (+ (* v (* v 3)) 1)) 16)))))) * * * * [misc]progress: [ 455 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (31 enodes) * * [misc]simplify: iters left: 5 (78 enodes) * * [misc]simplify: iters left: 4 (235 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* (* v 3) v)))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (+ (sqrt 2) (* (* v (- v)) (sqrt 2)))))) (sqrt (* (sqrt (+ 1 (* (* v 3) v))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* 4 (sqrt (+ 1 (* (* v 3) v)))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (+ (sqrt 2) (* (* v (- v)) (sqrt 2)))))) (sqrt (* (sqrt (+ 1 (* (* v 3) v))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * * [misc]simplify: iters left: 2 (51 enodes) * * [misc]simplify: iters left: 1 (87 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* 48 (* v v)) 16)) (sqrt (+ 4 (* (* 12 v) v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* 4 (sqrt (+ 1 (* (* v 3) v)))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (+ (sqrt 2) (* (* v (- v)) (sqrt 2)))))) (sqrt (* (sqrt (+ 1 (* (* v 3) v))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))))))) (* (sqrt (+ (* 48 (* v v)) 16)) (sqrt (+ 4 (* (* 12 v) v)))))) * * * * [misc]progress: [ 456 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (375 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (* (* v v) 3) 1)) 4) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (* (sqrt (+ (* (* v v) 3) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (* (* v v) 3) 1)) 4) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (* (sqrt (+ (* (* v v) 3) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (248 enodes) * * [misc]simplify: iters left: 1 (328 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ (* (* v 3) v) 1))) (sqrt (+ (+ (* (pow v 4) 9) (* (* v 3) v)) 1)))) (sqrt (+ (* 12 (* v v)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ (* (* v v) 3) 1)) 4) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (* (sqrt (+ (* (* v v) 3) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))))) (* (sqrt (* (* 4 (sqrt (+ (* (* v 3) v) 1))) (sqrt (+ (+ (* (pow v 4) 9) (* (* v 3) v)) 1)))) (sqrt (+ (* 12 (* v v)) 4))))) * * * * [misc]progress: [ 457 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (82 enodes) * * [misc]simplify: iters left: 4 (261 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (* (* v v) (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) (sqrt (* (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (* (* v v) (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) (sqrt (* (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (64 enodes) * [exit]simplify: Simplified to (+ 4 (* (* 12 v) v)) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (* (* v v) (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) (sqrt (* (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))) (+ 4 (* (* 12 v) v)))) * * * * [misc]progress: [ 458 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (91 enodes) * * [misc]simplify: iters left: 4 (289 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (sqrt (+ 1 (* (* v 3) v))) (* 4 (sqrt 2))) (* (sqrt (- 1 (* (* v 3) v))) (* v v))))) (sqrt (* (sqrt (+ 1 (* (* v 3) v))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (sqrt (+ 1 (* (* v 3) v))) (* 4 (sqrt 2))) (* (sqrt (- 1 (* (* v 3) v))) (* v v))))) (sqrt (* (sqrt (+ 1 (* (* v 3) v))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * * [misc]simplify: iters left: 2 (42 enodes) * * [misc]simplify: iters left: 1 (59 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 16)) (sqrt (+ 4 (* 12 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (sqrt (+ 1 (* (* v 3) v))) (* 4 (sqrt 2))) (* (sqrt (- 1 (* (* v 3) v))) (* v v))))) (sqrt (* (sqrt (+ 1 (* (* v 3) v))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))))))) (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 16)) (sqrt (+ 4 (* 12 (* v v))))))) * * * * [misc]progress: [ 459 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (399 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2)))))) (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2)))))) (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (165 enodes) * * [misc]simplify: iters left: 2 (315 enodes) * * [misc]simplify: iters left: 1 (493 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* v 12) v) 4)) (sqrt (+ 4 (+ (* (* v 12) v) (* 36 (pow v 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2)))))) (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))))))) (* (sqrt (+ (* (* v 12) v) 4)) (sqrt (+ 4 (+ (* (* v 12) v) (* 36 (pow v 4)))))))) * * * * [misc]progress: [ 460 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (110 enodes) * * [misc]simplify: iters left: 4 (356 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (/ (sqrt 2) 4))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt 2) (* v v))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (/ (sqrt 2) 4))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt 2) (* v v))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (260 enodes) * * [misc]simplify: iters left: 1 (361 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (sqrt (+ (+ (* 9 (pow v 4)) (* 3 (* v v))) 1)))) (sqrt (+ (* v (* v 12)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (/ (sqrt 2) 4))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt 2) (* v v))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (sqrt (+ (+ (* 9 (pow v 4)) (* 3 (* v v))) 1)))) (sqrt (+ (* v (* v 12)) 4))))) * * * * [misc]progress: [ 461 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (370 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (sqrt 2) 4)) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (sqrt 2) 4)) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (284 enodes) * * [misc]simplify: iters left: 1 (403 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ (* 9 (pow v 4)) (* v (* v 3))) 1)) (sqrt (+ 4 (* (* v 12) v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (sqrt 2) 4)) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))))))) (* (sqrt (+ (+ (* 9 (pow v 4)) (* v (* v 3))) 1)) (sqrt (+ 4 (* (* v 12) v)))))) * * * * [misc]progress: [ 462 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (370 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))))) (sqrt (* (sqrt (+ 1 (* (* v 3) v))) (+ (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt 2) (- (* v v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))))) (sqrt (* (sqrt (+ 1 (* (* v 3) v))) (+ (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt 2) (- (* v v)))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (136 enodes) * * [misc]simplify: iters left: 2 (244 enodes) * * [misc]simplify: iters left: 1 (322 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* v 3) v) 1)) (sqrt (+ (+ (* 9 (pow v 4)) (* (* v 3) v)) 1)))) (sqrt (+ 4 (* (* v 12) v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3)))) (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))))) (sqrt (* (sqrt (+ 1 (* (* v 3) v))) (+ (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt 2) (- (* v v)))))))) (* (sqrt (* (sqrt (+ (* (* v 3) v) 1)) (sqrt (+ (+ (* 9 (pow v 4)) (* (* v 3) v)) 1)))) (sqrt (+ 4 (* (* v 12) v)))))) * * * * [misc]progress: [ 463 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (390 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ 1 (* v (* v -3)))) (* (* v v) (sqrt 2))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ 1 (* v (* v -3)))) (* (* v v) (sqrt 2))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (136 enodes) * * [misc]simplify: iters left: 2 (244 enodes) * * [misc]simplify: iters left: 1 (322 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ (+ (* 9 (pow v 4)) (* (* v 3) v)) 1)))) (sqrt (+ 4 (* (* v 12) v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ 1 (* v (* v -3)))) (* (* v v) (sqrt 2))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* 4 (sqrt (+ (+ (* 9 (pow v 4)) (* (* v 3) v)) 1)))) (sqrt (+ 4 (* (* v 12) v)))))) * * * * [misc]progress: [ 464 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (112 enodes) * * [misc]simplify: iters left: 4 (373 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ 1 (* v (* v 3))) (* (* v (* v 3)) (* v (* v 3))))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))))) (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v 3)))))))) (sqrt (* (sqrt (+ 1 (* v (* v 3)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (* (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ 1 (* v (* v 3))) (* (* v (* v 3)) (* v (* v 3))))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))))) (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v 3)))))))) (sqrt (* (sqrt (+ 1 (* v (* v 3)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (* (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (165 enodes) * * [misc]simplify: iters left: 2 (281 enodes) * * [misc]simplify: iters left: 1 (358 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 4 (* (* 12 v) v))) (sqrt (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (sqrt (+ (+ (* 9 (pow v 4)) (* (* v v) 3)) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ 1 (* v (* v 3))) (* (* v (* v 3)) (* v (* v 3))))) (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))))) (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v 3)))))))) (sqrt (* (sqrt (+ 1 (* v (* v 3)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (* (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))) (* (* v v) (sqrt 2))))))) (* (sqrt (+ 4 (* (* 12 v) v))) (sqrt (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (sqrt (+ (+ (* 9 (pow v 4)) (* (* v v) 3)) 1))))))) * * * * [misc]progress: [ 465 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (62 enodes) * * [misc]simplify: iters left: 4 (195 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* (* v 3) v))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) (* (* v v) 9))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v v) (* (* v v) 9))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ 1 (* (* v 3) v))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) (* (* v v) 9))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v v) (* (* v v) 9))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * * [misc]simplify: iters left: 2 (35 enodes) * * [misc]simplify: iters left: 1 (52 enodes) * [exit]simplify: Simplified to (+ (* (* v v) 12) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ 1 (* (* v 3) v))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) (* (* v v) 9))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v v) (* (* v v) 9))))))) (+ (* (* v v) 12) 4))) * * * * [misc]progress: [ 466 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (111 enodes) * * [misc]simplify: iters left: 4 (375 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (136 enodes) * * [misc]simplify: iters left: 2 (244 enodes) * * [misc]simplify: iters left: 1 (322 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* v 3) v) 1)) (sqrt (+ (+ (* 9 (pow v 4)) (* (* v 3) v)) 1)))) (sqrt (+ 4 (* (* v 12) v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ (* (* v 3) v) 1)) (sqrt (+ (+ (* 9 (pow v 4)) (* (* v 3) v)) 1)))) (sqrt (+ 4 (* (* v 12) v)))))) * * * * [misc]progress: [ 467 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (31 enodes) * * [misc]simplify: iters left: 5 (78 enodes) * * [misc]simplify: iters left: 4 (262 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* v 3) v)))) (sqrt (- 1 (* (* v v) (* (* v v) 9))))) (* (* (sqrt (- 1 (* (* v v) (* (* v v) 9)))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* (* v 3) v))) (* v v))))) (sqrt (* (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) (* (* v v) 9))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v v) (* (* v v) 9)))))) (sqrt (+ 1 (* (* v 3) v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* v 3) v)))) (sqrt (- 1 (* (* v v) (* (* v v) 9))))) (* (* (sqrt (- 1 (* (* v v) (* (* v v) 9)))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* (* v 3) v))) (* v v))))) (sqrt (* (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) (* (* v v) 9))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v v) (* (* v v) 9)))))) (sqrt (+ 1 (* (* v 3) v)))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (46 enodes) * * [misc]simplify: iters left: 1 (64 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* (* v v) 3))) (sqrt (+ 4 (* (* v v) 12)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* v 3) v)))) (sqrt (- 1 (* (* v v) (* (* v v) 9))))) (* (* (sqrt (- 1 (* (* v v) (* (* v v) 9)))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* (* v 3) v))) (* v v))))) (sqrt (* (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) (* (* v v) 9))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v v) (* (* v v) 9)))))) (sqrt (+ 1 (* (* v 3) v)))))) (* (sqrt (+ 1 (* (* v v) 3))) (sqrt (+ 4 (* (* v v) 12)))))) * * * * [misc]progress: [ 468 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (85 enodes) * * [misc]simplify: iters left: 4 (276 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (* (* v v) (* (* v v) -9)) 1)) (* (sqrt (+ 1 (* v (* v 3)))) (* 4 (/ (sqrt 2) 4)))) (* (sqrt (+ (* (* v v) (* (* v v) -9)) 1)) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v 3)))))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) (* (* v v) -9)) 1))) (* (sqrt (+ (* (* v -3) v) 1)) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v 3))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* (* v v) (* (* v v) -9)) 1)) (* (sqrt (+ 1 (* v (* v 3)))) (* 4 (/ (sqrt 2) 4)))) (* (sqrt (+ (* (* v v) (* (* v v) -9)) 1)) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v 3)))))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) (* (* v v) -9)) 1))) (* (sqrt (+ (* (* v -3) v) 1)) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v 3))))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (27 enodes) * * [misc]simplify: iters left: 2 (36 enodes) * * [misc]simplify: iters left: 1 (53 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ 1 (* (* v v) 3))))) (sqrt (+ 4 (* (* 12 v) v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* (* v v) (* (* v v) -9)) 1)) (* (sqrt (+ 1 (* v (* v 3)))) (* 4 (/ (sqrt 2) 4)))) (* (sqrt (+ (* (* v v) (* (* v v) -9)) 1)) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v 3)))))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) (* (* v v) -9)) 1))) (* (sqrt (+ (* (* v -3) v) 1)) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v 3))))))))) (* (sqrt (* 4 (sqrt (+ 1 (* (* v v) 3))))) (sqrt (+ 4 (* (* 12 v) v)))))) * * * * [misc]progress: [ 469 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (123 enodes) * * [misc]simplify: iters left: 4 (393 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* v 3) v)))) (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (sqrt 2) (* v v)) 4)))) (sqrt (* (sqrt (+ (* (* v 3) v) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt 2) (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* v 3) v)))) (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (sqrt 2) (* v v)) 4)))) (sqrt (* (sqrt (+ (* (* v 3) v) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt 2) (* v v))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (169 enodes) * * [misc]simplify: iters left: 2 (290 enodes) * * [misc]simplify: iters left: 1 (382 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 4 (* (* v v) 12))) (sqrt (* 16 (sqrt (+ (+ (* 9 (pow v 4)) (* v (* v 3))) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* v 3) v)))) (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (sqrt 2) (* v v)) 4)))) (sqrt (* (sqrt (+ (* (* v 3) v) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt 2) (* v v))))))) (* (sqrt (+ 4 (* (* v v) 12))) (sqrt (* 16 (sqrt (+ (+ (* 9 (pow v 4)) (* v (* v 3))) 1))))))) * * * * [misc]progress: [ 470 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (85 enodes) * * [misc]simplify: iters left: 4 (266 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* (* v 3) v))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (sqrt (+ (* (* (* v v) -9) (* v v)) 1)) (* (sqrt 2) (* v v)))))) (sqrt (- (* (* 4 (sqrt (+ 1 (* (* v 3) v)))) (* (sqrt 2) (sqrt (+ (* (* v v) -3) 1)))) (* (sqrt (+ (* (* (* v v) -9) (* v v)) 1)) (* (* (* v v) (sqrt 2)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ 1 (* (* v 3) v))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (sqrt (+ (* (* (* v v) -9) (* v v)) 1)) (* (sqrt 2) (* v v)))))) (sqrt (- (* (* 4 (sqrt (+ 1 (* (* v 3) v)))) (* (sqrt 2) (sqrt (+ (* (* v v) -3) 1)))) (* (sqrt (+ (* (* (* v v) -9) (* v v)) 1)) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * * [misc]simplify: iters left: 2 (42 enodes) * * [misc]simplify: iters left: 1 (59 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 16)) (sqrt (+ 4 (* 12 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ 1 (* (* v 3) v))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (sqrt (+ (* (* (* v v) -9) (* v v)) 1)) (* (sqrt 2) (* v v)))))) (sqrt (- (* (* 4 (sqrt (+ 1 (* (* v 3) v)))) (* (sqrt 2) (sqrt (+ (* (* v v) -3) 1)))) (* (sqrt (+ (* (* (* v v) -9) (* v v)) 1)) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 16)) (sqrt (+ 4 (* 12 (* v v))))))) * * * * [misc]progress: [ 471 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (398 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt 2) (sqrt (- 1 (* (* v 3) v))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (* (sqrt (+ (* (* v 3) v) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt 2) (sqrt (- 1 (* (* v 3) v))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (* (sqrt (+ (* (* v 3) v) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (136 enodes) * * [misc]simplify: iters left: 2 (244 enodes) * * [misc]simplify: iters left: 1 (322 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ (+ (* 9 (pow v 4)) (* (* v 3) v)) 1)))) (sqrt (+ 4 (* (* v 12) v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt 2) (sqrt (- 1 (* (* v 3) v))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (* (sqrt (+ (* (* v 3) v) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* v v) (sqrt 2))))))) (* (sqrt (* 4 (sqrt (+ (+ (* 9 (pow v 4)) (* (* v 3) v)) 1)))) (sqrt (+ 4 (* (* v 12) v)))))) * * * * [misc]progress: [ 472 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (89 enodes) * * [misc]simplify: iters left: 4 (283 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* (- v) v) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (sqrt (+ 1 (* (* v 3) v))) (* (sqrt 2) (sqrt (- 1 (* (* v 3) v))))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v 3) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (* (- v) v) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (sqrt (+ 1 (* (* v 3) v))) (* (sqrt 2) (sqrt (- 1 (* (* v 3) v))))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v 3) v)))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (27 enodes) * * [misc]simplify: iters left: 2 (36 enodes) * * [misc]simplify: iters left: 1 (53 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 4 (* (* 12 v) v))) (sqrt (* 4 (sqrt (+ 1 (* (* v v) 3)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (* (- v) v) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (sqrt (+ 1 (* (* v 3) v))) (* (sqrt 2) (sqrt (- 1 (* (* v 3) v))))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v 3) v)))))))) (* (sqrt (+ 4 (* (* 12 v) v))) (sqrt (* 4 (sqrt (+ 1 (* (* v v) 3)))))))) * * * * [misc]progress: [ 473 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (89 enodes) * * [misc]simplify: iters left: 4 (283 enodes) * [exit]simplify: Simplified to (* (sqrt (* (+ (* (- v) v) 1) (* (* 4 (sqrt 2)) (sqrt (+ (* -3 (* v v)) 1))))) (sqrt (- (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt (+ 1 (* (* v 3) v))) (* 4 (/ (sqrt 2) 4)))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v 3) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (+ (* (- v) v) 1) (* (* 4 (sqrt 2)) (sqrt (+ (* -3 (* v v)) 1))))) (sqrt (- (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt (+ 1 (* (* v 3) v))) (* 4 (/ (sqrt 2) 4)))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v 3) v)))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 4))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * * [misc]simplify: iters left: 2 (39 enodes) * * [misc]simplify: iters left: 1 (56 enodes) * [exit]simplify: Simplified to (* 4 (sqrt (+ (* (* v v) 12) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (+ (* (- v) v) 1) (* (* 4 (sqrt 2)) (sqrt (+ (* -3 (* v v)) 1))))) (sqrt (- (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt (+ 1 (* (* v 3) v))) (* 4 (/ (sqrt 2) 4)))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v 3) v)))))))) (* 4 (sqrt (+ (* (* v v) 12) 4))))) * * * * [misc]progress: [ 474 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3)))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (97 enodes) * * [misc]simplify: iters left: 4 (361 enodes) * [exit]simplify: Simplified to (* (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* v v) -3)))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v v) -3)))) 3))) (sqrt (* (sqrt (+ 1 (* (* v 3) v))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* v v) -3)))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v v) -3)))) 3))) (sqrt (* (sqrt (+ 1 (* (* v 3) v))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (71 enodes) * * [misc]simplify: iters left: 4 (231 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (sqrt (- 1 (* (* v 3) v))) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (- 1 (* (* v 3) v))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v 3) v)))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v 3) v))))))) (sqrt (* 4 (+ 1 (* (* v 3) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* v v) -3)))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v v) -3)))) 3))) (sqrt (* (sqrt (+ 1 (* (* v 3) v))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* (* v v) (sqrt 2))))))) (* (sqrt (+ (* (* (sqrt (- 1 (* (* v 3) v))) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (- 1 (* (* v 3) v))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v 3) v)))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v 3) v))))))) (sqrt (* 4 (+ 1 (* (* v 3) v))))))) * * * * [misc]progress: [ 475 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (98 enodes) * * [misc]simplify: iters left: 4 (357 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ 1 (* -3 (* v v)))) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* v (- v))))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* -3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* (* v 3) v))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 9) (* v v))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 9) (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ 1 (* -3 (* v v)))) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* v (- v))))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* -3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* (* v 3) v))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 9) (* v v))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 9) (* v v))))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (133 enodes) * * [misc]simplify: iters left: 3 (415 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* 4 (* (* v 3) v)) 4)) (sqrt (* (/ (* (sqrt 2) (+ (* v v) 1)) 4) (sqrt (- 1 (* (* v 3) v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ 1 (* -3 (* v v)))) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* v (- v))))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* -3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* (* v 3) v))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 9) (* v v))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 9) (* v v))))))))) (* (sqrt (+ (* 4 (* (* v 3) v)) 4)) (sqrt (* (/ (* (sqrt 2) (+ (* v v) 1)) 4) (sqrt (- 1 (* (* v 3) v)))))))) * * * * [misc]progress: [ 476 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (372 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) 4) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (sqrt 2) (* (- v) (* v (sqrt 2))))))) (sqrt (+ (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ 1 (* (* v v) 3))) (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) 4) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (sqrt 2) (* (- v) (* v (sqrt 2))))))) (sqrt (+ (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ 1 (* (* v v) 3))) (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (95 enodes) * * [misc]simplify: iters left: 3 (152 enodes) * * [misc]simplify: iters left: 2 (274 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* v 9) (pow v 3)))) (sqrt (+ 1 (* (* v 3) v))))) (sqrt (* 4 (+ (* (* 4 v) (* (* v 9) (* v v))) (+ 4 (* 12 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) 4) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (sqrt 2) (* (- v) (* v (sqrt 2))))))) (sqrt (+ (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ 1 (* (* v v) 3))) (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (* (sqrt (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* v 9) (pow v 3)))) (sqrt (+ 1 (* (* v 3) v))))) (sqrt (* 4 (+ (* (* 4 v) (* (* v 9) (* v v))) (+ 4 (* 12 (* v v))))))))) * * * * [misc]progress: [ 477 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (403 enodes) * [exit]simplify: Simplified to (* (sqrt (- (/ (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)) (/ 4 (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v v) 3))))))) (sqrt (- (* (sqrt 2) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* 4 (sqrt (+ 1 (* (* v v) 3)))))) (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) 4) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (/ (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)) (/ 4 (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v v) 3))))))) (sqrt (- (* (sqrt 2) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* 4 (sqrt (+ 1 (* (* v v) 3)))))) (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) 4) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (197 enodes) * * [misc]simplify: iters left: 2 (314 enodes) * * [misc]simplify: iters left: 1 (353 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* v (* v 3))) (* (pow v 4) 9))) (sqrt (+ 1 (* v (* v 3)))))) (sqrt (* (* 16 (sqrt (+ 1 (* v (* v 3))))) (sqrt (+ (+ 1 (* v (* v 3))) (* (pow v 4) 9)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (/ (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)) (/ 4 (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v v) 3))))))) (sqrt (- (* (sqrt 2) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* 4 (sqrt (+ 1 (* (* v v) 3)))))) (* (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) 4) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ (+ 1 (* v (* v 3))) (* (pow v 4) 9))) (sqrt (+ 1 (* v (* v 3)))))) (sqrt (* (* 16 (sqrt (+ 1 (* v (* v 3))))) (sqrt (+ (+ 1 (* v (* v 3))) (* (pow v 4) 9)))))))) * * * * [misc]progress: [ 478 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (108 enodes) * * [misc]simplify: iters left: 4 (344 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt 2) (sqrt (- 1 (pow (* (* v 3) v) 3))))) (* (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (/ (sqrt 2) 4) (* v v))) (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) 4)))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (/ (sqrt 2) 4) (* v v)) (sqrt (+ 1 (* (* v 3) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt 2) (sqrt (- 1 (pow (* (* v 3) v) 3))))) (* (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (/ (sqrt 2) 4) (* v v))) (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) 4)))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (/ (sqrt 2) 4) (* v v)) (sqrt (+ 1 (* (* v 3) v)))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (85 enodes) * * [misc]simplify: iters left: 3 (167 enodes) * * [misc]simplify: iters left: 2 (341 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 3) (* v 9)))) (sqrt (+ 1 (* (* v 3) v))))) (sqrt (+ (* (* (* 4 v) (* v 9)) (* v v)) (+ 4 (* 12 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt 2) (sqrt (- 1 (pow (* (* v 3) v) 3))))) (* (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (/ (sqrt 2) 4) (* v v))) (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) 4)))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (/ (sqrt 2) 4) (* v v)) (sqrt (+ 1 (* (* v 3) v)))))))) (* (sqrt (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 3) (* v 9)))) (sqrt (+ 1 (* (* v 3) v))))) (sqrt (+ (* (* (* 4 v) (* v 9)) (* v v)) (+ 4 (* 12 (* v v)))))))) * * * * [misc]progress: [ 479 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (386 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* 4 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))))) (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* 4 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))))) (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (235 enodes) * * [misc]simplify: iters left: 1 (290 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 4) 9))) (sqrt (+ 1 (* (* v 3) v))))) (sqrt (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 4) 9))) (* 4 (sqrt (+ 1 (* (* v 3) v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* 4 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))))) (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 4) 9))) (sqrt (+ 1 (* (* v 3) v))))) (sqrt (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 4) 9))) (* 4 (sqrt (+ 1 (* (* v 3) v))))))))) * * * * [misc]progress: [ 480 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (395 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (* (sqrt 2) (* (- v) v))) (sqrt (+ 1 (* v (* -3 v)))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))) (sqrt (- (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (/ (sqrt 2) 4) (* v v)) (sqrt (+ 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (* (sqrt 2) (* (- v) v))) (sqrt (+ 1 (* v (* -3 v)))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))) (sqrt (- (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (/ (sqrt 2) 4) (* v v)) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (229 enodes) * * [misc]simplify: iters left: 1 (280 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 4) 9))) (sqrt (+ 1 (* (* v 3) v))))) (sqrt (* 16 (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 4) 9)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (* (sqrt 2) (* (- v) v))) (sqrt (+ 1 (* v (* -3 v)))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))) (sqrt (- (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (/ (sqrt 2) 4) (* v v)) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 4) 9))) (sqrt (+ 1 (* (* v 3) v))))) (sqrt (* 16 (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 4) 9)))))))) * * * * [misc]progress: [ 481 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (359 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* (sqrt (+ 1 (* (* v 3) v))) (* (/ (sqrt 2) 4) (* (- v) v))) (sqrt (- 1 (pow (* (* v 3) v) 3)))))) (sqrt (- (* (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) 4) (* (sqrt 2) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))) (* (* 4 (sqrt (+ 1 (* (* v 3) v)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v 3) v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* (sqrt (+ 1 (* (* v 3) v))) (* (/ (sqrt 2) 4) (* (- v) v))) (sqrt (- 1 (pow (* (* v 3) v) 3)))))) (sqrt (- (* (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) 4) (* (sqrt 2) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))) (* (* 4 (sqrt (+ 1 (* (* v 3) v)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v 3) v) 3)))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (198 enodes) * * [misc]simplify: iters left: 2 (319 enodes) * * [misc]simplify: iters left: 1 (359 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* v (* v 3))) (* (pow v 4) 9))) (sqrt (+ 1 (* v (* v 3)))))) (sqrt (* (sqrt (+ (+ 1 (* v (* v 3))) (* (pow v 4) 9))) (* 16 (sqrt (+ 1 (* v (* v 3)))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* (sqrt (+ 1 (* (* v 3) v))) (* (/ (sqrt 2) 4) (* (- v) v))) (sqrt (- 1 (pow (* (* v 3) v) 3)))))) (sqrt (- (* (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) 4) (* (sqrt 2) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))) (* (* 4 (sqrt (+ 1 (* (* v 3) v)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v 3) v) 3)))))))) (* (sqrt (* (sqrt (+ (+ 1 (* v (* v 3))) (* (pow v 4) 9))) (sqrt (+ 1 (* v (* v 3)))))) (sqrt (* (sqrt (+ (+ 1 (* v (* v 3))) (* (pow v 4) 9))) (* 16 (sqrt (+ 1 (* v (* v 3)))))))))) * * * * [misc]progress: [ 482 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (364 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (sqrt 2) (- (* (* v v) (sqrt 2))))) (* (sqrt (+ 1 (* (* v v) 3))) 4))) (sqrt (- (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt (+ 1 (* (* v v) 3)))) (* (/ (sqrt 2) 4) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (sqrt 2) (- (* (* v v) (sqrt 2))))) (* (sqrt (+ 1 (* (* v v) 3))) 4))) (sqrt (- (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt (+ 1 (* (* v v) 3)))) (* (/ (sqrt 2) 4) (* v v)))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (95 enodes) * * [misc]simplify: iters left: 3 (152 enodes) * * [misc]simplify: iters left: 2 (265 enodes) * * [misc]simplify: iters left: 1 (366 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* v 3) v)) (* 9 (pow v 4)))) (sqrt (+ 1 (* (* v 3) v))))) (sqrt (+ 16 (* 48 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (sqrt 2) (- (* (* v v) (sqrt 2))))) (* (sqrt (+ 1 (* (* v v) 3))) 4))) (sqrt (- (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (sqrt (+ 1 (* (* v v) 3)))) (* (/ (sqrt 2) 4) (* v v)))))) (* (sqrt (* (sqrt (+ (+ 1 (* (* v 3) v)) (* 9 (pow v 4)))) (sqrt (+ 1 (* (* v 3) v))))) (sqrt (+ 16 (* 48 (* v v))))))) * * * * [misc]progress: [ 483 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (106 enodes) * * [misc]simplify: iters left: 4 (313 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (* (sqrt 2) (* v v)) 4)) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (* (sqrt 2) (* v v)) 4)) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (237 enodes) * * [misc]simplify: iters left: 1 (291 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (pow v 4) 9))) (sqrt (+ 1 (* (* v v) 3))))) (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (pow v 4) 9))) (* 4 (sqrt (+ 1 (* (* v v) 3))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (* (sqrt 2) (* v v)) 4)) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (pow v 4) 9))) (sqrt (+ 1 (* (* v v) 3))))) (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (pow v 4) 9))) (* 4 (sqrt (+ 1 (* (* v v) 3))))))))) * * * * [misc]progress: [ 484 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (371 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) 4)))) (sqrt (+ (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) 4)))) (sqrt (+ (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (85 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * * [misc]simplify: iters left: 2 (279 enodes) * * [misc]simplify: iters left: 1 (400 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 4) 9))) (sqrt (+ 1 (* (* v 3) v))))) (sqrt (+ 4 (* v (* 12 v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) 4)))) (sqrt (+ (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (* (sqrt (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 4) 9))) (sqrt (+ 1 (* (* v 3) v))))) (sqrt (+ 4 (* v (* 12 v))))))) * * * * [misc]progress: [ 485 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (373 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt 2))) (* (sqrt (+ (* -3 (* v v)) 1)) (- (* v v)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt 2))) (* (sqrt (+ (* -3 (* v v)) 1)) (- (* v v)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (229 enodes) * * [misc]simplify: iters left: 1 (280 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 4) 9))) (sqrt (+ 1 (* (* v 3) v))))) (sqrt (* (sqrt (+ 1 (* (* v 3) v))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt 2))) (* (sqrt (+ (* -3 (* v v)) 1)) (- (* v v)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 4) 9))) (sqrt (+ 1 (* (* v 3) v))))) (sqrt (* (sqrt (+ 1 (* (* v 3) v))) 16))))) * * * * [misc]progress: [ 486 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (364 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt 2) (* v v))))) (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (sqrt (+ 1 (* 3 (* v v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt 2) (* v v))))) (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (sqrt (+ 1 (* 3 (* v v)))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (259 enodes) * * [misc]simplify: iters left: 1 (451 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* v (* v 3))) (* (pow v 4) 9))) (sqrt (+ 1 (* v (* v 3)))))) (sqrt (+ 4 (+ (* v (* 12 v)) (* (pow v 3) (* v 36)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt 2) (* v v))))) (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (sqrt (+ 1 (* 3 (* v v)))))))) (* (sqrt (* (sqrt (+ (+ 1 (* v (* v 3))) (* (pow v 4) 9))) (sqrt (+ 1 (* v (* v 3)))))) (sqrt (+ 4 (+ (* v (* 12 v)) (* (pow v 3) (* v 36)))))))) * * * * [misc]progress: [ 487 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (374 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* v v) (sqrt 2))))) (sqrt (- (/ (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)) (/ 4 (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* v v) (sqrt 2))))) (sqrt (- (/ (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)) (/ 4 (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* v v))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (231 enodes) * * [misc]simplify: iters left: 1 (287 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* v (* v 3))) (* (pow v 4) 9))) (sqrt (+ 1 (* v (* v 3)))))) (sqrt (* (sqrt (+ (+ 1 (* v (* v 3))) (* (pow v 4) 9))) (* 4 (sqrt (+ 1 (* v (* v 3)))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* v v) (sqrt 2))))) (sqrt (- (/ (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)) (/ 4 (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* v v))))) (* (sqrt (* (sqrt (+ (+ 1 (* v (* v 3))) (* (pow v 4) 9))) (sqrt (+ 1 (* v (* v 3)))))) (sqrt (* (sqrt (+ (+ 1 (* v (* v 3))) (* (pow v 4) 9))) (* 4 (sqrt (+ 1 (* v (* v 3)))))))))) * * * * [misc]progress: [ 488 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (38 enodes) * * [misc]simplify: iters left: 5 (102 enodes) * * [misc]simplify: iters left: 4 (297 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (sqrt 2) 4))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (sqrt 2) 4))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (243 enodes) * * [misc]simplify: iters left: 1 (334 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 4) 9))) (sqrt (+ 1 (* (* v 3) v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 4) 9)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (sqrt 2) 4))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))))) (* (sqrt (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 4) 9))) (sqrt (+ 1 (* (* v 3) v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 4) 9)))))) * * * * [misc]progress: [ 489 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (108 enodes) * * [misc]simplify: iters left: 4 (334 enodes) * [exit]simplify: Simplified to (* (sqrt (- (/ (* (sqrt 2) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (/ 4 (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* 3 (* v v))))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (/ (* (sqrt 2) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (/ 4 (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* 3 (* v v))))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (77 enodes) * * [misc]simplify: iters left: 3 (133 enodes) * * [misc]simplify: iters left: 2 (221 enodes) * * [misc]simplify: iters left: 1 (271 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (pow v 4) 9))) (sqrt (+ 1 (* (* v v) 3)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (/ (* (sqrt 2) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (/ 4 (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* 3 (* v v))))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (pow v 4) 9))) (sqrt (+ 1 (* (* v v) 3)))))) * * * * [misc]progress: [ 490 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (366 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (* 4 (sqrt 2)) 4)) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* v -3) v) 1)))))) (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (* 4 (sqrt 2)) 4)) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* v -3) v) 1)))))) (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (240 enodes) * * [misc]simplify: iters left: 1 (318 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 4) 9))) (sqrt (+ 1 (* (* v 3) v))))) (sqrt (* 4 (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 4) 9)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (* 4 (sqrt 2)) 4)) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* v -3) v) 1)))))) (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))))) (* (sqrt (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 4) 9))) (sqrt (+ 1 (* (* v 3) v))))) (sqrt (* 4 (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 4) 9)))))))) * * * * [misc]progress: [ 491 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (110 enodes) * * [misc]simplify: iters left: 4 (338 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) 4)) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) 4)) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (231 enodes) * * [misc]simplify: iters left: 1 (287 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* v (* v 3))) (* (pow v 4) 9))) (sqrt (+ 1 (* v (* v 3)))))) (sqrt (* (* 4 (sqrt (+ 1 (* v (* v 3))))) (sqrt (+ (+ 1 (* v (* v 3))) (* (pow v 4) 9)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) 4)) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ (+ 1 (* v (* v 3))) (* (pow v 4) 9))) (sqrt (+ 1 (* v (* v 3)))))) (sqrt (* (* 4 (sqrt (+ 1 (* v (* v 3))))) (sqrt (+ (+ 1 (* v (* v 3))) (* (pow v 4) 9)))))))) * * * * [misc]progress: [ 492 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (111 enodes) * * [misc]simplify: iters left: 4 (366 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 9 (* v v)) (* v v)))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (/ (sqrt 2) 4))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 9 (* v v)) (* v v)))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (/ (sqrt 2) 4))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (249 enodes) * * [misc]simplify: iters left: 1 (357 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* v (* v 3))) (* (pow v 4) 9))) (sqrt (+ 1 (* v (* v 3)))))) (sqrt (+ 4 (* 12 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 9 (* v v)) (* v v)))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (/ (sqrt 2) 4))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))))) (* (sqrt (* (sqrt (+ (+ 1 (* v (* v 3))) (* (pow v 4) 9))) (sqrt (+ 1 (* v (* v 3)))))) (sqrt (+ 4 (* 12 (* v v))))))) * * * * [misc]progress: [ 493 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (33 enodes) * * [misc]simplify: iters left: 5 (88 enodes) * * [misc]simplify: iters left: 4 (257 enodes) * [exit]simplify: Simplified to (- (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (/ (sqrt 2) 4) (* v v)) (sqrt (+ 1 (* (* v v) 3)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (/ (sqrt 2) 4) (* v v)) (sqrt (+ 1 (* (* v v) 3)))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (222 enodes) * * [misc]simplify: iters left: 1 (274 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (pow v 4) 9))) (sqrt (+ 1 (* (* v v) 3)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (/ (sqrt 2) 4) (* v v)) (sqrt (+ 1 (* (* v v) 3)))))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (pow v 4) 9))) (sqrt (+ 1 (* (* v v) 3)))))) * * * * [misc]progress: [ 494 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (38 enodes) * * [misc]simplify: iters left: 5 (105 enodes) * * [misc]simplify: iters left: 4 (338 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v 3) v))))))) (sqrt (+ (* (* (- v) v) (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))) (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v 3) v))))))) (sqrt (+ (* (* (- v) v) (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))) (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (134 enodes) * * [misc]simplify: iters left: 2 (239 enodes) * * [misc]simplify: iters left: 1 (323 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* (* v v) 3))) (sqrt (* (sqrt (+ 1 (+ (* (pow v 4) 9) (* (* v v) 3)))) (sqrt (+ 1 (* (* v v) 3)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v 3) v))))))) (sqrt (+ (* (* (- v) v) (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))) (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))))) (* (sqrt (+ 1 (* (* v v) 3))) (sqrt (* (sqrt (+ 1 (+ (* (pow v 4) 9) (* (* v v) 3)))) (sqrt (+ 1 (* (* v v) 3)))))))) * * * * [misc]progress: [ 495 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (112 enodes) * * [misc]simplify: iters left: 4 (352 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* (sqrt (+ 1 (* v (* -3 v)))) (sqrt 2)) (* (sqrt (+ 1 (* (* v 3) v))) (* v v))))) (sqrt (- (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (/ (sqrt 2) 4) (* v v)) (sqrt (+ 1 (* (* v 3) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* (sqrt (+ 1 (* v (* -3 v)))) (sqrt 2)) (* (sqrt (+ 1 (* (* v 3) v))) (* v v))))) (sqrt (- (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (/ (sqrt 2) 4) (* v v)) (sqrt (+ 1 (* (* v 3) v)))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (240 enodes) * * [misc]simplify: iters left: 1 (318 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 4) 9))) (sqrt (+ 1 (* (* v 3) v))))) (sqrt (* 4 (sqrt (+ 1 (* (* v 3) v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* (sqrt (+ 1 (* v (* -3 v)))) (sqrt 2)) (* (sqrt (+ 1 (* (* v 3) v))) (* v v))))) (sqrt (- (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (/ (sqrt 2) 4) (* v v)) (sqrt (+ 1 (* (* v 3) v)))))))) (* (sqrt (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 4) 9))) (sqrt (+ 1 (* (* v 3) v))))) (sqrt (* 4 (sqrt (+ 1 (* (* v 3) v)))))))) * * * * [misc]progress: [ 496 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (363 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (232 enodes) * * [misc]simplify: iters left: 1 (291 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* v (* v 3))) (* 9 (pow v 4)))) (sqrt (+ 1 (* v (* v 3)))))) (sqrt (* 16 (sqrt (+ (+ 1 (* v (* v 3))) (* 9 (pow v 4))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ (+ 1 (* v (* v 3))) (* 9 (pow v 4)))) (sqrt (+ 1 (* v (* v 3)))))) (sqrt (* 16 (sqrt (+ (+ 1 (* v (* v 3))) (* 9 (pow v 4))))))))) * * * * [misc]progress: [ 497 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (384 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (+ (* (* -3 v) v) 1))) (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (+ (* (* -3 v) v) 1))) (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* v v))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (232 enodes) * * [misc]simplify: iters left: 1 (291 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* v (* v 3))) (* 9 (pow v 4)))) (sqrt (+ 1 (* v (* v 3)))))) (sqrt (* (sqrt (+ 1 (* v (* v 3)))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (+ (* (* -3 v) v) 1))) (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* v v))))) (* (sqrt (* (sqrt (+ (+ 1 (* v (* v 3))) (* 9 (pow v 4)))) (sqrt (+ 1 (* v (* v 3)))))) (sqrt (* (sqrt (+ 1 (* v (* v 3)))) 16))))) * * * * [misc]progress: [ 498 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (109 enodes) * * [misc]simplify: iters left: 4 (322 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (+ 1 (* v (* v -3))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (+ 1 (* v (* v -3))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (240 enodes) * * [misc]simplify: iters left: 1 (318 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 4) 9))) (sqrt (+ 1 (* (* v 3) v))))) (sqrt (* 4 (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 4) 9)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (+ 1 (* v (* v -3))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 4) 9))) (sqrt (+ 1 (* (* v 3) v))))) (sqrt (* 4 (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 4) 9)))))))) * * * * [misc]progress: [ 499 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (366 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (sqrt 2) (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* v (* v -3)))))) (* (* (* v (- v)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (sqrt 2) (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* v (* v -3)))))) (* (* (* v (- v)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (240 enodes) * * [misc]simplify: iters left: 1 (318 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 4) 9))) (sqrt (+ 1 (* (* v 3) v))))) (sqrt (* 4 (sqrt (+ 1 (* (* v 3) v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (sqrt 2) (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* v (* v -3)))))) (* (* (* v (- v)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 4) 9))) (sqrt (+ 1 (* (* v 3) v))))) (sqrt (* 4 (sqrt (+ 1 (* (* v 3) v)))))))) * * * * [misc]progress: [ 500 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (353 enodes) * [exit]simplify: Simplified to (* (sqrt (* (+ (- (* v v)) 1) (* (* 4 (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))))) (sqrt (+ (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (+ (- (* v v)) 1) (* (* 4 (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))))) (sqrt (+ (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 4))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (134 enodes) * * [misc]simplify: iters left: 2 (230 enodes) * * [misc]simplify: iters left: 1 (292 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 4) 9))) (sqrt (+ 1 (* (* v 3) v))))) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (+ (- (* v v)) 1) (* (* 4 (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))))) (sqrt (+ (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (* (sqrt (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 4) 9))) (sqrt (+ 1 (* (* v 3) v))))) 4))) * * * * [misc]progress: [ 501 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3)))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (122 enodes) * * [misc]simplify: iters left: 4 (424 enodes) * [exit]simplify: Simplified to (* (sqrt (* (+ (* (- (* v v)) (* (* v v) (* v v))) 1) (pow (* (/ (sqrt 2) 4) (sqrt (+ (* v (* -3 v)) 1))) 3))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ 1 (* (* v v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (+ (* (- (* v v)) (* (* v v) (* v v))) 1) (pow (* (/ (sqrt 2) 4) (sqrt (+ (* v (* -3 v)) 1))) 3))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ 1 (* (* v v) 3)))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (89 enodes) * * [misc]simplify: iters left: 4 (280 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (+ 1 (* v (* -3 v))))) (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (+ 1 (* v (* -3 v)))))) (* (* (sqrt (+ 1 (* v (* -3 v)))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* v (* -3 v)))) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))))) (sqrt (* (sqrt (+ (+ 1 (* v (* v 3))) (* (* v (* v 3)) (* v (* v 3))))) (sqrt (+ 1 (* v (* v 3))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (+ (* (- (* v v)) (* (* v v) (* v v))) 1) (pow (* (/ (sqrt 2) 4) (sqrt (+ (* v (* -3 v)) 1))) 3))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ 1 (* (* v v) 3)))))))) (* (sqrt (- (* (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (+ 1 (* v (* -3 v))))) (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (+ 1 (* v (* -3 v)))))) (* (* (sqrt (+ 1 (* v (* -3 v)))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* v (* -3 v)))) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))))) (sqrt (* (sqrt (+ (+ 1 (* v (* v 3))) (* (* v (* v 3)) (* v (* v 3))))) (sqrt (+ 1 (* v (* v 3))))))))) * * * * [misc]progress: [ 502 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (124 enodes) * * [misc]simplify: iters left: 4 (422 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* (* v -3) v) 1)) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* (- v) v)))) (* (sqrt (+ (* (* v -3) v) 1)) (+ (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* (- v) v)))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* (* v -3) v) 1)) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* (- v) v)))) (* (sqrt (+ (* (* v -3) v) 1)) (+ (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* (- v) v)))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (28 enodes) * * [misc]simplify: iters left: 5 (70 enodes) * * [misc]simplify: iters left: 4 (182 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (+ (* v v) 1) (/ (sqrt 2) 4)) (sqrt (+ (* v (* -3 v)) 1)))) (sqrt (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (sqrt (+ 1 (* (* v 3) v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* (* v -3) v) 1)) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* (- v) v)))) (* (sqrt (+ (* (* v -3) v) 1)) (+ (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* (- v) v)))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (* (+ (* v v) 1) (/ (sqrt 2) 4)) (sqrt (+ (* v (* -3 v)) 1)))) (sqrt (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (sqrt (+ 1 (* (* v 3) v)))))))) * * * * [misc]progress: [ 503 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (112 enodes) * * [misc]simplify: iters left: 4 (357 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (sqrt 2) (* (* (- v) v) (sqrt 2)))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4))) (sqrt (+ (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (- (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (sqrt 2) (* (* (- v) v) (sqrt 2)))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4))) (sqrt (+ (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (- (* v v))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (96 enodes) * * [misc]simplify: iters left: 3 (170 enodes) * * [misc]simplify: iters left: 2 (325 enodes) * [exit]simplify: Simplified to (* (sqrt (* (+ (+ 4 (* 12 (* v v))) (* (* 12 (* v v)) (* (* v v) 3))) 4)) (sqrt (+ (* (* v v) 3) 1))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (sqrt 2) (* (* (- v) v) (sqrt 2)))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4))) (sqrt (+ (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (- (* v v))))))) (* (sqrt (* (+ (+ 4 (* 12 (* v v))) (* (* 12 (* v v)) (* (* v v) 3))) 4)) (sqrt (+ (* (* v v) 3) 1))))) * * * * [misc]progress: [ 504 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (362 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* v (* v 3)) 1)) 4) (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (sqrt 2))) (* (* (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))) (* (* v v) (sqrt 2))) (* (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3))))) 4)))) (sqrt (- (* (* (sqrt (+ (* v (* v 3)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (* (* (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))) (/ (sqrt 2) 4)) (* (sqrt (+ (* v (* v 3)) 1)) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* v (* v 3)) 1)) 4) (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (sqrt 2))) (* (* (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))) (* (* v v) (sqrt 2))) (* (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3))))) 4)))) (sqrt (- (* (* (sqrt (+ (* v (* v 3)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (* (* (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))) (/ (sqrt 2) 4)) (* (sqrt (+ (* v (* v 3)) 1)) (* v v)))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (178 enodes) * * [misc]simplify: iters left: 2 (289 enodes) * * [misc]simplify: iters left: 1 (402 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* v (* v 3)) 1)) (sqrt (* (sqrt (+ (+ 1 (* 9 (pow v 4))) (* v (* v 3)))) (* (sqrt (+ (* v (* v 3)) 1)) 16)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* v (* v 3)) 1)) 4) (* (sqrt (- 1 (pow (* v (* v 3)) 3))) (sqrt 2))) (* (* (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))) (* (* v v) (sqrt 2))) (* (sqrt (+ (+ (* v (* v 3)) 1) (* (* v (* v 3)) (* v (* v 3))))) 4)))) (sqrt (- (* (* (sqrt (+ (* v (* v 3)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (* (* (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3))))) (/ (sqrt 2) 4)) (* (sqrt (+ (* v (* v 3)) 1)) (* v v)))))) (* (sqrt (+ (* v (* v 3)) 1)) (sqrt (* (sqrt (+ (+ 1 (* 9 (pow v 4))) (* v (* v 3)))) (* (sqrt (+ (* v (* v 3)) 1)) 16)))))) * * * * [misc]progress: [ 505 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (384 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (+ (* (* v 3) v) 1)) (* v v))))) (sqrt (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (+ (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (sqrt 2)) (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v 3) v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (+ (* (* v 3) v) 1)) (* v v))))) (sqrt (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (+ (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (sqrt 2)) (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v 3) v) 3)))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (172 enodes) * * [misc]simplify: iters left: 2 (372 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* 9 (* v v)) (* 4 (* v v))) (+ (* (* v v) 12) 4))) (sqrt (+ (* v (* v 3)) 1))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* v 3) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (+ (* (* v 3) v) 1)) (* v v))))) (sqrt (* (sqrt (+ (+ (* (* v 3) v) 1) (* (* (* v 3) v) (* (* v 3) v)))) (+ (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (sqrt 2)) (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v 3) v) 3)))))))) (* (sqrt (+ (* (* 9 (* v v)) (* 4 (* v v))) (+ (* (* v v) 12) 4))) (sqrt (+ (* v (* v 3)) 1))))) * * * * [misc]progress: [ 506 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (104 enodes) * * [misc]simplify: iters left: 4 (312 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* 4 (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ 1 (* (* v v) 3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* 4 (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ 1 (* (* v v) 3))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (247 enodes) * * [misc]simplify: iters left: 1 (338 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* v v) 3) 1)) (sqrt (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (sqrt (+ (* 9 (pow v 4)) (+ (* (* v v) 3) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* 4 (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ 1 (* (* v v) 3))))))) (* (sqrt (+ (* (* v v) 3) 1)) (sqrt (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (sqrt (+ (* 9 (pow v 4)) (+ (* (* v v) 3) 1)))))))) * * * * [misc]progress: [ 507 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (117 enodes) * * [misc]simplify: iters left: 4 (373 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))) (sqrt (+ (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (sqrt 2))) (* (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (+ 1 (* -3 (* v v))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))) (sqrt (+ (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (sqrt 2))) (* (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (+ 1 (* -3 (* v v))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (245 enodes) * * [misc]simplify: iters left: 1 (322 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ (* (pow v 4) 9) (+ (* v (* v 3)) 1))))) (sqrt (+ (* v (* v 3)) 1))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))) (sqrt (+ (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (sqrt 2))) (* (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (+ 1 (* -3 (* v v))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))))) (* (sqrt (* 16 (sqrt (+ (* (pow v 4) 9) (+ (* v (* v 3)) 1))))) (sqrt (+ (* v (* v 3)) 1))))) * * * * [misc]progress: [ 508 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (378 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (sqrt 2) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (* (sqrt (+ 1 (* 3 (* v v)))) 4))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* 3 (* v v))))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (- (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (sqrt 2) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (* (sqrt (+ 1 (* 3 (* v v)))) 4))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* 3 (* v v))))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (- (* v v))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (109 enodes) * * [misc]simplify: iters left: 3 (181 enodes) * * [misc]simplify: iters left: 2 (292 enodes) * * [misc]simplify: iters left: 1 (404 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* v (* v 3)) 1)) 16) (sqrt (+ (+ (* v (* v 3)) 1) (* (pow v 4) 9))))) (sqrt (+ (* v (* v 3)) 1))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (sqrt 2) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (* (sqrt (+ 1 (* 3 (* v v)))) 4))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* 3 (* v v))))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (- (* v v))))))) (* (sqrt (* (* (sqrt (+ (* v (* v 3)) 1)) 16) (sqrt (+ (+ (* v (* v 3)) 1) (* (pow v 4) 9))))) (sqrt (+ (* v (* v 3)) 1))))) * * * * [misc]progress: [ 509 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (82 enodes) * * [misc]simplify: iters left: 4 (256 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* 3 (* v v))))) (sqrt (- 1 (* (* (* v v) 9) (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* 3 (* v v))))) (* (- (* v v)) (sqrt (- 1 (* (* (* v v) 9) (* v v)))))))) (sqrt (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (* (sqrt (- 1 (* (* (* v v) 9) (* v v)))) (+ (* (- (* v v)) (sqrt 2)) (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* 3 (* v v))))) (sqrt (- 1 (* (* (* v v) 9) (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* 3 (* v v))))) (* (- (* v v)) (sqrt (- 1 (* (* (* v v) 9) (* v v)))))))) (sqrt (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (* (sqrt (- 1 (* (* (* v v) 9) (* v v)))) (+ (* (- (* v v)) (sqrt 2)) (sqrt 2)))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (60 enodes) * * [misc]simplify: iters left: 1 (74 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* v v) 3) 16) 16)) (sqrt (+ 1 (* (* v v) 3)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* 3 (* v v))))) (sqrt (- 1 (* (* (* v v) 9) (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* 3 (* v v))))) (* (- (* v v)) (sqrt (- 1 (* (* (* v v) 9) (* v v)))))))) (sqrt (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (* (sqrt (- 1 (* (* (* v v) 9) (* v v)))) (+ (* (- (* v v)) (sqrt 2)) (sqrt 2)))))) (* (sqrt (+ (* (* (* v v) 3) 16) 16)) (sqrt (+ 1 (* (* v v) 3)))))) * * * * [misc]progress: [ 510 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (113 enodes) * * [misc]simplify: iters left: 4 (371 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (- (* v v))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))) (* (* (* 4 (sqrt (+ 1 (* (* v 3) v)))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (- (* v v))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))) (* (* (* 4 (sqrt (+ 1 (* (* v 3) v)))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* v v)))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (149 enodes) * * [misc]simplify: iters left: 2 (256 enodes) * * [misc]simplify: iters left: 1 (355 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (sqrt (+ (+ (* (* v v) 3) 1) (* 9 (pow v 4)))))) (sqrt (+ (* (* v v) 3) 1))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (- (* v v))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))) (* (* (* 4 (sqrt (+ 1 (* (* v 3) v)))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (sqrt (+ (+ (* (* v v) 3) 1) (* 9 (pow v 4)))))) (sqrt (+ (* (* v v) 3) 1))))) * * * * [misc]progress: [ 511 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (31 enodes) * * [misc]simplify: iters left: 5 (74 enodes) * * [misc]simplify: iters left: 4 (220 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) (sqrt 2)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (sqrt (+ 1 (* (* v 3) v))) 4) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) (* v v)) 9))))))) (sqrt (+ (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (sqrt (+ 1 (* (* v 3) v))) (* (/ (sqrt 2) 4) (* v (- v)))) (sqrt (- 1 (* (* (* v v) (* v v)) 9))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) (sqrt 2)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (sqrt (+ 1 (* (* v 3) v))) 4) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) (* v v)) 9))))))) (sqrt (+ (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (sqrt (+ 1 (* (* v 3) v))) (* (/ (sqrt 2) 4) (* v (- v)))) (sqrt (- 1 (* (* (* v v) (* v v)) 9))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 4 (* 12 (* v v)))) (sqrt (+ 1 (* (* v v) 3)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) (sqrt 2)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (sqrt (+ 1 (* (* v 3) v))) 4) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) (* v v)) 9))))))) (sqrt (+ (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (sqrt (+ 1 (* (* v 3) v))) (* (/ (sqrt 2) 4) (* v (- v)))) (sqrt (- 1 (* (* (* v v) (* v v)) 9))))))) (* (sqrt (+ 4 (* 12 (* v v)))) (sqrt (+ 1 (* (* v v) 3)))))) * * * * [misc]progress: [ 512 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (88 enodes) * * [misc]simplify: iters left: 4 (281 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (* (* (sqrt (+ 1 (* v (* v 3)))) (* 4 (sqrt 2))) (* (sqrt (+ (* -3 (* v v)) 1)) (* v v))))) (sqrt (- (* (* (sqrt (+ 1 (* v (* v 3)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (* (* (* v (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (* v (sqrt (+ 1 (* v (* v 3))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (* (* (sqrt (+ 1 (* v (* v 3)))) (* 4 (sqrt 2))) (* (sqrt (+ (* -3 (* v v)) 1)) (* v v))))) (sqrt (- (* (* (sqrt (+ 1 (* v (* v 3)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (* (* (* v (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (* v (sqrt (+ 1 (* v (* v 3))))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (40 enodes) * * [misc]simplify: iters left: 1 (42 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ 1 (* (* v v) 3))))) (sqrt (+ 1 (* (* v v) 3)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (* (* (sqrt (+ 1 (* v (* v 3)))) (* 4 (sqrt 2))) (* (sqrt (+ (* -3 (* v v)) 1)) (* v v))))) (sqrt (- (* (* (sqrt (+ 1 (* v (* v 3)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (* (* (* v (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v (* v 3)) (* v (* v 3)))))) (* v (sqrt (+ 1 (* v (* v 3))))))))) (* (sqrt (* 16 (sqrt (+ 1 (* (* v v) 3))))) (sqrt (+ 1 (* (* v v) 3)))))) * * * * [misc]progress: [ 513 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (377 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (* 3 (* v v)) 1))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (/ (sqrt 2) 4) (sqrt (+ (* 3 (* v v)) 1))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* v v)))) (sqrt (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (* 3 (* v v)) 1))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (/ (sqrt 2) 4) (sqrt (+ (* 3 (* v v)) 1))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* v v)))) (sqrt (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (270 enodes) * * [misc]simplify: iters left: 1 (463 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* (* v v) 3))) (sqrt (+ (* (* v 36) (pow v 3)) (+ (* (* v 12) v) 4)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (* 3 (* v v)) 1))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (/ (sqrt 2) 4) (sqrt (+ (* 3 (* v v)) 1))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* v v)))) (sqrt (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2))))))) (* (sqrt (+ 1 (* (* v v) 3))) (sqrt (+ (* (* v 36) (pow v 3)) (+ (* (* v 12) v) 4)))))) * * * * [misc]progress: [ 514 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (113 enodes) * * [misc]simplify: iters left: 4 (353 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (* v v)) (/ (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ 4 (sqrt 2)))))) (sqrt (- (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (sqrt 2) 4))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt 2) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (* v v)) (/ (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ 4 (sqrt 2)))))) (sqrt (- (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (sqrt 2) 4))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt 2) (* v v)))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (251 enodes) * * [misc]simplify: iters left: 1 (348 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (+ (* (* v v) 3) (+ 1 (* (pow v 4) 9)))))) (sqrt (+ 1 (* (* v v) 3)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (* v v)) (/ (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ 4 (sqrt 2)))))) (sqrt (- (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (sqrt 2) 4))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt 2) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (+ (* (* v v) 3) (+ 1 (* (pow v 4) 9)))))) (sqrt (+ 1 (* (* v v) 3)))))) * * * * [misc]progress: [ 515 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (108 enodes) * * [misc]simplify: iters left: 4 (340 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* v v))))) (sqrt (+ (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (- (* v v))) (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* v v))))) (sqrt (+ (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (- (* v v))) (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (133 enodes) * * [misc]simplify: iters left: 2 (238 enodes) * * [misc]simplify: iters left: 1 (317 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* (* v 3) v))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 4) 9)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* v v))))) (sqrt (+ (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (- (* v v))) (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)))))) (* (sqrt (+ 1 (* (* v 3) v))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (pow v 4) 9)))))) * * * * [misc]progress: [ 516 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (38 enodes) * * [misc]simplify: iters left: 5 (102 enodes) * * [misc]simplify: iters left: 4 (310 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (/ (sqrt 2) 4) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (/ (sqrt 2) 4) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* v v))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (136 enodes) * * [misc]simplify: iters left: 2 (238 enodes) * * [misc]simplify: iters left: 1 (327 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* v v) 3) (+ 1 (* 9 (pow v 4))))) (sqrt (+ 1 (* (* v v) 3))))) (sqrt (+ 1 (* (* v v) 3)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (/ (sqrt 2) 4) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* v v))))) (* (sqrt (* (sqrt (+ (* (* v v) 3) (+ 1 (* 9 (pow v 4))))) (sqrt (+ 1 (* (* v v) 3))))) (sqrt (+ 1 (* (* v v) 3)))))) * * * * [misc]progress: [ 517 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (358 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (+ (* (* -3 v) v) 1)) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ 1 (* (* v v) 3))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (+ (* (* -3 v) v) 1)) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ 1 (* (* v v) 3))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (280 enodes) * * [misc]simplify: iters left: 1 (341 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ (+ 1 (* (* v v) 3)) (* (pow v 4) 9))))) (sqrt (+ 1 (* (* v v) 3)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (+ (* (* -3 v) v) 1)) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ 1 (* (* v v) 3))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))))) (* (sqrt (* 4 (sqrt (+ (+ 1 (* (* v v) 3)) (* (pow v 4) 9))))) (sqrt (+ 1 (* (* v v) 3)))))) * * * * [misc]progress: [ 518 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (107 enodes) * * [misc]simplify: iters left: 4 (352 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* 4 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt 2) (* v v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* 3 (* v v))))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* 3 (* v v))))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* 4 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt 2) (* v v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* 3 (* v v))))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* 3 (* v v))))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (170 enodes) * * [misc]simplify: iters left: 2 (292 enodes) * * [misc]simplify: iters left: 1 (375 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (pow v 4) 9) (+ (* (* v 3) v) 1))) (* 4 (sqrt (+ (* (* v 3) v) 1))))) (sqrt (+ (* (* v 3) v) 1))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* 4 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt 2) (* v v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* 3 (* v v))))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* 3 (* v v))))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (* (sqrt (* (sqrt (+ (* (pow v 4) 9) (+ (* (* v 3) v) 1))) (* 4 (sqrt (+ (* (* v 3) v) 1))))) (sqrt (+ (* (* v 3) v) 1))))) * * * * [misc]progress: [ 519 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (31 enodes) * * [misc]simplify: iters left: 5 (78 enodes) * * [misc]simplify: iters left: 4 (258 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* (* v 3) v))) (+ (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) (* (* v v) 9))))) (* (sqrt (- 1 (* (* v v) (* (* v v) 9)))) (- (* (* v v) (sqrt 2))))))) (sqrt (+ (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) (* (* v v) 9))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) (* (* v v) 9))))) (- (sqrt (+ 1 (* (* v 3) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ 1 (* (* v 3) v))) (+ (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) (* (* v v) 9))))) (* (sqrt (- 1 (* (* v v) (* (* v v) 9)))) (- (* (* v v) (sqrt 2))))))) (sqrt (+ (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) (* (* v v) 9))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) (* (* v v) 9))))) (- (sqrt (+ 1 (* (* v 3) v)))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * * [misc]simplify: iters left: 1 (66 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 4 (* (* v 12) v))) (sqrt (+ 1 (* (* v v) 3)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ 1 (* (* v 3) v))) (+ (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) (* (* v v) 9))))) (* (sqrt (- 1 (* (* v v) (* (* v v) 9)))) (- (* (* v v) (sqrt 2))))))) (sqrt (+ (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) (* (* v v) 9))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) (* (* v v) 9))))) (- (sqrt (+ 1 (* (* v 3) v)))))))) (* (sqrt (+ 4 (* (* v 12) v))) (sqrt (+ 1 (* (* v v) 3)))))) * * * * [misc]progress: [ 520 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (38 enodes) * * [misc]simplify: iters left: 5 (105 enodes) * * [misc]simplify: iters left: 4 (344 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4))) (* (* v v) (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (sqrt (+ (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4))) (* (* v v) (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (sqrt (+ (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (136 enodes) * * [misc]simplify: iters left: 2 (238 enodes) * * [misc]simplify: iters left: 1 (327 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* v v) 3) (+ 1 (* 9 (pow v 4))))) (sqrt (+ 1 (* (* v v) 3))))) (sqrt (+ 1 (* (* v v) 3)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4))) (* (* v v) (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (sqrt (+ (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (* (sqrt (* (sqrt (+ (* (* v v) 3) (+ 1 (* 9 (pow v 4))))) (sqrt (+ 1 (* (* v v) 3))))) (sqrt (+ 1 (* (* v v) 3)))))) * * * * [misc]progress: [ 521 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (56 enodes) * * [misc]simplify: iters left: 4 (160 enodes) * [exit]simplify: Simplified to (- (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* v (* v 3))))) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (sqrt (+ 1 (* v (* v 3)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* v (* v 3))))) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (sqrt (+ 1 (* v (* v 3)))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * [exit]simplify: Simplified to (+ 1 (* (* v v) 3)) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* v (* v 3))))) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (sqrt (+ 1 (* v (* v 3)))))) (+ 1 (* (* v v) 3)))) * * * * [misc]progress: [ 522 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (80 enodes) * * [misc]simplify: iters left: 4 (258 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* v v) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (- (* (* (/ (sqrt 2) 4) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (+ (* (* v v) -3) 1))) (* (* v v) (sqrt (+ 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* v v) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (- (* (* (/ (sqrt 2) 4) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (+ (* (* v v) -3) 1))) (* (* v v) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ 1 (* (* v v) 3))))) (sqrt (+ 1 (* (* v v) 3)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* v v) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (- (* (* (/ (sqrt 2) 4) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (+ (* (* v v) -3) 1))) (* (* v v) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* 4 (sqrt (+ 1 (* (* v v) 3))))) (sqrt (+ 1 (* (* v v) 3)))))) * * * * [misc]progress: [ 523 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (117 enodes) * * [misc]simplify: iters left: 4 (368 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (243 enodes) * * [misc]simplify: iters left: 1 (325 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* 3 (* v v)) 1)) (sqrt (* (sqrt (+ (* (pow v 4) 9) (+ (* 3 (* v v)) 1))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (+ (* 3 (* v v)) 1)) (sqrt (* (sqrt (+ (* (pow v 4) 9) (+ (* 3 (* v v)) 1))) 16))))) * * * * [misc]progress: [ 524 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (88 enodes) * * [misc]simplify: iters left: 4 (270 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* v (* v 3)))) (sqrt 2)) (* (sqrt (+ (* (* v v) -3) 1)) 4)) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* v (* v 3))))) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (/ (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (/ 4 (sqrt 2))) (* (sqrt (+ 1 (* v (* v 3)))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* v (* v 3)))) (sqrt 2)) (* (sqrt (+ (* (* v v) -3) 1)) 4)) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* v (* v 3))))) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (/ (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (/ 4 (sqrt 2))) (* (sqrt (+ 1 (* v (* v 3)))) (* v v)))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (39 enodes) * * [misc]simplify: iters left: 1 (40 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 16)) (sqrt (+ 1 (* (* v v) 3)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* v (* v 3)))) (sqrt 2)) (* (sqrt (+ (* (* v v) -3) 1)) 4)) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* v (* v 3))))) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (/ (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (/ 4 (sqrt 2))) (* (sqrt (+ 1 (* v (* v 3)))) (* v v)))))) (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 16)) (sqrt (+ 1 (* (* v v) 3)))))) * * * * [misc]progress: [ 525 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (368 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (- 1 (* (* v v) 3))) (sqrt 2))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* v v) 3)))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ 1 (* (* v v) 3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (- 1 (* (* v v) 3))) (sqrt 2))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* v v) 3)))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ 1 (* (* v v) 3))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (267 enodes) * * [misc]simplify: iters left: 1 (392 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* v 3) v) 1)) (sqrt (* 4 (sqrt (+ (* (pow v 4) 9) (+ (* (* v 3) v) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (- 1 (* (* v v) 3))) (sqrt 2))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* v v) 3)))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ 1 (* (* v v) 3))))))) (* (sqrt (+ (* (* v 3) v) 1)) (sqrt (* 4 (sqrt (+ (* (pow v 4) 9) (+ (* (* v 3) v) 1)))))))) * * * * [misc]progress: [ 526 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (77 enodes) * * [misc]simplify: iters left: 4 (219 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (* (- (* v v)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))))) (sqrt (+ (* (sqrt (+ 1 (* (* v 3) v))) (* (sqrt 2) (sqrt (+ 1 (* v (* v -3)))))) (* (* (- (* v v)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (* (- (* v v)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))))) (sqrt (+ (* (sqrt (+ 1 (* (* v 3) v))) (* (sqrt 2) (sqrt (+ 1 (* v (* v -3)))))) (* (* (- (* v v)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ 1 (* (* v v) 3))))) (sqrt (+ 1 (* (* v v) 3)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (* (- (* v v)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))))) (sqrt (+ (* (sqrt (+ 1 (* (* v 3) v))) (* (sqrt 2) (sqrt (+ 1 (* v (* v -3)))))) (* (* (- (* v v)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))))) (* (sqrt (* 4 (sqrt (+ 1 (* (* v v) 3))))) (sqrt (+ 1 (* (* v v) 3)))))) * * * * [misc]progress: [ 527 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (33 enodes) * * [misc]simplify: iters left: 5 (83 enodes) * * [misc]simplify: iters left: 4 (250 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (- 1 (* (* v 3) v))) (sqrt 2)) (+ (* (* 4 v) (- v)) 4))) (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (sqrt (+ 1 (* (* v 3) v))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* (* v 3) v))) (sqrt 2)) (+ (* (* 4 v) (- v)) 4))) (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (sqrt (+ 1 (* (* v 3) v))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 4))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * [exit]simplify: Simplified to (* 4 (sqrt (+ 1 (* (* v v) 3)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* (* v 3) v))) (sqrt 2)) (+ (* (* 4 v) (- v)) 4))) (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (sqrt (+ 1 (* (* v 3) v))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))))))) (* 4 (sqrt (+ 1 (* (* v v) 3)))))) * * * * [misc]progress: [ 528 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3)))) * * [misc]simplify: iters left: 6 (33 enodes) * * [misc]simplify: iters left: 5 (91 enodes) * * [misc]simplify: iters left: 4 (324 enodes) * [exit]simplify: Simplified to (* (sqrt (* (pow (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* v v) -3)))) 3) (+ (* (* (* v v) (* v v)) (* (- v) v)) 1))) (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* (* v v) -9) (* v v))))) (* (* (sqrt (+ 1 (* (* (* v v) -9) (* v v)))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* (* v 3) v))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (pow (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* v v) -3)))) 3) (+ (* (* (* v v) (* v v)) (* (- v) v)) 1))) (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* (* v v) -9) (* v v))))) (* (* (sqrt (+ 1 (* (* (* v v) -9) (* v v)))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* (* v 3) v))) (* v v)))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (70 enodes) * * [misc]simplify: iters left: 4 (228 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* (* v v) 3))) (sqrt (+ (* (* (sqrt (- 1 (* (* v v) 3))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* v v) 3))) (/ (sqrt 2) 4))) (* (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (- 1 (* (* v v) 3)))) (* (sqrt (- 1 (* (* v v) 3))) (- (* (/ (sqrt 2) 4) (- (* v v))) (/ (sqrt 2) 4))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (pow (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* v v) -3)))) 3) (+ (* (* (* v v) (* v v)) (* (- v) v)) 1))) (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* (* v v) -9) (* v v))))) (* (* (sqrt (+ 1 (* (* (* v v) -9) (* v v)))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* (* v 3) v))) (* v v)))))) (* (sqrt (+ 1 (* (* v v) 3))) (sqrt (+ (* (* (sqrt (- 1 (* (* v v) 3))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* v v) 3))) (/ (sqrt 2) 4))) (* (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (- 1 (* (* v v) 3)))) (* (sqrt (- 1 (* (* v v) 3))) (- (* (/ (sqrt 2) 4) (- (* v v))) (/ (sqrt 2) 4))))))))) * * * * [misc]progress: [ 529 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (33 enodes) * * [misc]simplify: iters left: 5 (92 enodes) * * [misc]simplify: iters left: 4 (320 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* -3 v))))) (* (sqrt (+ 1 (* v (* -3 v)))) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* (* v v) -9) (* v v))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* (* (* v v) -9) (* v v)))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* -3 v))))) (* (sqrt (+ 1 (* v (* -3 v)))) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* (* v v) -9) (* v v))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* (* (* v v) -9) (* v v)))) (* v v)))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (130 enodes) * * [misc]simplify: iters left: 3 (425 enodes) * [exit]simplify: Simplified to (* (sqrt (* (/ (* (sqrt 2) (+ (* v v) 1)) 4) (sqrt (- 1 (* (* v v) 3))))) (sqrt (+ 1 (* (* v v) 3)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* -3 v))))) (* (sqrt (+ 1 (* v (* -3 v)))) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* (* v v) -9) (* v v))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* (* (* v v) -9) (* v v)))) (* v v)))))) (* (sqrt (* (/ (* (sqrt 2) (+ (* v v) 1)) 4) (sqrt (- 1 (* (* v v) 3))))) (sqrt (+ 1 (* (* v v) 3)))))) * * * * [misc]progress: [ 530 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (119 enodes) * * [misc]simplify: iters left: 4 (375 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (sqrt 2) (* (* (- v) v) (sqrt 2)))) (* 4 (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v)))))))) (sqrt (- (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (* v v)) (* (sqrt (+ 1 (* -3 (* v v)))) (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (sqrt 2) (* (* (- v) v) (sqrt 2)))) (* 4 (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v)))))))) (sqrt (- (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (* v v)) (* (sqrt (+ 1 (* -3 (* v v)))) (sqrt 2)))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (176 enodes) * * [misc]simplify: iters left: 2 (322 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ (* 3 (* v v)) 1)))) (sqrt (* 4 (+ (+ (* 12 (* v v)) 4) (* (* 3 (* v v)) (* 12 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (sqrt 2) (* (* (- v) v) (sqrt 2)))) (* 4 (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v)))))))) (sqrt (- (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (* v v)) (* (sqrt (+ 1 (* -3 (* v v)))) (sqrt 2)))))) (* (sqrt (* 4 (sqrt (+ (* 3 (* v v)) 1)))) (sqrt (* 4 (+ (+ (* 12 (* v v)) 4) (* (* 3 (* v v)) (* 12 (* v v))))))))) * * * * [misc]progress: [ 531 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (123 enodes) * * [misc]simplify: iters left: 4 (396 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (sqrt 2)))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))))) (sqrt (- (* (* (/ (sqrt 2) 4) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (sqrt (+ 1 (* (* v -3) v)))) (* (sqrt 2) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (sqrt 2)))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))))) (sqrt (- (* (* (/ (sqrt 2) 4) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (sqrt (+ 1 (* (* v -3) v)))) (* (sqrt 2) (* v v)))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (190 enodes) * * [misc]simplify: iters left: 2 (308 enodes) * * [misc]simplify: iters left: 1 (348 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 16 (sqrt (+ (* v (* v 3)) 1))) (sqrt (+ (+ (* v (* v 3)) 1) (* (pow v 4) 9))))) (sqrt (* 4 (sqrt (+ (* v (* v 3)) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (sqrt 2)))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))))) (sqrt (- (* (* (/ (sqrt 2) 4) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (sqrt (+ 1 (* (* v -3) v)))) (* (sqrt 2) (* v v)))))) (* (sqrt (* (* 16 (sqrt (+ (* v (* v 3)) 1))) (sqrt (+ (+ (* v (* v 3)) 1) (* (pow v 4) 9))))) (sqrt (* 4 (sqrt (+ (* v (* v 3)) 1))))))) * * * * [misc]progress: [ 532 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (405 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* v (* v -3))))) (* (* v v) (sqrt 2))))) (sqrt (- (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt 2))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (/ (sqrt 2) 4))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* v (* v -3))))) (* (* v v) (sqrt 2))))) (sqrt (- (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt 2))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (/ (sqrt 2) 4))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (166 enodes) * * [misc]simplify: iters left: 2 (338 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ (* (* v 3) v) 1)))) (sqrt (+ (+ (* (* 12 v) v) 4) (* (* (* v 3) v) (* (* 12 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* v (* v -3))))) (* (* v v) (sqrt 2))))) (sqrt (- (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt 2))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (/ (sqrt 2) 4))))))) (* (sqrt (* 4 (sqrt (+ (* (* v 3) v) 1)))) (sqrt (+ (+ (* (* 12 v) v) 4) (* (* (* v 3) v) (* (* 12 v) v))))))) * * * * [misc]progress: [ 533 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (379 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* 4 (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* v (* -3 v)))) (* (* v v) (sqrt 2))) (sqrt (+ 1 (* 3 (* v v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* 4 (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* v (* -3 v)))) (* (* v v) (sqrt 2))) (sqrt (+ 1 (* 3 (* v v)))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (169 enodes) * * [misc]simplify: iters left: 2 (292 enodes) * * [misc]simplify: iters left: 1 (358 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ (* (* v 3) v) 1)))) (sqrt (* (sqrt (+ (+ (* (* v 3) v) 1) (* 9 (pow v 4)))) (* 4 (sqrt (+ (* (* v 3) v) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* 4 (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* v (* -3 v)))) (* (* v v) (sqrt 2))) (sqrt (+ 1 (* 3 (* v v)))))))) (* (sqrt (* 4 (sqrt (+ (* (* v 3) v) 1)))) (sqrt (* (sqrt (+ (+ (* (* v 3) v) 1) (* 9 (pow v 4)))) (* 4 (sqrt (+ (* (* v 3) v) 1)))))))) * * * * [misc]progress: [ 534 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (111 enodes) * * [misc]simplify: iters left: 4 (340 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (sqrt 2) 4)) (* (* (* 4 (* v (* (- v) (sqrt 2)))) (sqrt (+ (* (* v -3) v) 1))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))))) (sqrt (- (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (+ (* (* v -3) v) 1)) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (sqrt 2) 4)) (* (* (* 4 (* v (* (- v) (sqrt 2)))) (sqrt (+ (* (* v -3) v) 1))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))))) (sqrt (- (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (+ (* (* v -3) v) 1)) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v v) 3)))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (138 enodes) * * [misc]simplify: iters left: 2 (225 enodes) * * [misc]simplify: iters left: 1 (264 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ (* (* v 3) v) 1)))) (sqrt (* 16 (sqrt (+ (+ (* (* v 3) v) 1) (* (pow v 4) 9)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (sqrt 2) 4)) (* (* (* 4 (* v (* (- v) (sqrt 2)))) (sqrt (+ (* (* v -3) v) 1))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))))) (sqrt (- (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (+ (* (* v -3) v) 1)) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v v) 3)))))))) (* (sqrt (* 4 (sqrt (+ (* (* v 3) v) 1)))) (sqrt (* 16 (sqrt (+ (+ (* (* v 3) v) 1) (* (pow v 4) 9)))))))) * * * * [misc]progress: [ 535 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (122 enodes) * * [misc]simplify: iters left: 4 (378 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))) (* (* (sqrt (+ 1 (* (* v 3) v))) 4) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* (sqrt 2) (sqrt (+ 1 (* (* v 3) v)))) (* (sqrt (+ 1 (* (* v v) -3))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))) (* (* (sqrt (+ 1 (* (* v 3) v))) 4) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* (sqrt 2) (sqrt (+ 1 (* (* v 3) v)))) (* (sqrt (+ 1 (* (* v v) -3))) (* v v)))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (108 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (256 enodes) * * [misc]simplify: iters left: 1 (290 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* 9 (pow v 4)) (* v (* v 3))) 1)) (* (sqrt (+ (* v (* v 3)) 1)) 16))) (sqrt (* 4 (sqrt (+ (* v (* v 3)) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))) (* (* (sqrt (+ 1 (* (* v 3) v))) 4) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* (sqrt 2) (sqrt (+ 1 (* (* v 3) v)))) (* (sqrt (+ 1 (* (* v v) -3))) (* v v)))))) (* (sqrt (* (sqrt (+ (+ (* 9 (pow v 4)) (* v (* v 3))) 1)) (* (sqrt (+ (* v (* v 3)) 1)) 16))) (sqrt (* 4 (sqrt (+ (* v (* v 3)) 1))))))) * * * * [misc]progress: [ 536 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (90 enodes) * * [misc]simplify: iters left: 4 (278 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (* (* (* v v) 9) (* v v)))) (* (/ (sqrt 2) 4) 4)) (* (* (sqrt (+ 1 (* (* v 3) v))) (sqrt 2)) (* (* v v) (sqrt (- 1 (* (* v 3) v))))))) (sqrt (* (* (sqrt (- 1 (* (* (* v v) 9) (* v v)))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ 1 (* (* v 3) v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (* (* (* v v) 9) (* v v)))) (* (/ (sqrt 2) 4) 4)) (* (* (sqrt (+ 1 (* (* v 3) v))) (sqrt 2)) (* (* v v) (sqrt (- 1 (* (* v 3) v))))))) (sqrt (* (* (sqrt (- 1 (* (* (* v v) 9) (* v v)))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ 1 (* (* v 3) v))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ 1 (* (* v v) 3))))) (sqrt (+ (* (* v v) 48) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (* (* (* v v) 9) (* v v)))) (* (/ (sqrt 2) 4) 4)) (* (* (sqrt (+ 1 (* (* v 3) v))) (sqrt 2)) (* (* v v) (sqrt (- 1 (* (* v 3) v))))))) (sqrt (* (* (sqrt (- 1 (* (* (* v v) 9) (* v v)))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ 1 (* (* v 3) v))))))) (* (sqrt (* 4 (sqrt (+ 1 (* (* v v) 3))))) (sqrt (+ (* (* v v) 48) 16))))) * * * * [misc]progress: [ 537 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (375 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (/ (* 4 (sqrt 2)) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt (- 1 (* (* v v) 3)))) (* (sqrt 2) (* v v))))) (sqrt (- (* (sqrt 2) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))))) (* (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (/ (sqrt 2) 4)) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (/ (* 4 (sqrt 2)) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt (- 1 (* (* v v) 3)))) (* (sqrt 2) (* v v))))) (sqrt (- (* (sqrt 2) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))))) (* (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (/ (sqrt 2) 4)) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* v v)))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (172 enodes) * * [misc]simplify: iters left: 2 (289 enodes) * * [misc]simplify: iters left: 1 (367 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ (* (* v v) 3) 1)))) (sqrt (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (sqrt (+ (+ (* (pow v 4) 9) (* (* v v) 3)) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (/ (* 4 (sqrt 2)) 4) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (sqrt (+ 1 (* (* v v) 3))) (sqrt (- 1 (* (* v v) 3)))) (* (sqrt 2) (* v v))))) (sqrt (- (* (sqrt 2) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))))) (* (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (/ (sqrt 2) 4)) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* v v)))))) (* (sqrt (* 4 (sqrt (+ (* (* v v) 3) 1)))) (sqrt (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (sqrt (+ (+ (* (pow v 4) 9) (* (* v v) 3)) 1))))))) * * * * [misc]progress: [ 538 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (89 enodes) * * [misc]simplify: iters left: 4 (290 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (/ (sqrt 2) 4) 4)) (* (* (sqrt (+ (* -3 (* v v)) 1)) (* (* v v) (sqrt 2))) (sqrt (+ 1 (* v (* v 3))))))) (sqrt (- (* (* (sqrt 2) (sqrt (+ 1 (* v (* v 3))))) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (* (* v v) (* 4 (sqrt (+ 1 (* v (* v 3)))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (/ (sqrt 2) 4) 4)) (* (* (sqrt (+ (* -3 (* v v)) 1)) (* (* v v) (sqrt 2))) (sqrt (+ 1 (* v (* v 3))))))) (sqrt (- (* (* (sqrt 2) (sqrt (+ 1 (* v (* v 3))))) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (* (* v v) (* 4 (sqrt (+ 1 (* v (* v 3)))))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (53 enodes) * * [misc]simplify: iters left: 1 (61 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ 1 (* (* v v) 3))))) (sqrt (+ 4 (* 12 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (/ (sqrt 2) 4) 4)) (* (* (sqrt (+ (* -3 (* v v)) 1)) (* (* v v) (sqrt 2))) (sqrt (+ 1 (* v (* v 3))))))) (sqrt (- (* (* (sqrt 2) (sqrt (+ 1 (* v (* v 3))))) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (* (* v v) (* 4 (sqrt (+ 1 (* v (* v 3)))))))))) (* (sqrt (* 4 (sqrt (+ 1 (* (* v v) 3))))) (sqrt (+ 4 (* 12 (* v v))))))) * * * * [misc]progress: [ 539 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (81 enodes) * * [misc]simplify: iters left: 4 (236 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (* (* v v) (sqrt (- 1 (* 3 (* v v)))))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (* (* v v) (sqrt (- 1 (* 3 (* v v)))))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ 1 (* (* v v) 3))))) (sqrt (* 16 (sqrt (+ 1 (* (* v v) 3)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (* (* v v) (sqrt (- 1 (* 3 (* v v)))))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))))))) (* (sqrt (* 4 (sqrt (+ 1 (* (* v v) 3))))) (sqrt (* 16 (sqrt (+ 1 (* (* v v) 3)))))))) * * * * [misc]progress: [ 540 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (390 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (/ (* 4 (sqrt 2)) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (* (sqrt (+ 1 (* v (* v -3)))) (* v v))))) (sqrt (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (- (* (/ (* 4 (sqrt 2)) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (/ (* 4 (sqrt 2)) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (* (sqrt (+ 1 (* v (* v -3)))) (* v v))))) (sqrt (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (- (* (/ (* 4 (sqrt 2)) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (138 enodes) * * [misc]simplify: iters left: 2 (260 enodes) * * [misc]simplify: iters left: 1 (455 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ (* (* v v) 3) 1)))) (sqrt (+ 4 (+ (* (* v 36) (pow v 3)) (* v (* v 12)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (/ (* 4 (sqrt 2)) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (* (sqrt (+ 1 (* v (* v -3)))) (* v v))))) (sqrt (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (- (* (/ (* 4 (sqrt 2)) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2))))))) (* (sqrt (* 4 (sqrt (+ (* (* v v) 3) 1)))) (sqrt (+ 4 (+ (* (* v 36) (pow v 3)) (* v (* v 12)))))))) * * * * [misc]progress: [ 541 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (380 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt (+ (* -3 (* v v)) 1)) (sqrt (+ (* 3 (* v v)) 1))) (* (sqrt 2) (* v v))))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (sqrt 2)) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt (+ (* -3 (* v v)) 1)) (sqrt (+ (* 3 (* v v)) 1))) (* (sqrt 2) (* v v))))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (sqrt 2)) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (154 enodes) * * [misc]simplify: iters left: 2 (253 enodes) * * [misc]simplify: iters left: 1 (304 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ (* v (* v 3)) 1)))) (sqrt (* (sqrt (+ (+ (* v (* v 3)) 1) (* 9 (pow v 4)))) (* 4 (sqrt (+ (* v (* v 3)) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt (+ (* -3 (* v v)) 1)) (sqrt (+ (* 3 (* v v)) 1))) (* (sqrt 2) (* v v))))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (sqrt 2)) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* v v)))))) (* (sqrt (* 4 (sqrt (+ (* v (* v 3)) 1)))) (sqrt (* (sqrt (+ (+ (* v (* v 3)) 1) (* 9 (pow v 4)))) (* 4 (sqrt (+ (* v (* v 3)) 1)))))))) * * * * [misc]progress: [ 542 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (363 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ 1 (* (* v 3) v)))))) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ 1 (* (* v 3) v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3))))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* (sqrt (+ 1 (* (* v 3) v))) (sqrt 2)) (* (sqrt (+ (* v (* v -3)) 1)) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ 1 (* (* v 3) v)))))) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ 1 (* (* v 3) v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3))))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* (sqrt (+ 1 (* (* v 3) v))) (sqrt 2)) (* (sqrt (+ (* v (* v -3)) 1)) (* v v)))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (132 enodes) * * [misc]simplify: iters left: 2 (223 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ (* (* v 3) v) 1) (* 9 (pow v 4)))) (sqrt (* 4 (sqrt (+ (* (* v 3) v) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ 1 (* (* v 3) v)))))) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ 1 (* (* v 3) v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v 3) v) 3))))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (* (* (sqrt (+ 1 (* (* v 3) v))) (sqrt 2)) (* (sqrt (+ (* v (* v -3)) 1)) (* v v)))))) (* (sqrt (+ (+ (* (* v 3) v) 1) (* 9 (pow v 4)))) (sqrt (* 4 (sqrt (+ (* (* v 3) v) 1))))))) * * * * [misc]progress: [ 543 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (374 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))))) (sqrt (- (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt (+ (* v (* v -3)) 1)) (sqrt 2)) (* (sqrt (+ 1 (* (* v v) 3))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))))) (sqrt (- (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt (+ (* v (* v -3)) 1)) (sqrt 2)) (* (sqrt (+ 1 (* (* v v) 3))) (* v v)))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (132 enodes) * * [misc]simplify: iters left: 2 (220 enodes) * * [misc]simplify: iters left: 1 (259 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) 1) (* 9 (pow v 4)))) (sqrt (+ (* (* v v) 3) 1)))) (sqrt (* 4 (sqrt (+ (* (* v v) 3) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* v v) 3))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))))) (sqrt (- (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt (+ (* v (* v -3)) 1)) (sqrt 2)) (* (sqrt (+ 1 (* (* v v) 3))) (* v v)))))) (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) 1) (* 9 (pow v 4)))) (sqrt (+ (* (* v v) 3) 1)))) (sqrt (* 4 (sqrt (+ (* (* v v) 3) 1))))))) * * * * [misc]progress: [ 544 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (109 enodes) * * [misc]simplify: iters left: 4 (329 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (* 4 (sqrt 2)) 4)) (* (sqrt (+ 1 (* v (* -3 v)))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* v (* -3 v)))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (* 4 (sqrt 2)) 4)) (* (sqrt (+ 1 (* v (* -3 v)))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* v (* -3 v)))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (132 enodes) * * [misc]simplify: iters left: 2 (220 enodes) * * [misc]simplify: iters left: 1 (259 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) 1) (* 9 (pow v 4)))) 4)) (sqrt (* 4 (sqrt (+ (* (* v v) 3) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (* 4 (sqrt 2)) 4)) (* (sqrt (+ 1 (* v (* -3 v)))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* v (* -3 v)))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) 1) (* 9 (pow v 4)))) 4)) (sqrt (* 4 (sqrt (+ (* (* v v) 3) 1))))))) * * * * [misc]progress: [ 545 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (113 enodes) * * [misc]simplify: iters left: 4 (349 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* 3 (* v v)) 1)))))) (sqrt (- (* (* (/ (sqrt 2) 4) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (* v v)) (* (sqrt (- 1 (* 3 (* v v)))) (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* 3 (* v v)) 1)))))) (sqrt (- (* (* (/ (sqrt 2) 4) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (* v v)) (* (sqrt (- 1 (* 3 (* v v)))) (sqrt 2)))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (228 enodes) * * [misc]simplify: iters left: 1 (264 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ (* 3 (* v v)) 1)))) (sqrt (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (pow v 4) 9))) (* 4 (sqrt (+ (* 3 (* v v)) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* 3 (* v v)) 1)))))) (sqrt (- (* (* (/ (sqrt 2) 4) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (* v v)) (* (sqrt (- 1 (* 3 (* v v)))) (sqrt 2)))))) (* (sqrt (* 4 (sqrt (+ (* 3 (* v v)) 1)))) (sqrt (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (pow v 4) 9))) (* 4 (sqrt (+ (* 3 (* v v)) 1)))))))) * * * * [misc]progress: [ 546 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (85 enodes) * * [misc]simplify: iters left: 4 (276 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (* (* (* v v) -9) (* v v)) 1)) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt (+ 1 (* v (* v 3)))) (sqrt (+ (* (* v v) -3) 1))) (* (* v v) (sqrt 2))))) (sqrt (* (sqrt (+ 1 (* v (* v 3)))) (* (sqrt (+ (* (* (* v v) -9) (* v v)) 1)) (+ (* 4 (/ (sqrt 2) 4)) (* v (* (- v) (sqrt 2)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* (* (* v v) -9) (* v v)) 1)) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt (+ 1 (* v (* v 3)))) (sqrt (+ (* (* v v) -3) 1))) (* (* v v) (sqrt 2))))) (sqrt (* (sqrt (+ 1 (* v (* v 3)))) (* (sqrt (+ (* (* (* v v) -9) (* v v)) 1)) (+ (* 4 (/ (sqrt 2) 4)) (* v (* (- v) (sqrt 2)))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ 1 (* (* v v) 3))))) (sqrt (* 4 (+ 1 (* (* v v) 3))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* (* (* v v) -9) (* v v)) 1)) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt (+ 1 (* v (* v 3)))) (sqrt (+ (* (* v v) -3) 1))) (* (* v v) (sqrt 2))))) (sqrt (* (sqrt (+ 1 (* v (* v 3)))) (* (sqrt (+ (* (* (* v v) -9) (* v v)) 1)) (+ (* 4 (/ (sqrt 2) 4)) (* v (* (- v) (sqrt 2)))))))) (* (sqrt (* 4 (sqrt (+ 1 (* (* v v) 3))))) (sqrt (* 4 (+ 1 (* (* v v) 3))))))) * * * * [misc]progress: [ 547 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (112 enodes) * * [misc]simplify: iters left: 4 (351 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* 4 (/ (sqrt 2) 4))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v -3) v)))) (sqrt (+ (* (* v 3) v) 1))))) (sqrt (+ (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))) (* (* (sqrt (+ (* (* v 3) v) 1)) (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v 3) v) 3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* 4 (/ (sqrt 2) 4))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v -3) v)))) (sqrt (+ (* (* v 3) v) 1))))) (sqrt (+ (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))) (* (* (sqrt (+ (* (* v 3) v) 1)) (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v 3) v) 3))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (132 enodes) * * [misc]simplify: iters left: 2 (220 enodes) * * [misc]simplify: iters left: 1 (259 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) 1) (* 9 (pow v 4)))) (sqrt (+ (* (* v v) 3) 1)))) (sqrt (* 4 (sqrt (+ (* (* v v) 3) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))) (* 4 (/ (sqrt 2) 4))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v -3) v)))) (sqrt (+ (* (* v 3) v) 1))))) (sqrt (+ (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v)))))) (* (* (sqrt (+ (* (* v 3) v) 1)) (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v 3) v) 3))))))) (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) 1) (* 9 (pow v 4)))) (sqrt (+ (* (* v v) 3) 1)))) (sqrt (* 4 (sqrt (+ (* (* v v) 3) 1))))))) * * * * [misc]progress: [ 548 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (80 enodes) * * [misc]simplify: iters left: 4 (258 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* v v) -3) 1))) (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* (sqrt (+ (* (* (* v v) -9) (* v v)) 1)) (/ (sqrt 2) 4)) (* (* v v) (sqrt (+ 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* v v) -3) 1))) (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* (sqrt (+ (* (* (* v v) -9) (* v v)) 1)) (/ (sqrt 2) 4)) (* (* v v) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* (* v v) 3))) (sqrt (* 4 (sqrt (+ 1 (* (* v v) 3)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* v v) -3) 1))) (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* (sqrt (+ (* (* (* v v) -9) (* v v)) 1)) (/ (sqrt 2) 4)) (* (* v v) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (+ 1 (* (* v v) 3))) (sqrt (* 4 (sqrt (+ 1 (* (* v v) 3)))))))) * * * * [misc]progress: [ 549 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (63 enodes) * * [misc]simplify: iters left: 4 (177 enodes) * * [misc]simplify: iters left: 3 (431 enodes) * [exit]simplify: Simplified to (- (* (sqrt (- 1 (* (pow v 3) (* 9 v)))) (/ (* 4 (sqrt 2)) 4)) (* (* (sqrt (+ 1 (* v (* v 3)))) (sqrt (+ 1 (* v (* v -3))))) (* (sqrt 2) (* v v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (* (sqrt (- 1 (* (pow v 3) (* 9 v)))) (/ (* 4 (sqrt 2)) 4)) (* (* (sqrt (+ 1 (* v (* v 3)))) (sqrt (+ 1 (* v (* v -3))))) (* (sqrt 2) (* v v)))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * [exit]simplify: Simplified to (* 4 (sqrt (+ 1 (* (* v v) 3)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (* (sqrt (- 1 (* (pow v 3) (* 9 v)))) (/ (* 4 (sqrt 2)) 4)) (* (* (sqrt (+ 1 (* v (* v 3)))) (sqrt (+ 1 (* v (* v -3))))) (* (sqrt 2) (* v v)))) (* 4 (sqrt (+ 1 (* (* v v) 3)))))) * * * * [misc]progress: [ 550 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (365 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (230 enodes) * * [misc]simplify: iters left: 1 (291 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ (* (* v v) 3) 1)))) (sqrt (* (sqrt (+ (+ (* (* v v) 3) 1) (* (pow v 4) 9))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))))) (* (sqrt (* 4 (sqrt (+ (* (* v v) 3) 1)))) (sqrt (* (sqrt (+ (+ (* (* v v) 3) 1) (* (pow v 4) 9))) 16))))) * * * * [misc]progress: [ 551 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (90 enodes) * * [misc]simplify: iters left: 4 (278 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* -3 v)) 1))) (sqrt (+ 1 (* v (* v 3))))))) (sqrt (- (* (sqrt (+ 1 (* v (* v 3)))) (* (* 4 (sqrt 2)) (sqrt (+ (* v (* -3 v)) 1)))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (* (* v v) (sqrt 2)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* -3 v)) 1))) (sqrt (+ 1 (* v (* v 3))))))) (sqrt (- (* (sqrt (+ 1 (* v (* v 3)))) (* (* 4 (sqrt 2)) (sqrt (+ (* v (* -3 v)) 1)))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ 1 (* (* v v) 3))))) (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* -3 v)) 1))) (sqrt (+ 1 (* v (* v 3))))))) (sqrt (- (* (sqrt (+ 1 (* v (* v 3)))) (* (* 4 (sqrt 2)) (sqrt (+ (* v (* -3 v)) 1)))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* 4 (sqrt (+ 1 (* (* v v) 3))))) (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 16))))) * * * * [misc]progress: [ 552 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (368 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (- 1 (* (* v v) 3))) (sqrt 2)) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v v) 3)))) (sqrt (+ 1 (* (* v v) 3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* v v) 3))) (sqrt 2)) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v v) 3)))) (sqrt (+ 1 (* (* v v) 3))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (132 enodes) * * [misc]simplify: iters left: 2 (220 enodes) * * [misc]simplify: iters left: 1 (259 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) 1) (* 9 (pow v 4)))) 4)) (sqrt (* 4 (sqrt (+ (* (* v v) 3) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* v v) 3))) (sqrt 2)) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* v v) 3)))) (sqrt (+ 1 (* (* v v) 3))))))) (* (sqrt (* (sqrt (+ (+ (* (* v v) 3) 1) (* 9 (pow v 4)))) 4)) (sqrt (* 4 (sqrt (+ (* (* v v) 3) 1))))))) * * * * [misc]progress: [ 553 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (33 enodes) * * [misc]simplify: iters left: 5 (83 enodes) * * [misc]simplify: iters left: 4 (253 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (/ (* 4 (sqrt 2)) 4) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (sqrt 2) (sqrt (- 1 (* (* v 3) v)))) (* (* v v) (sqrt (+ 1 (* (* v 3) v))))))) (sqrt (+ (* (sqrt (+ 1 (* (* v 3) v))) (* (sqrt 2) (sqrt (- 1 (* (* v 3) v))))) (* (* 4 (* (* v (- v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* v v) (* v v)) 9))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (/ (* 4 (sqrt 2)) 4) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (sqrt 2) (sqrt (- 1 (* (* v 3) v)))) (* (* v v) (sqrt (+ 1 (* (* v 3) v))))))) (sqrt (+ (* (sqrt (+ 1 (* (* v 3) v))) (* (sqrt 2) (sqrt (- 1 (* (* v 3) v))))) (* (* 4 (* (* v (- v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* v v) (* v v)) 9))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * [exit]simplify: Simplified to (* 4 (sqrt (+ 1 (* (* v v) 3)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (/ (* 4 (sqrt 2)) 4) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (sqrt 2) (sqrt (- 1 (* (* v 3) v)))) (* (* v v) (sqrt (+ 1 (* (* v 3) v))))))) (sqrt (+ (* (sqrt (+ 1 (* (* v 3) v))) (* (sqrt 2) (sqrt (- 1 (* (* v 3) v))))) (* (* 4 (* (* v (- v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* v v) (* v v)) 9))))))) (* 4 (sqrt (+ 1 (* (* v v) 3)))))) * * * * [misc]progress: [ 554 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (77 enodes) * * [misc]simplify: iters left: 4 (218 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (* (sqrt (+ 1 (* (* v 3) v))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v v) -3))))))) (sqrt (* (+ (- (* v v)) 1) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* v v) -3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (* (sqrt (+ 1 (* (* v 3) v))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v v) -3))))))) (sqrt (* (+ (- (* v v)) 1) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* v v) -3))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* 4 4))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (* 4 4))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * [exit]simplify: Simplified to (* 4 (sqrt (* 4 (sqrt (+ 1 (* (* v v) 3)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 9 (* v v)) (* v v))))) (* (sqrt (+ 1 (* (* v 3) v))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v v) -3))))))) (sqrt (* (+ (- (* v v)) 1) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* v v) -3))))))) (* 4 (sqrt (* 4 (sqrt (+ 1 (* (* v v) 3)))))))) * * * * [misc]progress: [ 555 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3)))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (92 enodes) * * [misc]simplify: iters left: 4 (325 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (* (* v v) (* (* v v) 9)))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (+ 1 (* (* v 3) v))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* v v) -3) 1)))))) (sqrt (* (pow (* (sqrt (+ (* (* v v) -3) 1)) (/ (sqrt 2) 4)) 3) (+ (* (- (* v v)) (* (* v v) (* v v))) 1)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (* (* v v) (* (* v v) 9)))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (+ 1 (* (* v 3) v))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* v v) -3) 1)))))) (sqrt (* (pow (* (sqrt (+ (* (* v v) -3) 1)) (/ (sqrt 2) 4)) 3) (+ (* (- (* v v)) (* (* v v) (* v v))) 1)))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (69 enodes) * * [misc]simplify: iters left: 4 (227 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))) (* (* (* (/ (sqrt 2) 4) (* v (- v))) (sqrt (- 1 (* 3 (* v v))))) (* (sqrt (- 1 (* 3 (* v v)))) (- (* (/ (sqrt 2) 4) (* v (- v))) (/ (sqrt 2) 4))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (* (* v v) (* (* v v) 9)))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (+ 1 (* (* v 3) v))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* v v) -3) 1)))))) (sqrt (* (pow (* (sqrt (+ (* (* v v) -3) 1)) (/ (sqrt 2) 4)) 3) (+ (* (- (* v v)) (* (* v v) (* v v))) 1)))) (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))) (* (* (* (/ (sqrt 2) 4) (* v (- v))) (sqrt (- 1 (* 3 (* v v))))) (* (sqrt (- 1 (* 3 (* v v)))) (- (* (/ (sqrt 2) 4) (* v (- v))) (/ (sqrt 2) 4))))))))) * * * * [misc]progress: [ 556 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (93 enodes) * * [misc]simplify: iters left: 4 (321 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (* v v)) (* (sqrt 2) (sqrt (+ (* -3 (* v v)) 1)))))) (sqrt (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* -3 (* v v)) 1))) (* (sqrt (+ (* -3 (* v v)) 1)) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (* v v)) (* (sqrt 2) (sqrt (+ (* -3 (* v v)) 1)))))) (sqrt (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* -3 (* v v)) 1))) (* (sqrt (+ (* -3 (* v v)) 1)) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4))))))) (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * [enter]simplify: Simplifying (* (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (129 enodes) * * [misc]simplify: iters left: 3 (429 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (- 1 (* (* v v) 3))) (+ (* (/ (sqrt 2) 4) (* v v)) (/ (sqrt 2) 4)))) (sqrt (* 4 (sqrt (+ 1 (* (* v v) 3)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (* v v)) (* (sqrt 2) (sqrt (+ (* -3 (* v v)) 1)))))) (sqrt (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* -3 (* v v)) 1))) (* (sqrt (+ (* -3 (* v v)) 1)) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4))))))) (* (sqrt (* (sqrt (- 1 (* (* v v) 3))) (+ (* (/ (sqrt 2) 4) (* v v)) (/ (sqrt 2) 4)))) (sqrt (* 4 (sqrt (+ 1 (* (* v v) 3)))))))) * * * * [misc]progress: [ 557 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (36 enodes) * * [misc]simplify: iters left: 5 (102 enodes) * * [misc]simplify: iters left: 4 (322 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) 4) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (+ (sqrt 2) (* (sqrt 2) (* v (- v))))))) (sqrt (+ (* (* (* 4 (sqrt 2)) (sqrt (+ 1 (* v (* v -3))))) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (* 4 (sqrt 2)) (* v (- v))) (sqrt (- 1 (pow (* v (* 3 v)) 3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) 4) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (+ (sqrt 2) (* (sqrt 2) (* v (- v))))))) (sqrt (+ (* (* (* 4 (sqrt 2)) (sqrt (+ 1 (* v (* v -3))))) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (* 4 (sqrt 2)) (* v (- v))) (sqrt (- 1 (pow (* v (* 3 v)) 3))))))) (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (159 enodes) * * [misc]simplify: iters left: 2 (308 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* 9 v) (pow v 3)) (* 3 (* v v))) 1)) 16)) (sqrt (+ (* (* 3 (* v v)) (* (* v v) 48)) (+ 16 (* (* v v) 48))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) 4) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (+ (sqrt 2) (* (sqrt 2) (* v (- v))))))) (sqrt (+ (* (* (* 4 (sqrt 2)) (sqrt (+ 1 (* v (* v -3))))) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v)))))) (* (* (* 4 (sqrt 2)) (* v (- v))) (sqrt (- 1 (pow (* v (* 3 v)) 3))))))) (* (sqrt (* (sqrt (+ (+ (* (* 9 v) (pow v 3)) (* 3 (* v v))) 1)) 16)) (sqrt (+ (* (* 3 (* v v)) (* (* v v) 48)) (+ 16 (* (* v v) 48))))))) * * * * [misc]progress: [ 558 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (383 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* (* (sqrt 2) 4) (sqrt (+ (* (* v -3) v) 1)))) (* (* (* (- v) v) (* (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (* (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* 4 (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* (* (sqrt 2) 4) (sqrt (+ (* (* v -3) v) 1)))) (* (* (* (- v) v) (* (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (* (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* 4 (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (104 enodes) * * [misc]simplify: iters left: 3 (198 enodes) * * [misc]simplify: iters left: 2 (320 enodes) * * [misc]simplify: iters left: 1 (370 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))))) (sqrt (* (* (sqrt (+ 1 (* (* 3 v) v))) 16) (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* (* (sqrt 2) 4) (sqrt (+ (* (* v -3) v) 1)))) (* (* (* (- v) v) (* (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (* (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* 4 (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (* 16 (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))))) (sqrt (* (* (sqrt (+ 1 (* (* 3 v) v))) 16) (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1)))))))) * * * * [misc]progress: [ 559 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (111 enodes) * * [misc]simplify: iters left: 4 (375 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* v -3) v))))) (* (* 4 (* (sqrt 2) (* v (- v)))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))) (sqrt (- (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt 2)) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (* (sqrt 2) (* v v)) 4)) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* v -3) v))))) (* (* 4 (* (sqrt 2) (* v (- v)))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))) (sqrt (- (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt 2)) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (* (sqrt 2) (* v v)) 4)) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4))))) (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (179 enodes) * * [misc]simplify: iters left: 2 (356 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* v v) 3) (+ (* (* v 9) (pow v 3)) 1))) 16)) (sqrt (+ (+ (* (* v 12) v) 4) (* (* (* v v) (* v 12)) (* 3 v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* v -3) v))))) (* (* 4 (* (sqrt 2) (* v (- v)))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))) (sqrt (- (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt 2)) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (* (sqrt 2) (* v v)) 4)) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4))))) (* (sqrt (* (sqrt (+ (* (* v v) 3) (+ (* (* v 9) (pow v 3)) 1))) 16)) (sqrt (+ (+ (* (* v 12) v) 4) (* (* (* v v) (* v 12)) (* 3 v))))))) * * * * [misc]progress: [ 560 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (386 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* (* 4 (sqrt 2)) (sqrt (+ (* -3 (* v v)) 1)))) (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* 4 (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* (* 4 (sqrt 2)) (sqrt (+ (* -3 (* v v)) 1)))) (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* 4 (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (96 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (252 enodes) * * [misc]simplify: iters left: 1 (319 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ (+ 1 (* v (* 3 v))) (* (pow v 4) 9))))) (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ (+ 1 (* v (* 3 v))) (* (pow v 4) 9)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* (* 4 (sqrt 2)) (sqrt (+ (* -3 (* v v)) 1)))) (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* 4 (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (* 16 (sqrt (+ (+ 1 (* v (* 3 v))) (* (pow v 4) 9))))) (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ (+ 1 (* v (* 3 v))) (* (pow v 4) 9)))))))) * * * * [misc]progress: [ 561 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (37 enodes) * * [misc]simplify: iters left: 5 (106 enodes) * * [misc]simplify: iters left: 4 (338 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* 4 (sqrt 2)) (sqrt (+ (* v (* -3 v)) 1))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* v (- v)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))))) (sqrt (+ (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* 4 (sqrt 2))) (* (* (* 4 (* (- v) (* v (sqrt 2)))) (sqrt (+ (* v (* -3 v)) 1))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (* 4 (sqrt 2)) (sqrt (+ (* v (* -3 v)) 1))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* v (- v)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))))) (sqrt (+ (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* 4 (sqrt 2))) (* (* (* 4 (* (- v) (* v (sqrt 2)))) (sqrt (+ (* v (* -3 v)) 1))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))))))) (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (148 enodes) * * [misc]simplify: iters left: 2 (239 enodes) * * [misc]simplify: iters left: 1 (309 enodes) * [exit]simplify: Simplified to (* 16 (sqrt (+ (* (* v v) 3) (+ (* 9 (pow v 4)) 1)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (* 4 (sqrt 2)) (sqrt (+ (* v (* -3 v)) 1))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* v (- v)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))))) (sqrt (+ (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* 4 (sqrt 2))) (* (* (* 4 (* (- v) (* v (sqrt 2)))) (sqrt (+ (* v (* -3 v)) 1))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))))))) (* 16 (sqrt (+ (* (* v v) 3) (+ (* 9 (pow v 4)) 1)))))) * * * * [misc]progress: [ 562 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (348 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) 4)) (* (* (* (sqrt (+ (* (* 3 v) v) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* v v)))) (sqrt (+ (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* v (* -3 v)))))) (* (* (* 4 (sqrt 2)) (* v (- v))) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) 4)) (* (* (* (sqrt (+ (* (* 3 v) v) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* v v)))) (sqrt (+ (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* v (* -3 v)))))) (* (* (* 4 (sqrt 2)) (* v (- v))) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (53 enodes) * * [misc]simplify: iters left: 4 (105 enodes) * * [misc]simplify: iters left: 3 (197 enodes) * * [misc]simplify: iters left: 2 (312 enodes) * * [misc]simplify: iters left: 1 (362 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))) (* (sqrt (+ 1 (* (* 3 v) v))) 16)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) 4)) (* (* (* (sqrt (+ (* (* 3 v) v) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* v v)))) (sqrt (+ (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* v (* -3 v)))))) (* (* (* 4 (sqrt 2)) (* v (- v))) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) (* (sqrt (* 16 (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))) (* (sqrt (+ 1 (* (* 3 v) v))) 16)))))) * * * * [misc]progress: [ 563 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (381 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* 9 (* v v)) (* v v)))) (* (* 4 (sqrt 2)) (sqrt (+ (* v (* v -3)) 1)))) (* (* (- (* v v)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* v v) 3) 3)))))) (sqrt (* (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ (* (* v v) 3) 1)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* 9 (* v v)) (* v v)))) (* (* 4 (sqrt 2)) (sqrt (+ (* v (* v -3)) 1)))) (* (* (- (* v v)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* v v) 3) 3)))))) (sqrt (* (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ (* (* v v) 3) 1)))))) (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (53 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (270 enodes) * * [misc]simplify: iters left: 1 (381 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ (+ 1 (* (* 3 v) v)) (* (pow v 4) 9))))) (sqrt (+ (* 48 (* v v)) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* 9 (* v v)) (* v v)))) (* (* 4 (sqrt 2)) (sqrt (+ (* v (* v -3)) 1)))) (* (* (- (* v v)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* v v) 3) 3)))))) (sqrt (* (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))) (* 4 (sqrt (+ (* (* v v) 3) 1)))))) (* (sqrt (* 16 (sqrt (+ (+ 1 (* (* 3 v) v)) (* (pow v 4) 9))))) (sqrt (+ (* 48 (* v v)) 16))))) * * * * [misc]progress: [ 564 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (122 enodes) * * [misc]simplify: iters left: 4 (380 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* (* 4 (sqrt 2)) (sqrt (+ (* v (* -3 v)) 1)))) (* (* (* 4 (sqrt 2)) (- (* v v))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (sqrt (+ (* 3 (* v v)) 1)))) (* (/ (sqrt 2) 4) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* (* 4 (sqrt 2)) (sqrt (+ (* v (* -3 v)) 1)))) (* (* (* 4 (sqrt 2)) (- (* v v))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (sqrt (+ (* 3 (* v v)) 1)))) (* (/ (sqrt 2) 4) (* v v)))))) (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (241 enodes) * * [misc]simplify: iters left: 1 (287 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* (* 4 (sqrt 2)) (sqrt (+ (* v (* -3 v)) 1)))) (* (* (* 4 (sqrt 2)) (- (* v v))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (sqrt (+ (* 3 (* v v)) 1)))) (* (/ (sqrt 2) 4) (* v v)))))) (* (sqrt (* 16 (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v))))))))) * * * * [misc]progress: [ 565 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (123 enodes) * * [misc]simplify: iters left: 4 (409 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (+ (* (* -3 v) v) 1))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (+ (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)) (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (+ (* (* -3 v) v) 1))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (+ (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)) (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))))))) (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (290 enodes) * * [misc]simplify: iters left: 1 (403 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))))) (sqrt (+ 4 (* (* v v) 12)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (+ (* (* -3 v) v) 1))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (+ (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2)) (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))))))) (* (sqrt (* 16 (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))))) (sqrt (+ 4 (* (* v v) 12)))))) * * * * [misc]progress: [ 566 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (119 enodes) * * [misc]simplify: iters left: 4 (369 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* v (* v -3)))))) (* (* (- (* v v)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (sqrt 2))) (* (sqrt (+ 1 (* v (* v -3)))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* v (* v -3)))))) (* (* (- (* v v)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (sqrt 2))) (* (sqrt (+ 1 (* v (* v -3)))) (* v v)))))) (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (223 enodes) * * [misc]simplify: iters left: 1 (252 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))))) (sqrt (* 16 (sqrt (+ 1 (* (* 3 v) v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* v (* v -3)))))) (* (* (- (* v v)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (sqrt 2))) (* (sqrt (+ 1 (* v (* v -3)))) (* v v)))))) (* (sqrt (* 16 (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))))) (sqrt (* 16 (sqrt (+ 1 (* (* 3 v) v)))))))) * * * * [misc]progress: [ 567 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (38 enodes) * * [misc]simplify: iters left: 5 (105 enodes) * * [misc]simplify: iters left: 4 (341 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (+ (* (* v v) -3) 1))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (+ (* (* v v) -3) 1))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* v v) (sqrt 2))))))) (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * * [misc]simplify: iters left: 2 (272 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* (* 9 v) (pow v 3)) 1))) 16)) (sqrt (+ (+ (* (* v v) 12) 4) (* (* 4 (* v v)) (* (* v v) 9))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (+ (* (* v v) -3) 1))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* v v) (sqrt 2))))))) (* (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* (* 9 v) (pow v 3)) 1))) 16)) (sqrt (+ (+ (* (* v v) 12) 4) (* (* 4 (* v v)) (* (* v v) 9))))))) * * * * [misc]progress: [ 568 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (123 enodes) * * [misc]simplify: iters left: 4 (396 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3))))) (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (sqrt 2) v)) (* v (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3))))) (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (sqrt 2) v)) (* v (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))))))) (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (95 enodes) * * [misc]simplify: iters left: 3 (149 enodes) * * [misc]simplify: iters left: 2 (242 enodes) * * [misc]simplify: iters left: 1 (287 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))) 16)) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3))))) (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (sqrt 2) v)) (* v (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))))))) (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))) 16)) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))) (* 4 (sqrt (+ 1 (* (* 3 v) v))))))))) * * * * [misc]progress: [ 569 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (108 enodes) * * [misc]simplify: iters left: 4 (350 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (+ (* v (* v -3)) 1)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (/ (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (/ 4 (sqrt 2))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (+ (* v (* v -3)) 1)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (/ (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (/ 4 (sqrt 2))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))))) (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (151 enodes) * * [misc]simplify: iters left: 2 (250 enodes) * * [misc]simplify: iters left: 1 (342 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) (* (* v v) 3)) 1)) 16)) (sqrt (+ (+ (* (pow v 4) 9) (* (* v v) 3)) 1))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (+ (* v (* v -3)) 1)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (/ (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (/ 4 (sqrt 2))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))))) (* (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) (* (* v v) 3)) 1)) 16)) (sqrt (+ (+ (* (pow v 4) 9) (* (* v v) 3)) 1))))) * * * * [misc]progress: [ 570 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (390 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (* (/ (sqrt 2) 4) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (* (/ (sqrt 2) 4) (* v v)))))) (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (171 enodes) * * [misc]simplify: iters left: 2 (296 enodes) * * [misc]simplify: iters left: 1 (368 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (pow v 4) 9))) 16)) (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (pow v 4) 9))) (sqrt (+ 1 (* v (* 3 v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (* (/ (sqrt 2) 4) (* v v)))))) (* (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (pow v 4) 9))) 16)) (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (pow v 4) 9))) (sqrt (+ 1 (* v (* 3 v))))))))) * * * * [misc]progress: [ 571 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (110 enodes) * * [misc]simplify: iters left: 4 (357 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* -3 v) v))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* -3 v) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* -3 v) v))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* -3 v) v)))))))) (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (241 enodes) * * [misc]simplify: iters left: 1 (316 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* 9 (pow v 4)) 1))) 16)) (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* 9 (pow v 4)) 1))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* -3 v) v))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* -3 v) v)))))))) (* (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* 9 (pow v 4)) 1))) 16)) (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* 9 (pow v 4)) 1))) 4))))) * * * * [misc]progress: [ 572 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (113 enodes) * * [misc]simplify: iters left: 4 (349 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) 4)) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* 3 v) v) 1)))))) (sqrt (+ (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* -3 v) v))))) (* (* (* v (- v)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) 4)) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* 3 v) v) 1)))))) (sqrt (+ (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* -3 v) v))))) (* (* (* v (- v)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (149 enodes) * * [misc]simplify: iters left: 2 (242 enodes) * * [misc]simplify: iters left: 1 (300 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ (+ 1 (* (* 3 v) v)) (* 9 (pow v 4)))))) (sqrt (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ (+ 1 (* (* 3 v) v)) (* 9 (pow v 4))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) 4)) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* 3 v) v) 1)))))) (sqrt (+ (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* -3 v) v))))) (* (* (* v (- v)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) (* (sqrt (* 16 (sqrt (+ (+ 1 (* (* 3 v) v)) (* 9 (pow v 4)))))) (sqrt (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ (+ 1 (* (* 3 v) v)) (* 9 (pow v 4))))))))) * * * * [misc]progress: [ 573 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (123 enodes) * * [misc]simplify: iters left: 4 (399 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* 4 (sqrt 2)) (sqrt (+ (* (* v -3) v) 1))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (* (- (* v v)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))))) (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (* 4 (sqrt 2)) (sqrt (+ (* (* v -3) v) 1))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (* (- (* v v)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))))) (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* v v) (sqrt 2))))))) (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (257 enodes) * * [misc]simplify: iters left: 1 (353 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))))) (sqrt (+ 4 (* 12 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (* 4 (sqrt 2)) (sqrt (+ (* (* v -3) v) 1))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (* (- (* v v)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))))) (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* v v) (sqrt 2))))))) (* (sqrt (* 16 (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))))) (sqrt (+ 4 (* 12 (* v v))))))) * * * * [misc]progress: [ 574 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (369 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (+ (* -3 (* v v)) 1))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ (* (* v v) 3) 1))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (+ (* -3 (* v v)) 1))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ (* (* v v) 3) 1))))))) (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (171 enodes) * * [misc]simplify: iters left: 2 (296 enodes) * * [misc]simplify: iters left: 1 (368 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (pow v 4) 9))) 16)) (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (pow v 4) 9))) (sqrt (+ 1 (* v (* 3 v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (+ (* -3 (* v v)) 1))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ (* (* v v) 3) 1))))))) (* (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (pow v 4) 9))) 16)) (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (pow v 4) 9))) (sqrt (+ 1 (* v (* 3 v))))))))) * * * * [misc]progress: [ 575 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (117 enodes) * * [misc]simplify: iters left: 4 (368 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* (* 4 (sqrt 2)) (sqrt (+ (* (* v v) -3) 1)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (* 3 (* v v)) 1))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ (* 3 (* v v)) 1)) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* (* 4 (sqrt 2)) (sqrt (+ (* (* v v) -3) 1)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (* 3 (* v v)) 1))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ (* 3 (* v v)) 1)) (* v v)))))) (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (251 enodes) * * [misc]simplify: iters left: 1 (338 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* (* 4 (sqrt 2)) (sqrt (+ (* (* v v) -3) 1)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (* 3 (* v v)) 1))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ (* 3 (* v v)) 1)) (* v v)))))) (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) 16))))) * * * * [misc]progress: [ 576 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (365 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* (sqrt 2) 4) (sqrt (+ (* -3 (* v v)) 1))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (* (* (- (* v v)) (* (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))) (sqrt (- (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt 2) (sqrt (+ (* 3 (* v v)) 1))) (* (sqrt (+ (* -3 (* v v)) 1)) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (* (sqrt 2) 4) (sqrt (+ (* -3 (* v v)) 1))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (* (* (- (* v v)) (* (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))) (sqrt (- (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt 2) (sqrt (+ (* 3 (* v v)) 1))) (* (sqrt (+ (* -3 (* v v)) 1)) (* v v)))))) (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (171 enodes) * * [misc]simplify: iters left: 2 (296 enodes) * * [misc]simplify: iters left: 1 (368 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (pow v 4) 9))) 16)) (sqrt (* 4 (sqrt (+ 1 (* v (* 3 v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (* (sqrt 2) 4) (sqrt (+ (* -3 (* v v)) 1))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (* (* (- (* v v)) (* (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))) (sqrt (- (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* 4 (/ (sqrt 2) 4))) (* (* (sqrt 2) (sqrt (+ (* 3 (* v v)) 1))) (* (sqrt (+ (* -3 (* v v)) 1)) (* v v)))))) (* (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (pow v 4) 9))) 16)) (sqrt (* 4 (sqrt (+ 1 (* v (* 3 v))))))))) * * * * [misc]progress: [ 577 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (31 enodes) * * [misc]simplify: iters left: 5 (84 enodes) * * [misc]simplify: iters left: 4 (259 enodes) * [exit]simplify: Simplified to (+ (* (* (* 4 (sqrt 2)) (sqrt (+ (* v (* v -3)) 1))) (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ (* v (* 3 v)) 1)))) (* (* (* 4 (sqrt 2)) (* v (- v))) (sqrt (- 1 (pow (* v (* 3 v)) 3))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (+ (* (* (* 4 (sqrt 2)) (sqrt (+ (* v (* v -3)) 1))) (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ (* v (* 3 v)) 1)))) (* (* (* 4 (sqrt 2)) (* v (- v))) (sqrt (- 1 (pow (* v (* 3 v)) 3))))) (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (85 enodes) * * [misc]simplify: iters left: 3 (138 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * * [misc]simplify: iters left: 1 (245 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (pow v 4) 9))) 16) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (+ (* (* (* 4 (sqrt 2)) (sqrt (+ (* v (* v -3)) 1))) (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ (* v (* 3 v)) 1)))) (* (* (* 4 (sqrt 2)) (* v (- v))) (sqrt (- 1 (pow (* v (* 3 v)) 3))))) (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (pow v 4) 9))) 16))) * * * * [misc]progress: [ 578 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (352 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (+ 1 (* v (* -3 v))))) (* (sqrt (+ (* (* 3 v) v) 1)) 4)) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (+ (* (* (* (sqrt 2) 4) (sqrt (+ 1 (* v (* -3 v))))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* v (- v)) (* (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (+ 1 (* v (* -3 v))))) (* (sqrt (+ (* (* 3 v) v) 1)) 4)) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (+ (* (* (* (sqrt 2) 4) (sqrt (+ 1 (* v (* -3 v))))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* v (- v)) (* (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (238 enodes) * * [misc]simplify: iters left: 1 (284 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))) 16)) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (+ 1 (* v (* -3 v))))) (* (sqrt (+ (* (* 3 v) v) 1)) 4)) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (+ (* (* (* (sqrt 2) 4) (sqrt (+ 1 (* v (* -3 v))))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* v (- v)) (* (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))) 16)) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) 16))))) * * * * [misc]progress: [ 579 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (38 enodes) * * [misc]simplify: iters left: 5 (105 enodes) * * [misc]simplify: iters left: 4 (329 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (+ (* (* v -3) v) 1))) (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ (* v (* 3 v)) 1)))) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (sqrt 2) (sqrt (+ (* (* v -3) v) 1))) (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ (* v (* 3 v)) 1)))) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (+ (* (* v -3) v) 1))) (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ (* v (* 3 v)) 1)))) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (sqrt 2) (sqrt (+ (* (* v -3) v) 1))) (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ (* v (* 3 v)) 1)))) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4))))) (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (235 enodes) * * [misc]simplify: iters left: 1 (308 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* 9 (pow v 4)) (* 3 (* v v))) 1)) 4)) (sqrt (* (sqrt (+ (+ (* 9 (pow v 4)) (* 3 (* v v))) 1)) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (+ (* (* v -3) v) 1))) (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ (* v (* 3 v)) 1)))) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (sqrt 2) (sqrt (+ (* (* v -3) v) 1))) (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ (* v (* 3 v)) 1)))) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4))))) (* (sqrt (* (sqrt (+ (+ (* 9 (pow v 4)) (* 3 (* v v))) 1)) 4)) (sqrt (* (sqrt (+ (+ (* 9 (pow v 4)) (* 3 (* v v))) 1)) 16))))) * * * * [misc]progress: [ 580 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (360 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (+ (* (* 3 v) v) 1))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (+ (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* v (- v)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (+ (* (* 3 v) v) 1))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (+ (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* v (- v)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (171 enodes) * * [misc]simplify: iters left: 2 (296 enodes) * * [misc]simplify: iters left: 1 (368 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (pow v 4) 9))) 16)) (sqrt (* 4 (sqrt (+ 1 (* v (* 3 v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (+ (* (* 3 v) v) 1))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (+ (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* v (- v)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) (* (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (pow v 4) 9))) 16)) (sqrt (* 4 (sqrt (+ 1 (* v (* 3 v))))))))) * * * * [misc]progress: [ 581 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (36 enodes) * * [misc]simplify: iters left: 5 (100 enodes) * * [misc]simplify: iters left: 4 (324 enodes) * [exit]simplify: Simplified to (* (sqrt (* (+ (* v (- v)) 1) (* (* 4 (sqrt 2)) (sqrt (+ (* (* -3 v) v) 1))))) (sqrt (+ (* (* (* 4 (sqrt 2)) (sqrt (+ (* (* -3 v) v) 1))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (* (* v (- v)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (+ (* v (- v)) 1) (* (* 4 (sqrt 2)) (sqrt (+ (* (* -3 v) v) 1))))) (sqrt (+ (* (* (* 4 (sqrt 2)) (sqrt (+ (* (* -3 v) v) 1))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (* (* v (- v)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 4))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (* 4 4))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (243 enodes) * * [misc]simplify: iters left: 1 (321 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ (+ (* (pow v 4) 9) (* (* v v) 3)) 1)))) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (+ (* v (- v)) 1) (* (* 4 (sqrt 2)) (sqrt (+ (* (* -3 v) v) 1))))) (sqrt (+ (* (* (* 4 (sqrt 2)) (sqrt (+ (* (* -3 v) v) 1))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (* (* v (- v)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) (* (sqrt (* 16 (sqrt (+ (+ (* (pow v 4) 9) (* (* v v) 3)) 1)))) 4))) * * * * [misc]progress: [ 582 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3)))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (113 enodes) * * [misc]simplify: iters left: 4 (405 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* (sqrt 2) 4) (sqrt (+ 1 (* (* -3 v) v)))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (* (+ (* (- (* v v)) (* (* v v) (* v v))) 1) (pow (* (sqrt (+ 1 (* (* -3 v) v))) (/ (sqrt 2) 4)) 3)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (* (sqrt 2) 4) (sqrt (+ 1 (* (* -3 v) v)))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (* (+ (* (- (* v v)) (* (* v v) (* v v))) 1) (pow (* (sqrt (+ 1 (* (* -3 v) v))) (/ (sqrt 2) 4)) 3)))) (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * * [misc]simplify: iters left: 6 (31 enodes) * * [misc]simplify: iters left: 5 (91 enodes) * * [misc]simplify: iters left: 4 (291 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))) (sqrt (+ (* (* (sqrt (+ (* v (* v -3)) 1)) (- (* (/ (sqrt 2) 4) (- (* v v))) (/ (sqrt 2) 4))) (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (+ (* v (* v -3)) 1)))) (* (* (sqrt (+ (* v (* v -3)) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* v (* v -3)) 1)) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (* (sqrt 2) 4) (sqrt (+ 1 (* (* -3 v) v)))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (* (+ (* (- (* v v)) (* (* v v) (* v v))) 1) (pow (* (sqrt (+ 1 (* (* -3 v) v))) (/ (sqrt 2) 4)) 3)))) (* (sqrt (* 16 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))) (sqrt (+ (* (* (sqrt (+ (* v (* v -3)) 1)) (- (* (/ (sqrt 2) 4) (- (* v v))) (/ (sqrt 2) 4))) (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (+ (* v (* v -3)) 1)))) (* (* (sqrt (+ (* v (* v -3)) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* v (* v -3)) 1)) (/ (sqrt 2) 4)))))))) * * * * [misc]progress: [ 583 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (403 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* (sqrt 2) 4) (sqrt (+ (* v (* v -3)) 1))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (* (* (sqrt (+ (* v (* v -3)) 1)) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))) (* (* (+ 1 (* v (- v))) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (* (sqrt 2) 4) (sqrt (+ (* v (* v -3)) 1))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (* (* (sqrt (+ (* v (* v -3)) 1)) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))) (* (* (+ 1 (* v (- v))) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1)))))) (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (72 enodes) * * [misc]simplify: iters left: 4 (193 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 16)) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* -3 v) v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (* (sqrt 2) 4) (sqrt (+ (* v (* v -3)) 1))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (* (* (sqrt (+ (* v (* v -3)) 1)) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))) (* (* (+ 1 (* v (- v))) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1)))))) (* (sqrt (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 16)) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* -3 v) v)))))))) * * * * [misc]progress: [ 584 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (383 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (* (- v) (* v (sqrt 2))) (sqrt 2))))) (sqrt (- (* (sqrt (+ 1 (* (* v v) 3))) (* (* 4 (sqrt 2)) (sqrt (+ (* (* v -3) v) 1)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* 4 (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (* (- v) (* v (sqrt 2))) (sqrt 2))))) (sqrt (- (* (sqrt (+ 1 (* (* v v) 3))) (* (* 4 (sqrt 2)) (sqrt (+ (* (* v -3) v) 1)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (53 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (148 enodes) * * [misc]simplify: iters left: 2 (265 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ (* v (* 3 v)) 1)))) (sqrt (+ (* (+ (* (* v 9) (pow v 3)) (* v (* 3 v))) 16) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* 4 (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (* (- v) (* v (sqrt 2))) (sqrt 2))))) (sqrt (- (* (sqrt (+ 1 (* (* v v) 3))) (* (* 4 (sqrt 2)) (sqrt (+ (* (* v -3) v) 1)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* 16 (sqrt (+ (* v (* 3 v)) 1)))) (sqrt (+ (* (+ (* (* v 9) (pow v 3)) (* v (* 3 v))) 16) 16))))) * * * * [misc]progress: [ 585 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (350 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt 2))) (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* (* v v) (sqrt 2)) 4))))) (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (+ 1 (* v (* -3 v))))) (sqrt (+ 1 (* v (* 3 v))))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* (* v v) (sqrt 2)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt 2))) (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* (* v v) (sqrt 2)) 4))))) (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (+ 1 (* v (* -3 v))))) (sqrt (+ 1 (* v (* 3 v))))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (53 enodes) * * [misc]simplify: iters left: 4 (104 enodes) * * [misc]simplify: iters left: 3 (194 enodes) * * [misc]simplify: iters left: 2 (312 enodes) * * [misc]simplify: iters left: 1 (366 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ (* v (* 3 v)) 1)))) (sqrt (* (* 16 (sqrt (+ (* v (* 3 v)) 1))) (sqrt (+ (* 9 (pow v 4)) (+ (* v (* 3 v)) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt 2))) (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* (* v v) (sqrt 2)) 4))))) (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (+ 1 (* v (* -3 v))))) (sqrt (+ 1 (* v (* 3 v))))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* 16 (sqrt (+ (* v (* 3 v)) 1)))) (sqrt (* (* 16 (sqrt (+ (* v (* 3 v)) 1))) (sqrt (+ (* 9 (pow v 4)) (+ (* v (* 3 v)) 1)))))))) * * * * [misc]progress: [ 586 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (123 enodes) * * [misc]simplify: iters left: 4 (411 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (sqrt 2))))) (sqrt (- (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (* (sqrt (+ (* v (* -3 v)) 1)) (sqrt 2))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (* v v) (sqrt 2)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (sqrt 2))))) (sqrt (- (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (* (sqrt (+ (* v (* -3 v)) 1)) (sqrt 2))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (334 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) 16)) (sqrt (+ (+ (* v (* v 12)) 4) (* (* 4 (* v v)) (* (* v v) 9))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (sqrt 2))))) (sqrt (- (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (* (sqrt (+ (* v (* -3 v)) 1)) (sqrt 2))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) 16)) (sqrt (+ (+ (* v (* v 12)) 4) (* (* 4 (* v v)) (* (* v v) 9))))))) * * * * [misc]progress: [ 587 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (122 enodes) * * [misc]simplify: iters left: 4 (382 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))) (* 4 (/ (sqrt 2) 4))) (* (* v v) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))))) (sqrt (- (* (sqrt (+ 1 (* (* 3 v) v))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* v v) -3))))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (* v v) (sqrt 2)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))) (* 4 (/ (sqrt 2) 4))) (* (* v v) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))))) (sqrt (- (* (sqrt (+ 1 (* (* 3 v) v))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* v v) -3))))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (241 enodes) * * [misc]simplify: iters left: 1 (303 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) 16)) (sqrt (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (sqrt (+ (* 9 (pow v 4)) (+ (* v (* 3 v)) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))) (* 4 (/ (sqrt 2) 4))) (* (* v v) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))))) (sqrt (- (* (sqrt (+ 1 (* (* 3 v) v))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* v v) -3))))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) 16)) (sqrt (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (sqrt (+ (* 9 (pow v 4)) (+ (* v (* 3 v)) 1)))))))) * * * * [misc]progress: [ 588 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (119 enodes) * * [misc]simplify: iters left: 4 (371 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (* (- v) (* v (sqrt 2)))) (sqrt (- 1 (* 3 (* v v)))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))) (sqrt (- (* (sqrt (- 1 (* 3 (* v v)))) (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt 2)))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (* (- v) (* v (sqrt 2)))) (sqrt (- 1 (* 3 (* v v)))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))) (sqrt (- (* (sqrt (- 1 (* 3 (* v v)))) (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt 2)))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (221 enodes) * * [misc]simplify: iters left: 1 (257 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ (* v (* 3 v)) 1)))) (sqrt (* 16 (sqrt (+ (* (pow v 4) 9) (+ (* v (* 3 v)) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (* (- v) (* v (sqrt 2)))) (sqrt (- 1 (* 3 (* v v)))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))) (sqrt (- (* (sqrt (- 1 (* 3 (* v v)))) (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt 2)))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* 16 (sqrt (+ (* v (* 3 v)) 1)))) (sqrt (* 16 (sqrt (+ (* (pow v 4) 9) (+ (* v (* 3 v)) 1)))))))) * * * * [misc]progress: [ 589 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (381 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ 1 (* (* v v) 3))) 4)))) (sqrt (+ (* (* (* (- v) v) (* (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* (sqrt 2) 4) (sqrt (+ 1 (* v (* v -3))))) (sqrt (+ 1 (* (* v v) 3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ 1 (* (* v v) 3))) 4)))) (sqrt (+ (* (* (* (- v) v) (* (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* (sqrt 2) 4) (sqrt (+ 1 (* v (* v -3))))) (sqrt (+ 1 (* (* v v) 3))))))) (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (190 enodes) * * [misc]simplify: iters left: 2 (303 enodes) * * [misc]simplify: iters left: 1 (328 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ (* v (* 3 v)) 1)))) (sqrt (* (* 16 (sqrt (+ (* v (* 3 v)) 1))) (sqrt (+ (* 9 (pow v 4)) (+ (* v (* 3 v)) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ 1 (* (* v v) 3))) 4)))) (sqrt (+ (* (* (* (- v) v) (* (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* (sqrt 2) 4) (sqrt (+ 1 (* v (* v -3))))) (sqrt (+ 1 (* (* v v) 3))))))) (* (sqrt (* 16 (sqrt (+ (* v (* 3 v)) 1)))) (sqrt (* (* 16 (sqrt (+ (* v (* 3 v)) 1))) (sqrt (+ (* 9 (pow v 4)) (+ (* v (* 3 v)) 1)))))))) * * * * [misc]progress: [ 590 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (82 enodes) * * [misc]simplify: iters left: 4 (240 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* (sqrt 2) 4) (* v (- v))) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (* (sqrt 2) (sqrt (+ 1 (* -3 (* v v)))))))) (sqrt (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (* (sqrt 2) 4) (* v (- v))) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (* (sqrt 2) (sqrt (+ 1 (* -3 (* v v)))))))) (sqrt (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2)))))) (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * * [misc]simplify: iters left: 2 (58 enodes) * * [misc]simplify: iters left: 1 (103 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 16 (* v (* 48 v)))) (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (* (sqrt 2) 4) (* v (- v))) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (* (sqrt 2) (sqrt (+ 1 (* -3 (* v v)))))))) (sqrt (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2)))))) (* (sqrt (+ 16 (* v (* 48 v)))) (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 16))))) * * * * [misc]progress: [ 591 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (384 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (+ (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* v v) -3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (+ (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* v v) -3)))))))) (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (95 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (234 enodes) * * [misc]simplify: iters left: 1 (269 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (sqrt (+ (* 9 (pow v 4)) (+ (* (* 3 v) v) 1))))) (sqrt (* 16 (sqrt (+ (* (* 3 v) v) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2)) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (+ (* (* 4 (- (* (* v v) (sqrt 2)))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* v v) -3)))))))) (* (sqrt (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (sqrt (+ (* 9 (pow v 4)) (+ (* (* 3 v) v) 1))))) (sqrt (* 16 (sqrt (+ (* (* 3 v) v) 1))))))) * * * * [misc]progress: [ 592 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (91 enodes) * * [misc]simplify: iters left: 4 (296 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* 4 (* (sqrt 2) (* v (- v)))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt 2) (sqrt (+ (* (* v -3) v) 1)))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (/ (sqrt 2) 4))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* 4 (* (sqrt 2) (* v (- v)))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt 2) (sqrt (+ (* (* v -3) v) 1)))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (/ (sqrt 2) 4))))))) (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (67 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 4 (* v (* 12 v)))) (sqrt (* 16 (sqrt (+ 1 (* v (* 3 v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* 4 (* (sqrt 2) (* v (- v)))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt 2) (sqrt (+ (* (* v -3) v) 1)))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (/ (sqrt 2) 4))))))) (* (sqrt (+ 4 (* v (* 12 v)))) (sqrt (* 16 (sqrt (+ 1 (* v (* 3 v))))))))) * * * * [misc]progress: [ 593 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (33 enodes) * * [misc]simplify: iters left: 5 (86 enodes) * * [misc]simplify: iters left: 4 (258 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* 4 (* (- v) (* v (sqrt 2)))) (sqrt (- 1 (* (* (* v v) 9) (* v v))))) (* (sqrt (+ (* v (* v -3)) 1)) (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt 2)))))) (sqrt (- (* (sqrt (- 1 (* (* (* v v) 9) (* v v)))) (* 4 (sqrt 2))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt 2))) (* (* v v) (sqrt (+ (* v (* v -3)) 1))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* 4 (* (- v) (* v (sqrt 2)))) (sqrt (- 1 (* (* (* v v) 9) (* v v))))) (* (sqrt (+ (* v (* v -3)) 1)) (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt 2)))))) (sqrt (- (* (sqrt (- 1 (* (* (* v v) 9) (* v v)))) (* 4 (sqrt 2))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt 2))) (* (* v v) (sqrt (+ (* v (* v -3)) 1))))))) (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * [exit]simplify: Simplified to (* 16 (sqrt (+ 1 (* v (* 3 v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* 4 (* (- v) (* v (sqrt 2)))) (sqrt (- 1 (* (* (* v v) 9) (* v v))))) (* (sqrt (+ (* v (* v -3)) 1)) (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt 2)))))) (sqrt (- (* (sqrt (- 1 (* (* (* v v) 9) (* v v)))) (* 4 (sqrt 2))) (* (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt 2))) (* (* v v) (sqrt (+ (* v (* v -3)) 1))))))) (* 16 (sqrt (+ 1 (* v (* 3 v))))))) * * * * [misc]progress: [ 594 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (123 enodes) * * [misc]simplify: iters left: 4 (401 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (sqrt (+ 1 (* (* v v) 3))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* v (* v -3)))))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (sqrt (+ 1 (* (* v v) 3))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* v (* v -3)))))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (136 enodes) * * [misc]simplify: iters left: 2 (254 enodes) * * [misc]simplify: iters left: 1 (418 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ (* v (* 3 v)) 1)))) (sqrt (+ 4 (+ (* (pow v 3) (* 36 v)) (* (* v v) 12))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (* (sqrt (+ 1 (* (* v v) 3))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* v (* v -3)))))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* 16 (sqrt (+ (* v (* 3 v)) 1)))) (sqrt (+ 4 (+ (* (pow v 3) (* 36 v)) (* (* v v) 12))))))) * * * * [misc]progress: [ 595 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (113 enodes) * * [misc]simplify: iters left: 4 (348 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (/ (sqrt 2) 4))) (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v)))))) (* (sqrt 2) (* v v))))) (sqrt (- (* (sqrt (+ (* v (* 3 v)) 1)) (* (* 4 (sqrt 2)) (sqrt (+ (* (* -3 v) v) 1)))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* (* v v) (sqrt 2)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (/ (sqrt 2) 4))) (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v)))))) (* (sqrt 2) (* v v))))) (sqrt (- (* (sqrt (+ (* v (* 3 v)) 1)) (* (* 4 (sqrt 2)) (sqrt (+ (* (* -3 v) v) 1)))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (166 enodes) * * [misc]simplify: iters left: 2 (265 enodes) * * [misc]simplify: iters left: 1 (306 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (sqrt (+ (* (pow v 4) 9) (+ (* (* 3 v) v) 1))))) (sqrt (* 16 (sqrt (+ (* (* 3 v) v) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (/ (sqrt 2) 4))) (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v)))))) (* (sqrt 2) (* v v))))) (sqrt (- (* (sqrt (+ (* v (* 3 v)) 1)) (* (* 4 (sqrt 2)) (sqrt (+ (* (* -3 v) v) 1)))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (sqrt (+ (* (pow v 4) 9) (+ (* (* 3 v) v) 1))))) (sqrt (* 16 (sqrt (+ (* (* 3 v) v) 1))))))) * * * * [misc]progress: [ 596 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (117 enodes) * * [misc]simplify: iters left: 4 (371 enodes) * [exit]simplify: Simplified to (* (sqrt (- (/ (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt 2)) (/ 4 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (sqrt 2) 4)) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* v v))))) (sqrt (- (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt 2) (sqrt (- 1 (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (/ (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt 2)) (/ 4 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (sqrt 2) 4)) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* v v))))) (sqrt (- (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt 2) (sqrt (- 1 (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (164 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (pow v 4) 9) (+ (* v (* 3 v)) 1))) (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (/ (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (sqrt 2)) (/ 4 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (sqrt 2) 4)) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* v v))))) (sqrt (- (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt 2) (sqrt (- 1 (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (+ (* (pow v 4) 9) (+ (* v (* 3 v)) 1))) (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) 16))))) * * * * [misc]progress: [ 597 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (371 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* (sqrt 2) 4) (* v (- v))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (* (* 3 v) v) 1)) (* (* (sqrt 2) 4) (sqrt (+ (* v (* v -3)) 1)))))) (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (* (sqrt 2) 4) (* v (- v))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (* (* 3 v) v) 1)) (* (* (sqrt 2) 4) (sqrt (+ (* v (* v -3)) 1)))))) (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* v v)))))) (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (163 enodes) * * [misc]simplify: iters left: 2 (280 enodes) * * [misc]simplify: iters left: 1 (309 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* v v) 3) 1)) (sqrt (+ (* (pow v 4) 9) (+ (* (* v v) 3) 1))))) (sqrt (* 16 (sqrt (+ (* (* v v) 3) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (* (sqrt 2) 4) (* v (- v))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (* (* 3 v) v) 1)) (* (* (sqrt 2) 4) (sqrt (+ (* v (* v -3)) 1)))))) (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* v v)))))) (* (sqrt (* (sqrt (+ (* (* v v) 3) 1)) (sqrt (+ (* (pow v 4) 9) (+ (* (* v v) 3) 1))))) (sqrt (* 16 (sqrt (+ (* (* v v) 3) 1))))))) * * * * [misc]progress: [ 598 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (367 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* v -3) v) 1))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (sqrt (+ (* (* v -3) v) 1))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* v -3) v) 1))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (sqrt (+ (* (* v -3) v) 1))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (163 enodes) * * [misc]simplify: iters left: 2 (280 enodes) * * [misc]simplify: iters left: 1 (309 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ (* (pow v 4) 9) (+ (* (* v v) 3) 1))))) (sqrt (* 16 (sqrt (+ (* (* v v) 3) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* v -3) v) 1))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (sqrt (+ (* (* v -3) v) 1))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* 4 (sqrt (+ (* (pow v 4) 9) (+ (* (* v v) 3) 1))))) (sqrt (* 16 (sqrt (+ (* (* v v) 3) 1))))))) * * * * [misc]progress: [ 599 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (123 enodes) * * [misc]simplify: iters left: 4 (390 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4))) (* (* (sqrt 2) (sqrt (+ (* (* v v) 3) 1))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* v v))))) (sqrt (- (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (* (sqrt 2) (sqrt (+ (* v (* -3 v)) 1)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4))) (* (* (sqrt 2) (sqrt (+ (* (* v v) 3) 1))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* v v))))) (sqrt (- (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (* (sqrt 2) (sqrt (+ (* v (* -3 v)) 1)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (174 enodes) * * [misc]simplify: iters left: 2 (294 enodes) * * [misc]simplify: iters left: 1 (346 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ (* v (* 3 v)) 1)))) (sqrt (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (sqrt (+ (* 9 (pow v 4)) (+ (* v (* 3 v)) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4))) (* (* (sqrt 2) (sqrt (+ (* (* v v) 3) 1))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* v v))))) (sqrt (- (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (* (sqrt 2) (sqrt (+ (* v (* -3 v)) 1)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* 16 (sqrt (+ (* v (* 3 v)) 1)))) (sqrt (* (* (sqrt (+ (* v (* 3 v)) 1)) 4) (sqrt (+ (* 9 (pow v 4)) (+ (* v (* 3 v)) 1)))))))) * * * * [misc]progress: [ 600 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (85 enodes) * * [misc]simplify: iters left: 4 (266 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ 1 (* 3 (* v v)))) (* (* 4 (sqrt 2)) (sqrt (+ (* (* v v) -3) 1)))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ 1 (* 3 (* v v)))) (* (* 4 (sqrt 2)) (sqrt (+ (* (* v v) -3) 1)))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * * [misc]simplify: iters left: 2 (42 enodes) * * [misc]simplify: iters left: 1 (59 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 4 (* (* 12 v) v))) (sqrt (* 16 (sqrt (+ 1 (* v (* 3 v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ 1 (* 3 (* v v)))) (* (* 4 (sqrt 2)) (sqrt (+ (* (* v v) -3) 1)))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (+ 4 (* (* 12 v) v))) (sqrt (* 16 (sqrt (+ 1 (* v (* 3 v))))))))) * * * * [misc]progress: [ 601 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (388 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* (sqrt 2) 4) (* v (- v))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (* (* 3 v) v) 1)) (* (* (sqrt 2) 4) (sqrt (+ (* v (* v -3)) 1)))))) (sqrt (- (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (/ (sqrt 2) 4))) (* (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (/ (sqrt 2) 4) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (* (sqrt 2) 4) (* v (- v))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (* (* 3 v) v) 1)) (* (* (sqrt 2) 4) (sqrt (+ (* v (* v -3)) 1)))))) (sqrt (- (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (/ (sqrt 2) 4))) (* (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (/ (sqrt 2) 4) (* v v)))))) (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (163 enodes) * * [misc]simplify: iters left: 2 (280 enodes) * * [misc]simplify: iters left: 1 (309 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* v v) 3) 1)) (sqrt (+ (* (pow v 4) 9) (+ (* (* v v) 3) 1))))) (sqrt (* 16 (sqrt (+ (* (* v v) 3) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (* (sqrt 2) 4) (* v (- v))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (* (* 3 v) v) 1)) (* (* (sqrt 2) 4) (sqrt (+ (* v (* v -3)) 1)))))) (sqrt (- (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (/ (sqrt 2) 4))) (* (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (/ (sqrt 2) 4) (* v v)))))) (* (sqrt (* (sqrt (+ (* (* v v) 3) 1)) (sqrt (+ (* (pow v 4) 9) (+ (* (* v v) 3) 1))))) (sqrt (* 16 (sqrt (+ (* (* v v) 3) 1))))))) * * * * [misc]progress: [ 602 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (88 enodes) * * [misc]simplify: iters left: 4 (271 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt 2) (sqrt (+ (* (* v -3) v) 1)))) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* v v) (sqrt (+ 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt 2) (sqrt (+ (* (* v -3) v) 1)))) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* v v) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (37 enodes) * * [misc]simplify: iters left: 1 (38 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* (* v v) 3))) (sqrt (* 16 (sqrt (+ 1 (* (* v v) 3)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt 2) (sqrt (+ (* (* v -3) v) 1)))) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* v v) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (+ 1 (* (* v v) 3))) (sqrt (* 16 (sqrt (+ 1 (* (* v v) 3)))))))) * * * * [misc]progress: [ 603 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (90 enodes) * * [misc]simplify: iters left: 4 (278 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (+ (* v (* -3 v)) 1))) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (sqrt (+ (* v (* -3 v)) 1)) (sqrt 2)) (* (* v v) (sqrt (+ 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (+ (* v (* -3 v)) 1))) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (sqrt (+ (* v (* -3 v)) 1)) (sqrt 2)) (* (* v v) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) 4)) (sqrt (* 16 (sqrt (+ 1 (* v (* 3 v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (+ (* v (* -3 v)) 1))) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (sqrt (+ (* v (* -3 v)) 1)) (sqrt 2)) (* (* v v) (sqrt (+ 1 (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) 4)) (sqrt (* 16 (sqrt (+ 1 (* v (* 3 v))))))))) * * * * [misc]progress: [ 604 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (345 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* 4 (sqrt 2)) (* v (- v))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 v) v))))))) (sqrt (- (* (* (sqrt (+ 1 (* (* 3 v) v))) 4) (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (* v v) (sqrt 2)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (* 4 (sqrt 2)) (* v (- v))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 v) v))))))) (sqrt (- (* (* (sqrt (+ 1 (* (* 3 v) v))) 4) (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (165 enodes) * * [misc]simplify: iters left: 2 (288 enodes) * * [misc]simplify: iters left: 1 (313 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ (* v (* 3 v)) 1)))) (sqrt (* (sqrt (+ (* 9 (pow v 4)) (+ (* v (* 3 v)) 1))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (* 4 (sqrt 2)) (* v (- v))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 v) v))))))) (sqrt (- (* (* (sqrt (+ 1 (* (* 3 v) v))) 4) (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* 16 (sqrt (+ (* v (* 3 v)) 1)))) (sqrt (* (sqrt (+ (* 9 (pow v 4)) (+ (* v (* 3 v)) 1))) 16))))) * * * * [misc]progress: [ 605 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (64 enodes) * * [misc]simplify: iters left: 4 (179 enodes) * [exit]simplify: Simplified to (- (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (* (sqrt 2) (sqrt (+ 1 (* (* -3 v) v))))) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (* (* (* v v) (sqrt 2)) 4))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (* (sqrt 2) (sqrt (+ 1 (* (* -3 v) v))))) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (* (* (* v v) (sqrt 2)) 4))) (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * [exit]simplify: Simplified to (* 16 (sqrt (+ 1 (* (* 3 v) v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (* (sqrt 2) (sqrt (+ 1 (* (* -3 v) v))))) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (* (* (* v v) (sqrt 2)) 4))) (* 16 (sqrt (+ 1 (* (* 3 v) v)))))) * * * * [misc]progress: [ 606 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (353 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (* (* (sqrt (+ 1 (* (* 3 v) v))) 4) (* (sqrt 2) (sqrt (- 1 (* (* 3 v) v))))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (sqrt 2) (* v v)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (* (* (sqrt (+ 1 (* (* 3 v) v))) 4) (* (sqrt 2) (sqrt (- 1 (* (* 3 v) v))))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (sqrt 2) (* v v)) 4))))) (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (163 enodes) * * [misc]simplify: iters left: 2 (280 enodes) * * [misc]simplify: iters left: 1 (309 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ (* (pow v 4) 9) (+ (* (* v v) 3) 1))))) (sqrt (* 16 (sqrt (+ (* (* v v) 3) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (* (* (sqrt (+ 1 (* (* 3 v) v))) 4) (* (sqrt 2) (sqrt (- 1 (* (* 3 v) v))))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (sqrt 2) (* v v)) 4))))) (* (sqrt (* 4 (sqrt (+ (* (pow v 4) 9) (+ (* (* v v) 3) 1))))) (sqrt (* 16 (sqrt (+ (* (* v v) 3) 1))))))) * * * * [misc]progress: [ 607 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (85 enodes) * * [misc]simplify: iters left: 4 (252 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* v (* -3 v)) 1)) (sqrt 2))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (sqrt (+ 1 (* 3 (* v v)))) (* (sqrt (+ (* v (* -3 v)) 1)) (sqrt 2))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* v (* -3 v)) 1)) (sqrt 2))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (sqrt (+ 1 (* 3 (* v v)))) (* (sqrt (+ (* v (* -3 v)) 1)) (sqrt 2))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ 1 (* (* 3 v) v))))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* v (* -3 v)) 1)) (sqrt 2))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (sqrt (+ 1 (* 3 (* v v)))) (* (sqrt (+ (* v (* -3 v)) 1)) (sqrt 2))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) (* (sqrt (* 16 (sqrt (+ 1 (* (* 3 v) v))))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) 4))))) * * * * [misc]progress: [ 608 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (80 enodes) * * [misc]simplify: iters left: 4 (241 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* -3 (* v v)))) (* (sqrt 2) 4)) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (* (* (sqrt (+ 1 (* -3 (* v v)))) (sqrt 2)) (+ (* (- v) (* v 4)) 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* -3 (* v v)))) (* (sqrt 2) 4)) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (* (* (sqrt (+ 1 (* -3 (* v v)))) (sqrt 2)) (+ (* (- v) (* v 4)) 4)))) (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 4))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (* 4 4))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * [exit]simplify: Simplified to (* 4 (sqrt (* 16 (sqrt (+ 1 (* (* v v) 3)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* -3 (* v v)))) (* (sqrt 2) 4)) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (* (* (sqrt (+ 1 (* -3 (* v v)))) (sqrt 2)) (+ (* (- v) (* v 4)) 4)))) (* 4 (sqrt (* 16 (sqrt (+ 1 (* (* v v) 3)))))))) * * * * [misc]progress: [ 609 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3)))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (94 enodes) * * [misc]simplify: iters left: 4 (330 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt 2) (sqrt (+ (* -3 (* v v)) 1)))) (* (sqrt (- 1 (* (* (* v v) 9) (* v v)))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (pow (* (sqrt (+ (* -3 (* v v)) 1)) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* -3 (* v v)) 1))) 3)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt 2) (sqrt (+ (* -3 (* v v)) 1)))) (* (sqrt (- 1 (* (* (* v v) 9) (* v v)))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (pow (* (sqrt (+ (* -3 (* v v)) 1)) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* -3 (* v v)) 1))) 3)))) (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (74 enodes) * * [misc]simplify: iters left: 4 (233 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (sqrt (+ 1 (* (* v v) -3))) (- (* (* v (- v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (* v (- v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v v) -3))))) (* (* (sqrt (+ 1 (* (* v v) -3))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* (* v v) -3))) (/ (sqrt 2) 4))))) (sqrt (* 16 (sqrt (+ 1 (* v (* 3 v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt 2) (sqrt (+ (* -3 (* v v)) 1)))) (* (sqrt (- 1 (* (* (* v v) 9) (* v v)))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (pow (* (sqrt (+ (* -3 (* v v)) 1)) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* -3 (* v v)) 1))) 3)))) (* (sqrt (+ (* (* (sqrt (+ 1 (* (* v v) -3))) (- (* (* v (- v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (* v (- v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v v) -3))))) (* (* (sqrt (+ 1 (* (* v v) -3))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* (* v v) -3))) (/ (sqrt 2) 4))))) (sqrt (* 16 (sqrt (+ 1 (* v (* 3 v))))))))) * * * * [misc]progress: [ 610 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (95 enodes) * * [misc]simplify: iters left: 4 (326 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (* (sqrt 2) (sqrt (+ (* (* v v) -3) 1)))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (* (* (sqrt (+ (* (* v v) -3) 1)) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (- (* v v))))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (* (sqrt 2) (sqrt (+ (* (* v v) -3) 1)))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (* (* (sqrt (+ (* (* v v) -3) 1)) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (- (* v v))))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1)))))) (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (55 enodes) * * [misc]simplify: iters left: 4 (135 enodes) * * [misc]simplify: iters left: 3 (423 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* (* v v) -3))) (* (/ (sqrt 2) 4) (+ (* v v) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (* (sqrt 2) (sqrt (+ (* (* v v) -3) 1)))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (* (* (sqrt (+ (* (* v v) -3) 1)) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (- (* v v))))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1)))))) (* (sqrt (* 16 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* (* v v) -3))) (* (/ (sqrt 2) 4) (+ (* v v) 1))))))) * * * * [misc]progress: [ 611 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (110 enodes) * * [misc]simplify: iters left: 4 (366 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* v v) 3)))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (sqrt 2) (* (- v) (* v (sqrt 2))))) (* 4 (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* v v) 3)))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (sqrt 2) (* (- v) (* v (sqrt 2))))) (* 4 (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))))))) (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (96 enodes) * * [misc]simplify: iters left: 3 (156 enodes) * * [misc]simplify: iters left: 2 (284 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* v v) 3) (+ (* (* 9 v) (pow v 3)) 1))) 4)) (sqrt (+ (* 16 (+ (* (* 9 v) (pow v 3)) (* (* v v) 3))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* v v) 3)))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (sqrt 2) (* (- v) (* v (sqrt 2))))) (* 4 (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))))))) (* (sqrt (* (sqrt (+ (* (* v v) 3) (+ (* (* 9 v) (pow v 3)) 1))) 4)) (sqrt (+ (* 16 (+ (* (* 9 v) (pow v 3)) (* (* v v) 3))) 16))))) * * * * [misc]progress: [ 612 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (123 enodes) * * [misc]simplify: iters left: 4 (407 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (+ (* v (* v -3)) 1)) (sqrt 2))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (sqrt (+ (* 3 (* v v)) 1)) 4) (sqrt 2))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (+ (* v (* v -3)) 1)) (sqrt 2))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (sqrt (+ (* 3 (* v v)) 1)) 4) (sqrt 2))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4))))) (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (102 enodes) * * [misc]simplify: iters left: 3 (187 enodes) * * [misc]simplify: iters left: 2 (304 enodes) * * [misc]simplify: iters left: 1 (341 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 16 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (+ (* v (* v -3)) 1)) (sqrt 2))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (sqrt (+ (* 3 (* v v)) 1)) 4) (sqrt 2))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4))))) (* (sqrt (* (* 16 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) 4))))) * * * * [misc]progress: [ 613 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (38 enodes) * * [misc]simplify: iters left: 5 (103 enodes) * * [misc]simplify: iters left: 4 (336 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt 2) (sqrt (+ (* (* -3 v) v) 1)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt 2) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (sqrt 2) 4) (* v v))) (* 4 (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt 2) (sqrt (+ (* (* -3 v) v) 1)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt 2) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (sqrt 2) 4) (* v v))) (* 4 (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (173 enodes) * * [misc]simplify: iters left: 2 (351 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* 9 v) (pow v 3)) (* 3 (* v v))) 1)) 4)) (sqrt (+ (* (* v v) (* (* 9 v) (* v 4))) (+ (* v (* 12 v)) 4)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt 2) (sqrt (+ (* (* -3 v) v) 1)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt 2) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (sqrt 2) 4) (* v v))) (* 4 (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))))))) (* (sqrt (* (sqrt (+ (+ (* (* 9 v) (pow v 3)) (* 3 (* v v))) 1)) 4)) (sqrt (+ (* (* v v) (* (* 9 v) (* v 4))) (+ (* v (* 12 v)) 4)))))) * * * * [misc]progress: [ 614 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (401 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* v v)))))) (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * * [misc]simplify: iters left: 2 (253 enodes) * * [misc]simplify: iters left: 1 (328 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (sqrt (+ (+ (* 9 (pow v 4)) (* (* v v) 3)) 1)))) (sqrt (* (sqrt (+ (+ (* 9 (pow v 4)) (* (* v v) 3)) 1)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* v v)))))) (* (sqrt (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (sqrt (+ (+ (* 9 (pow v 4)) (* (* v v) 3)) 1)))) (sqrt (* (sqrt (+ (+ (* 9 (pow v 4)) (* (* v v) 3)) 1)) 4))))) * * * * [misc]progress: [ 615 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (110 enodes) * * [misc]simplify: iters left: 4 (369 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* 3 (* v v)))) (sqrt 2))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (+ (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (* (sqrt 2) (* v (- v)))) (sqrt (- 1 (* 3 (* v v)))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* 3 (* v v)))) (sqrt 2))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (+ (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (* (sqrt 2) (* v (- v)))) (sqrt (- 1 (* 3 (* v v)))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (221 enodes) * * [misc]simplify: iters left: 1 (250 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* 9 (pow v 4)) (* (* v v) 3)) 1)) 4)) (sqrt (* (sqrt (+ (+ (* 9 (pow v 4)) (* (* v v) 3)) 1)) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* 3 (* v v)))) (sqrt 2))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (+ (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (* (sqrt 2) (* v (- v)))) (sqrt (- 1 (* 3 (* v v)))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (* (sqrt (* (sqrt (+ (+ (* 9 (pow v 4)) (* (* v v) 3)) 1)) 4)) (sqrt (* (sqrt (+ (+ (* 9 (pow v 4)) (* (* v v) 3)) 1)) 16))))) * * * * [misc]progress: [ 616 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (122 enodes) * * [misc]simplify: iters left: 4 (378 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) 4) (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* v v) (* (* (sqrt (+ (* (* 3 v) v) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) 4) (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* v v) (* (* (sqrt (+ (* (* 3 v) v) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))))))) (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (102 enodes) * * [misc]simplify: iters left: 3 (188 enodes) * * [misc]simplify: iters left: 2 (300 enodes) * * [misc]simplify: iters left: 1 (343 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 16 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) 4) (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))) (* (* v v) (* (* (sqrt (+ (* (* 3 v) v) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))))))) (* (sqrt (* (* 16 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) 4))))) * * * * [misc]progress: [ 617 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (119 enodes) * * [misc]simplify: iters left: 4 (381 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (- 1 (* (* v v) 3))) (sqrt 2)) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2))) (* (sqrt (+ (* (* v v) 3) 1)) 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* v v) 3))) (sqrt 2)) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2))) (* (sqrt (+ (* (* v v) 3) 1)) 4)))) (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (181 enodes) * * [misc]simplify: iters left: 2 (307 enodes) * * [misc]simplify: iters left: 1 (399 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 16 (* (* v v) 48))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* v v) 3))) (sqrt 2)) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (* (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (+ (* v (* (- v) (sqrt 2))) (sqrt 2))) (* (sqrt (+ (* (* v v) 3) 1)) 4)))) (* (sqrt (+ 16 (* (* v v) 48))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* 9 (pow v 4)) 1))) 4))))) * * * * [misc]progress: [ 618 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (111 enodes) * * [misc]simplify: iters left: 4 (334 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (sqrt 2))) (* (* (* v (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* v (* 4 (sqrt (+ (* v (* 3 v)) 1))))))) (sqrt (- (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt 2) (sqrt (- 1 (* v (* 3 v)))))) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (sqrt 2))) (* (* (* v (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* v (* 4 (sqrt (+ (* v (* 3 v)) 1))))))) (sqrt (- (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt 2) (sqrt (- 1 (* v (* 3 v)))))) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (248 enodes) * * [misc]simplify: iters left: 1 (325 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* (pow v 4) 9) 1))) (* (sqrt (+ 1 (* v (* 3 v)))) 4))) (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* (pow v 4) 9) 1))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (sqrt 2))) (* (* (* v (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* v (* 4 (sqrt (+ (* v (* 3 v)) 1))))))) (sqrt (- (* (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt 2) (sqrt (- 1 (* v (* 3 v)))))) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* (pow v 4) 9) 1))) (* (sqrt (+ 1 (* v (* 3 v)))) 4))) (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* (pow v 4) 9) 1))) 4))))) * * * * [misc]progress: [ 619 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (401 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* v v) (* (* (sqrt (+ (* (* 3 v) v) 1)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* v v) (* (* (sqrt (+ (* (* 3 v) v) 1)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))))))) (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (156 enodes) * * [misc]simplify: iters left: 2 (296 enodes) * * [misc]simplify: iters left: 1 (439 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* v v) 12) 4)) (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* (pow v 4) 9) 1))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* v v) (* (* (sqrt (+ (* (* 3 v) v) 1)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))))))) (* (sqrt (+ (* (* v v) 12) 4)) (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* (pow v 4) 9) 1))) 4))))) * * * * [misc]progress: [ 620 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (371 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* 3 (* v v)))) (sqrt 2))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* 4 (sqrt 2))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (sqrt 2))) (* (sqrt (- 1 (* 3 (* v v)))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* 3 (* v v)))) (sqrt 2))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* 4 (sqrt 2))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (sqrt 2))) (* (sqrt (- 1 (* 3 (* v v)))) (* v v)))))) (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (246 enodes) * * [misc]simplify: iters left: 1 (314 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ 1 (* v (* 3 v)))))) (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* (pow v 4) 9) 1))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (- 1 (* 3 (* v v)))) (sqrt 2))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* 4 (sqrt 2))) (* (* (sqrt (+ (* 3 (* v v)) 1)) (* 4 (sqrt 2))) (* (sqrt (- 1 (* 3 (* v v)))) (* v v)))))) (* (sqrt (* 16 (sqrt (+ 1 (* v (* 3 v)))))) (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* (pow v 4) 9) 1))) 4))))) * * * * [misc]progress: [ 621 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (109 enodes) * * [misc]simplify: iters left: 4 (363 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (sqrt (- 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (* 4 v) (- v)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))) (sqrt (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (* v (* (- v) (sqrt 2))) (/ (* 4 (sqrt 2)) 4))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt (- 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (* 4 v) (- v)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))) (sqrt (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (* v (* (- v) (sqrt 2))) (/ (* 4 (sqrt 2)) 4))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))))) (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (174 enodes) * * [misc]simplify: iters left: 2 (310 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) (* (* 3 v) v)) 1)) 4)) (sqrt (+ (+ (* (* v v) 12) (* (pow v 4) 36)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt (- 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (* (* 4 v) (- v)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))))) (sqrt (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (* v (* (- v) (sqrt 2))) (/ (* 4 (sqrt 2)) 4))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))))) (* (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) (* (* 3 v) v)) 1)) 4)) (sqrt (+ (+ (* (* v v) 12) (* (pow v 4) 36)) 4))))) * * * * [misc]progress: [ 622 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (380 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt 2) (sqrt (- 1 (* (* v v) 3))))) (* (* 4 (* (* (- v) v) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt 2) (sqrt (- 1 (* (* v v) 3))))) (* (* 4 (* (* (- v) v) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))))))) (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (236 enodes) * * [misc]simplify: iters left: 1 (298 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* (sqrt (+ 1 (* (* 3 v) v))) 4))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt 2) (sqrt (- 1 (* (* v v) 3))))) (* (* 4 (* (* (- v) v) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))))))) (* (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) (* (sqrt (+ 1 (* (* 3 v) v))) 4))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) 4))))) * * * * [misc]progress: [ 623 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (36 enodes) * * [misc]simplify: iters left: 5 (97 enodes) * * [misc]simplify: iters left: 4 (300 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* v v))))) (sqrt (+ (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* (sqrt (+ (* (* -3 v) v) 1)) (sqrt 2))) (* (* (- (* v v)) (/ (* 4 (sqrt 2)) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* v v))))) (sqrt (+ (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* (sqrt (+ (* (* -3 v) v) 1)) (sqrt 2))) (* (* (- (* v v)) (/ (* 4 (sqrt 2)) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (166 enodes) * * [misc]simplify: iters left: 2 (271 enodes) * * [misc]simplify: iters left: 1 (293 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* v v) 3) (+ (* 9 (pow v 4)) 1))) 4)) (sqrt (+ (* (* v v) 3) (+ (* 9 (pow v 4)) 1)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* v v))))) (sqrt (+ (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* (sqrt (+ (* (* -3 v) v) 1)) (sqrt 2))) (* (* (- (* v v)) (/ (* 4 (sqrt 2)) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3))))))) (* (sqrt (* (sqrt (+ (* (* v v) 3) (+ (* 9 (pow v 4)) 1))) 4)) (sqrt (+ (* (* v v) 3) (+ (* 9 (pow v 4)) 1)))))) * * * * [misc]progress: [ 624 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (376 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* v v))))) (sqrt (+ (* (* (sqrt (+ (* v (* -3 v)) 1)) (sqrt 2)) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* v (- v)) (/ (* 4 (sqrt 2)) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* v v))))) (sqrt (+ (* (* (sqrt (+ (* v (* -3 v)) 1)) (sqrt 2)) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* v (- v)) (/ (* 4 (sqrt 2)) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (243 enodes) * * [misc]simplify: iters left: 1 (324 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) (* (* v v) 3)) 1)) (sqrt (+ 1 (* (* v v) 3))))) (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) (* (* v v) 3)) 1)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* v v))))) (sqrt (+ (* (* (sqrt (+ (* v (* -3 v)) 1)) (sqrt 2)) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* v (- v)) (/ (* 4 (sqrt 2)) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) (* (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) (* (* v v) 3)) 1)) (sqrt (+ 1 (* (* v v) 3))))) (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) (* (* v v) 3)) 1)) 4))))) * * * * [misc]progress: [ 625 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (37 enodes) * * [misc]simplify: iters left: 5 (103 enodes) * * [misc]simplify: iters left: 4 (330 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* (* 4 v) (- v)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) (* (sqrt 2) (sqrt (+ (* v (* v -3)) 1)))))) (sqrt (- (* (* (/ (sqrt 2) 4) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* v -3)) 1))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (* (* 4 v) (- v)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) (* (sqrt 2) (sqrt (+ (* v (* v -3)) 1)))))) (sqrt (- (* (* (/ (sqrt 2) 4) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* v -3)) 1))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))))))) (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (239 enodes) * * [misc]simplify: iters left: 1 (324 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ (* (pow v 4) 9) (* (* 3 v) v)) 1)) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (* (* 4 v) (- v)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) (* (sqrt 2) (sqrt (+ (* v (* v -3)) 1)))))) (sqrt (- (* (* (/ (sqrt 2) 4) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* v -3)) 1))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))))))) (* (sqrt (+ (+ (* (pow v 4) 9) (* (* 3 v) v)) 1)) 4))) * * * * [misc]progress: [ 626 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (373 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) 4) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* 3 v) v) 1))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) 4) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* 3 v) v) 1))))))) (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * * [misc]simplify: iters left: 2 (248 enodes) * * [misc]simplify: iters left: 1 (317 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (sqrt (+ (+ (* (pow v 4) 9) (* (* v v) 3)) 1)))) (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) (* (* v v) 3)) 1)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) 4) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* 3 v) v) 1))))))) (* (sqrt (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (sqrt (+ (+ (* (pow v 4) 9) (* (* v v) 3)) 1)))) (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) (* (* v v) 3)) 1)) 4))))) * * * * [misc]progress: [ 627 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (398 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (- 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) (- (* (* (/ (sqrt 2) 4) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) (- (* (* (/ (sqrt 2) 4) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))))))) (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (85 enodes) * * [misc]simplify: iters left: 3 (138 enodes) * * [misc]simplify: iters left: 2 (249 enodes) * * [misc]simplify: iters left: 1 (358 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 4 (* (* v 12) v))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) (- (* (* (/ (sqrt 2) 4) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (sqrt 2))))))) (* (sqrt (+ 4 (* (* v 12) v))) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) 4))))) * * * * [misc]progress: [ 628 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (109 enodes) * * [misc]simplify: iters left: 4 (330 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* (sqrt 2) (sqrt (+ (* (* v v) -3) 1)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (/ (* (sqrt 2) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (/ 4 (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ (* 3 (* v v)) 1))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* (sqrt 2) (sqrt (+ (* (* v v) -3) 1)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (/ (* (sqrt 2) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (/ 4 (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ (* 3 (* v v)) 1))))))) (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (243 enodes) * * [misc]simplify: iters left: 1 (324 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) (* (* v v) 3)) 1)) (sqrt (+ 1 (* (* v v) 3))))) (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) (* (* v v) 3)) 1)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (* (sqrt 2) (sqrt (+ (* (* v v) -3) 1)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (/ (* (sqrt 2) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (/ 4 (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) (sqrt (+ (* 3 (* v v)) 1))))))) (* (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) (* (* v v) 3)) 1)) (sqrt (+ 1 (* (* v v) 3))))) (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) (* (* v v) 3)) 1)) 4))))) * * * * [misc]progress: [ 629 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (366 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (* (* v v) 3) 1))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (+ (* (* v v) 3) 1)) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (* (sqrt 2) (sqrt (+ 1 (* v (* -3 v))))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (* (* v v) 3) 1))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (+ (* (* v v) 3) 1)) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (* (sqrt 2) (sqrt (+ 1 (* v (* -3 v))))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4))))) (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (265 enodes) * * [misc]simplify: iters left: 1 (380 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* (* v v) 3))) (sqrt (* (sqrt (+ (* (* v v) 3) (+ (* 9 (pow v 4)) 1))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ (* (* v v) 3) 1))) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (+ (* (* v v) 3) 1)) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (- (* (* (sqrt 2) (sqrt (+ 1 (* v (* -3 v))))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4))))) (* (sqrt (+ 1 (* (* v v) 3))) (sqrt (* (sqrt (+ (* (* v v) 3) (+ (* 9 (pow v 4)) 1))) 4))))) * * * * [misc]progress: [ 630 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (367 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (* (* 3 v) v) 1)) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 v) v))))))) (sqrt (- (* (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (* (* 3 v) v) 1)) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 v) v))))))) (sqrt (- (* (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (243 enodes) * * [misc]simplify: iters left: 1 (324 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 4)) (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) (* (* v v) 3)) 1)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (* (* 3 v) v) 1)) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 v) v))))))) (sqrt (- (* (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 4)) (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) (* (* v v) 3)) 1)) 4))))) * * * * [misc]progress: [ 631 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (38 enodes) * * [misc]simplify: iters left: 5 (105 enodes) * * [misc]simplify: iters left: 4 (327 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* 9 (* v v)) (* v v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* 9 (* v v)) (* v v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (sqrt 2)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* 9 (* v v)) (* v v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* 9 (* v v)) (* v v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (220 enodes) * * [misc]simplify: iters left: 1 (254 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) (* 3 (* v v))) 1)) 4)) (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) (* 3 (* v v))) 1)) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* 9 (* v v)) (* v v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* 9 (* v v)) (* v v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) (* 3 (* v v))) 1)) 4)) (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) (* 3 (* v v))) 1)) 16))))) * * * * [misc]progress: [ 632 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (363 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (sqrt (+ (* (* 3 v) v) 1)) (* (* (sqrt 2) 4) (sqrt (- 1 (* (* 3 v) v))))) (* (* (* (sqrt 2) 4) (* v (- v))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))))) (sqrt (- (* (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (sqrt (+ (* (* 3 v) v) 1)) (* (* (sqrt 2) 4) (sqrt (- 1 (* (* 3 v) v))))) (* (* (* (sqrt 2) 4) (* v (- v))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))))) (sqrt (- (* (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (85 enodes) * * [misc]simplify: iters left: 3 (138 enodes) * * [misc]simplify: iters left: 2 (233 enodes) * * [misc]simplify: iters left: 1 (293 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) 16)) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (sqrt (+ (* (* 3 v) v) 1)) (* (* (sqrt 2) 4) (sqrt (- 1 (* (* 3 v) v))))) (* (* (* (sqrt 2) 4) (* v (- v))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))))) (sqrt (- (* (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) (* (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) 16)) (sqrt (* (sqrt (+ (* (* 3 v) v) (+ (* (pow v 4) 9) 1))) 4))))) * * * * [misc]progress: [ 633 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (31 enodes) * * [misc]simplify: iters left: 5 (83 enodes) * * [misc]simplify: iters left: 4 (258 enodes) * [exit]simplify: Simplified to (- (* (* (sqrt (+ (* (* v -3) v) 1)) (sqrt 2)) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (/ (sqrt 2) 4) (* v v)) 4))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (* (* (sqrt (+ (* (* v -3) v) 1)) (sqrt 2)) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (/ (sqrt 2) 4) (* v v)) 4))) (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (79 enodes) * * [misc]simplify: iters left: 3 (133 enodes) * * [misc]simplify: iters left: 2 (215 enodes) * * [misc]simplify: iters left: 1 (277 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (pow v 4) 9))) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (* (* (sqrt (+ (* (* v -3) v) 1)) (sqrt 2)) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (/ (sqrt 2) 4) (* v v)) 4))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (pow v 4) 9))) 4))) * * * * [misc]progress: [ 634 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (112 enodes) * * [misc]simplify: iters left: 4 (354 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (+ 1 (* v (* -3 v))))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (* (sqrt 2) (* (sqrt (+ 1 (* v (* -3 v)))) (sqrt (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (/ (sqrt 2) 4)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (+ 1 (* v (* -3 v))))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (* (sqrt 2) (* (sqrt (+ 1 (* v (* -3 v)))) (sqrt (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (/ (sqrt 2) 4)) 4))))) (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (243 enodes) * * [misc]simplify: iters left: 1 (324 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 4)) (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) (* (* v v) 3)) 1)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (+ 1 (* v (* -3 v))))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (* (sqrt 2) (* (sqrt (+ 1 (* v (* -3 v)))) (sqrt (+ (* (* v v) 3) 1)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (/ (sqrt 2) 4)) 4))))) (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 4)) (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) (* (* v v) 3)) 1)) 4))))) * * * * [misc]progress: [ 635 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (36 enodes) * * [misc]simplify: iters left: 5 (100 enodes) * * [misc]simplify: iters left: 4 (326 enodes) * [exit]simplify: Simplified to (* (sqrt (* (+ (- (* v v)) 1) (* (sqrt (- 1 (* (* v v) 3))) (* (sqrt 2) 4)))) (sqrt (- (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (* (sqrt (- 1 (* (* v v) 3))) (sqrt 2))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (+ (- (* v v)) 1) (* (sqrt (- 1 (* (* v v) 3))) (* (sqrt 2) 4)))) (sqrt (- (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (* (sqrt (- 1 (* (* v v) 3))) (sqrt 2))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4))))) (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 4))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (* 4 4))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (85 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (244 enodes) * * [misc]simplify: iters left: 1 (325 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* 3 (* v v)) (+ (* (pow v 4) 9) 1))) 4)) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (+ (- (* v v)) 1) (* (sqrt (- 1 (* (* v v) 3))) (* (sqrt 2) 4)))) (sqrt (- (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (* (sqrt (- 1 (* (* v v) 3))) (sqrt 2))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4))))) (* (sqrt (* (sqrt (+ (* 3 (* v v)) (+ (* (pow v 4) 9) 1))) 4)) 4))) * * * * [misc]progress: [ 636 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3)))) * * [misc]simplify: iters left: 6 (38 enodes) * * [misc]simplify: iters left: 5 (111 enodes) * * [misc]simplify: iters left: 4 (399 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 v) v)))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 v) v)))) 3)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 v) v)))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 v) v)))) 3)))) (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * * [misc]simplify: iters left: 6 (30 enodes) * * [misc]simplify: iters left: 5 (86 enodes) * * [misc]simplify: iters left: 4 (283 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (+ (* (* -3 v) v) 1))) (* (sqrt (+ (* (* -3 v) v) 1)) (- (* (/ (sqrt 2) 4) (- (* v v))) (/ (sqrt 2) 4)))) (* (* (sqrt (+ (* (* -3 v) v) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* -3 v) v) 1)) (/ (sqrt 2) 4))))) (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v (* 3 v)) (* v (* 3 v))))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 v) v)))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 v) v)))) 3)))) (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (+ (* (* -3 v) v) 1))) (* (sqrt (+ (* (* -3 v) v) 1)) (- (* (/ (sqrt 2) 4) (- (* v v))) (/ (sqrt 2) 4)))) (* (* (sqrt (+ (* (* -3 v) v) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* -3 v) v) 1)) (/ (sqrt 2) 4))))) (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v (* 3 v)) (* v (* 3 v))))) 4))))) * * * * [misc]progress: [ 637 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (38 enodes) * * [misc]simplify: iters left: 5 (113 enodes) * * [misc]simplify: iters left: 4 (397 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (* (* (sqrt (- 1 (* 3 (* v v)))) (+ (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (sqrt (- 1 (* 3 (* v v)))) (- (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (* (* (sqrt (- 1 (* 3 (* v v)))) (+ (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (sqrt (- 1 (* 3 (* v v)))) (- (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4))))))) (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (67 enodes) * * [misc]simplify: iters left: 4 (187 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) 4)) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (- 1 (* 3 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (* (* (sqrt (- 1 (* 3 (* v v)))) (+ (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (sqrt (- 1 (* 3 (* v v)))) (- (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4))))))) (* (sqrt (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) 4)) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (- 1 (* 3 (* v v))))))))) * * * * [misc]progress: [ 638 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (119 enodes) * * [misc]simplify: iters left: 4 (383 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))))) (sqrt (- (* (* (sqrt (+ (* -3 (* v v)) 1)) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))))) (sqrt (- (* (* (sqrt (+ (* -3 (* v v)) 1)) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (169 enodes) * * [misc]simplify: iters left: 2 (322 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) 4)) (sqrt (* (+ (* (* 4 (* v v)) (* 9 (* v v))) (+ (* 12 (* v v)) 4)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))))) (sqrt (- (* (* (sqrt (+ (* -3 (* v v)) 1)) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) 4)) (sqrt (* (+ (* (* 4 (* v v)) (* 9 (* v v))) (+ (* 12 (* v v)) 4)) 4))))) * * * * [misc]progress: [ 639 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (122 enodes) * * [misc]simplify: iters left: 4 (379 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (* 4 (sqrt (+ (* (* 3 v) v) 1)))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))))) (sqrt (- (* (* (sqrt 2) (sqrt (+ (* v (* v -3)) 1))) (sqrt (+ (* (* 3 v) v) 1))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (* 4 (sqrt (+ (* (* 3 v) v) 1)))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))))) (sqrt (- (* (* (sqrt 2) (sqrt (+ (* v (* v -3)) 1))) (sqrt (+ (* (* 3 v) v) 1))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (102 enodes) * * [misc]simplify: iters left: 3 (180 enodes) * * [misc]simplify: iters left: 2 (287 enodes) * * [misc]simplify: iters left: 1 (330 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* v v) 3) 1)) 4)) (sqrt (* (* (sqrt (+ (* (* v v) 3) 1)) 16) (sqrt (+ (+ (* (* v v) 3) 1) (* (pow v 4) 9)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (* 4 (sqrt (+ (* (* 3 v) v) 1)))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))))) (sqrt (- (* (* (sqrt 2) (sqrt (+ (* v (* v -3)) 1))) (sqrt (+ (* (* 3 v) v) 1))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (* (sqrt (+ (* (* v v) 3) 1)) 4)) (sqrt (* (* (sqrt (+ (* (* v v) 3) 1)) 16) (sqrt (+ (+ (* (* v v) 3) 1) (* (pow v 4) 9)))))))) * * * * [misc]progress: [ 640 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (407 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (+ (* v (* v -3)) 1))) (sqrt (+ 1 (* (* 3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (- (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (sqrt 2) (sqrt (- 1 (pow (* (* 3 v) v) 3))))) (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (/ (sqrt 2) 4) 4)) (* (* v v) (sqrt (- 1 (pow (* (* 3 v) v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (+ (* v (* v -3)) 1))) (sqrt (+ 1 (* (* 3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (- (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (sqrt 2) (sqrt (- 1 (pow (* (* 3 v) v) 3))))) (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (/ (sqrt 2) 4) 4)) (* (* v v) (sqrt (- 1 (pow (* (* 3 v) v) 3)))))))) (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (164 enodes) * * [misc]simplify: iters left: 2 (337 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) 4)) (sqrt (+ (+ (* v (* v 12)) 4) (* (* v v) (* (* 9 v) (* v 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (+ (* v (* v -3)) 1))) (sqrt (+ 1 (* (* 3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (- (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (sqrt 2) (sqrt (- 1 (pow (* (* 3 v) v) 3))))) (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (/ (sqrt 2) 4) 4)) (* (* v v) (sqrt (- 1 (pow (* (* 3 v) v) 3)))))))) (* (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) 4)) (sqrt (+ (+ (* v (* v 12)) 4) (* (* v v) (* (* 9 v) (* v 4)))))))) * * * * [misc]progress: [ 641 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (111 enodes) * * [misc]simplify: iters left: 4 (338 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* (* v v) (/ (sqrt 2) 4)) 4)) (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v)))))))) (sqrt (- (* (sqrt 2) (* (sqrt (+ (* -3 (* v v)) 1)) (sqrt (+ 1 (* v (* 3 v)))))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* (* v v) (/ (sqrt 2) 4)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* (* v v) (/ (sqrt 2) 4)) 4)) (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v)))))))) (sqrt (- (* (sqrt 2) (* (sqrt (+ (* -3 (* v v)) 1)) (sqrt (+ 1 (* v (* 3 v)))))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* (* v v) (/ (sqrt 2) 4)) 4))))) (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (228 enodes) * * [misc]simplify: iters left: 1 (264 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* v v) 3) 1)) 4)) (sqrt (* (sqrt (+ (+ (* (* v v) 3) 1) (* 9 (pow v 4)))) (* (sqrt (+ (* (* v v) 3) 1)) 4)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt 2)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* (* v v) (/ (sqrt 2) 4)) 4)) (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v)))))))) (sqrt (- (* (sqrt 2) (* (sqrt (+ (* -3 (* v v)) 1)) (sqrt (+ 1 (* v (* 3 v)))))) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (* (* v v) (/ (sqrt 2) 4)) 4))))) (* (sqrt (* (sqrt (+ (* (* v v) 3) 1)) 4)) (sqrt (* (sqrt (+ (+ (* (* v v) 3) 1) (* 9 (pow v 4)))) (* (sqrt (+ (* (* v v) 3) 1)) 4)))))) * * * * [misc]progress: [ 642 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (374 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (* 4 (* (* (- v) v) (sqrt 2))) (sqrt (+ (* (* v v) -3) 1)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (sqrt 2) 4)))) (sqrt (- (* (sqrt (+ 1 (* (* v v) 3))) (* (sqrt (+ (* (* v v) -3) 1)) (sqrt 2))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (* 4 (* (* (- v) v) (sqrt 2))) (sqrt (+ (* (* v v) -3) 1)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (sqrt 2) 4)))) (sqrt (- (* (sqrt (+ 1 (* (* v v) 3))) (* (sqrt (+ (* (* v v) -3) 1)) (sqrt 2))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (138 enodes) * * [misc]simplify: iters left: 2 (227 enodes) * * [misc]simplify: iters left: 1 (262 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) 4)) (sqrt (* 16 (sqrt (+ (+ (* (* 3 v) v) 1) (* (pow v 4) 9)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (* 4 (* (* (- v) v) (sqrt 2))) (sqrt (+ (* (* v v) -3) 1)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (sqrt 2) 4)))) (sqrt (- (* (sqrt (+ 1 (* (* v v) 3))) (* (sqrt (+ (* (* v v) -3) 1)) (sqrt 2))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) 4)) (sqrt (* 16 (sqrt (+ (+ (* (* 3 v) v) 1) (* (pow v 4) 9)))))))) * * * * [misc]progress: [ 643 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (123 enodes) * * [misc]simplify: iters left: 4 (399 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))) (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (- (* (* (sqrt (+ (* -3 (* v v)) 1)) (sqrt 2)) (sqrt (+ 1 (* (* v v) 3)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))) (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (- (* (* (sqrt (+ (* -3 (* v v)) 1)) (sqrt 2)) (sqrt (+ 1 (* (* v v) 3)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (102 enodes) * * [misc]simplify: iters left: 3 (179 enodes) * * [misc]simplify: iters left: 2 (286 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* v v) 3) 1)) 4)) (sqrt (* (* (sqrt (+ (* (* v v) 3) 1)) 16) (sqrt (+ (+ (* (* v v) 3) 1) (* (pow v 4) 9)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))) (* (* (sqrt (+ 1 (* (* v v) 3))) 4) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (- (* (* (sqrt (+ (* -3 (* v v)) 1)) (sqrt 2)) (sqrt (+ 1 (* (* v v) 3)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (* (sqrt (+ (* (* v v) 3) 1)) 4)) (sqrt (* (* (sqrt (+ (* (* v v) 3) 1)) 16) (sqrt (+ (+ (* (* v v) 3) 1) (* (pow v 4) 9)))))))) * * * * [misc]progress: [ 644 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (90 enodes) * * [misc]simplify: iters left: 4 (289 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt 2) (* (sqrt (+ (* (* v v) -3) 1)) (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (+ (* (* v (- v)) (sqrt 2)) (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt 2) (* (sqrt (+ (* (* v v) -3) 1)) (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (+ (* (* v (- v)) (sqrt 2)) (sqrt 2)))))) (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * * [misc]simplify: iters left: 2 (50 enodes) * * [misc]simplify: iters left: 1 (86 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 16 (* (* v v) 48))) (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt 2) (* (sqrt (+ (* (* v v) -3) 1)) (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (+ (* (* v (- v)) (sqrt 2)) (sqrt 2)))))) (* (sqrt (+ 16 (* (* v v) 48))) (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 4))))) * * * * [misc]progress: [ 645 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (394 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (+ 1 (* (* 3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))) (* (* (* (sqrt (+ 1 (* (* 3 v) v))) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* v v) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (+ 1 (* (* 3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))) (* (* (* (sqrt (+ 1 (* (* 3 v) v))) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* v v) (/ (sqrt 2) 4)))))) (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (231 enodes) * * [misc]simplify: iters left: 1 (268 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) 1) (* v (* 3 v)))) (* (sqrt (+ (* v (* 3 v)) 1)) 4))) (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (+ 1 (* (* 3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (* v v) (/ (sqrt 2) 4)) 4)))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))) (* (* (* (sqrt (+ 1 (* (* 3 v) v))) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* v v) (/ (sqrt 2) 4)))))) (* (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) 1) (* v (* 3 v)))) (* (sqrt (+ (* v (* 3 v)) 1)) 4))) (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) 4))))) * * * * [misc]progress: [ 646 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (83 enodes) * * [misc]simplify: iters left: 4 (259 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt 2) (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* (* v -3) v) 1)))) (* (sqrt (+ (* (* v v) (* (* v v) -9)) 1)) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (+ (* (sqrt 2) (sqrt (+ (* (* v v) (* (* v v) -9)) 1))) (* (* 4 (* (/ (sqrt 2) 4) (- (* v v)))) (sqrt (+ (* (* v v) (* (* v v) -9)) 1))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt 2) (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* (* v -3) v) 1)))) (* (sqrt (+ (* (* v v) (* (* v v) -9)) 1)) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (+ (* (sqrt 2) (sqrt (+ (* (* v v) (* (* v v) -9)) 1))) (* (* 4 (* (/ (sqrt 2) 4) (- (* v v)))) (sqrt (+ (* (* v v) (* (* v v) -9)) 1))))))) (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (53 enodes) * * [misc]simplify: iters left: 1 (63 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 4 (* (* v v) 12))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt 2) (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* (* v -3) v) 1)))) (* (sqrt (+ (* (* v v) (* (* v v) -9)) 1)) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (+ (* (sqrt 2) (sqrt (+ (* (* v v) (* (* v v) -9)) 1))) (* (* 4 (* (/ (sqrt 2) 4) (- (* v v)))) (sqrt (+ (* (* v v) (* (* v v) -9)) 1))))))) (* (sqrt (+ 4 (* (* v v) 12))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) 4))))) * * * * [misc]progress: [ 647 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (90 enodes) * * [misc]simplify: iters left: 4 (292 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ 1 (* 3 (* v v)))) (* (sqrt (+ (* v (* -3 v)) 1)) (sqrt 2))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* (* (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* -3 v)) 1))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ 1 (* 3 (* v v)))) (* (sqrt (+ (* v (* -3 v)) 1)) (sqrt 2))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* (* (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* -3 v)) 1))))))) (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ 1 (* (* 3 v) v))))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ 1 (* 3 (* v v)))) (* (sqrt (+ (* v (* -3 v)) 1)) (sqrt 2))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* (* (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* -3 v)) 1))))))) (* (sqrt (* 16 (sqrt (+ 1 (* (* 3 v) v))))) (sqrt (* (sqrt (+ 1 (* (* 3 v) v))) 4))))) * * * * [misc]progress: [ 648 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (121 enodes) * * [misc]simplify: iters left: 4 (404 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt 2) (* (sqrt (+ (* v (* v -3)) 1)) (sqrt (+ 1 (* (* v v) 3))))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (- (* (/ (* 4 (sqrt 2)) 4) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt 2) (* (sqrt (+ (* v (* v -3)) 1)) (sqrt (+ 1 (* (* v v) 3))))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (- (* (/ (* 4 (sqrt 2)) 4) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))))))) (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (85 enodes) * * [misc]simplify: iters left: 3 (152 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * * [misc]simplify: iters left: 1 (436 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) 4)) (sqrt (+ 4 (+ (* 12 (* v v)) (* (pow v 3) (* 36 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt 2) (* (sqrt (+ (* v (* v -3)) 1)) (sqrt (+ 1 (* (* v v) 3))))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (- (* (/ (* 4 (sqrt 2)) 4) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))))))) (* (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) 4)) (sqrt (+ 4 (+ (* 12 (* v v)) (* (pow v 3) (* 36 v)))))))) * * * * [misc]progress: [ 649 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (120 enodes) * * [misc]simplify: iters left: 4 (375 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (* (* 3 v) v) 1)) (* (sqrt 2) (sqrt (+ (* -3 (* v v)) 1)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* 4 (sqrt (+ (* (* 3 v) v) 1))))) (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt 2) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* (* 3 v) v) 1)) (* (sqrt 2) (sqrt (+ (* -3 (* v v)) 1)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* 4 (sqrt (+ (* (* 3 v) v) 1))))) (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt 2) (* v v)))))) (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * * [misc]simplify: iters left: 2 (253 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) 1) (* v (* 3 v)))) (* (sqrt (+ (* v (* 3 v)) 1)) 4))) (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* (* 3 v) v) 1)) (* (sqrt 2) (sqrt (+ (* -3 (* v v)) 1)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* 4 (sqrt (+ (* (* 3 v) v) 1))))) (* (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt 2) (* v v)))))) (* (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) 1) (* v (* 3 v)))) (* (sqrt (+ (* v (* 3 v)) 1)) 4))) (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) 4))))) * * * * [misc]progress: [ 650 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (369 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) (sqrt (- (* (* (sqrt (+ (* v (* -3 v)) 1)) (sqrt 2)) (sqrt (+ 1 (* (* 3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) (sqrt (- (* (* (sqrt (+ (* v (* -3 v)) 1)) (sqrt 2)) (sqrt (+ 1 (* (* 3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (79 enodes) * * [misc]simplify: iters left: 3 (131 enodes) * * [misc]simplify: iters left: 2 (221 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ (* 3 (* v v)) 1) (* 9 (pow v 4)))) (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3))))))) (sqrt (- (* (* (sqrt (+ (* v (* -3 v)) 1)) (sqrt 2)) (sqrt (+ 1 (* (* 3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* 9 (pow v 4)))) (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) 4))))) * * * * [misc]progress: [ 651 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (109 enodes) * * [misc]simplify: iters left: 4 (333 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (+ 1 (* v (* -3 v))))) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (/ (sqrt 2) 4) (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (+ 1 (* v (* -3 v))))) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (/ (sqrt 2) 4) (* v v))))))) (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (131 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (255 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) 1) (* v (* 3 v)))) (sqrt (+ (* v (* 3 v)) 1)))) (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (+ 1 (* v (* -3 v))))) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (/ (sqrt 2) 4) (* v v))))))) (* (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) 1) (* v (* 3 v)))) (sqrt (+ (* v (* 3 v)) 1)))) (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) 4))))) * * * * [misc]progress: [ 652 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (371 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (/ (sqrt 2) 4) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v -3))))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))))) (sqrt (- (* (* (sqrt (+ 1 (* v (* v -3)))) (sqrt 2)) (sqrt (+ 1 (* (* 3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v -3))))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))))) (sqrt (- (* (* (sqrt (+ 1 (* v (* v -3)))) (sqrt 2)) (sqrt (+ 1 (* (* 3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (131 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (255 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) 1) (* v (* 3 v)))) 4)) (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v -3))))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))))) (sqrt (- (* (* (sqrt (+ 1 (* v (* v -3)))) (sqrt 2)) (sqrt (+ 1 (* (* 3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) 1) (* v (* 3 v)))) 4)) (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) 4))))) * * * * [misc]progress: [ 653 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (378 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4)) (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* v v))))) (sqrt (+ (* (sqrt 2) (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* v (* v -3)))))) (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4)) (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* v v))))) (sqrt (+ (* (sqrt 2) (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* v (* v -3)))))) (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))))) (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (156 enodes) * * [misc]simplify: iters left: 2 (261 enodes) * * [misc]simplify: iters left: 1 (297 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) 4)) (sqrt (* (sqrt (+ (+ (* 3 (* v v)) 1) (* 9 (pow v 4)))) (* (sqrt (+ (* 3 (* v v)) 1)) 4)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4)) (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* v v))))) (sqrt (+ (* (sqrt 2) (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* v (* v -3)))))) (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))))) (* (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) 4)) (sqrt (* (sqrt (+ (+ (* 3 (* v v)) 1) (* 9 (pow v 4)))) (* (sqrt (+ (* 3 (* v v)) 1)) 4)))))) * * * * [misc]progress: [ 654 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (89 enodes) * * [misc]simplify: iters left: 4 (286 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (sqrt (+ 1 (* 3 (* v v)))) (* (sqrt 2) (sqrt (+ (* -3 (* v v)) 1)))) (* (* (* (/ (sqrt 2) 4) 4) (* v (- v))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (+ (- (* (* v v) (sqrt 2))) (* (/ (sqrt 2) 4) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (sqrt (+ 1 (* 3 (* v v)))) (* (sqrt 2) (sqrt (+ (* -3 (* v v)) 1)))) (* (* (* (/ (sqrt 2) 4) 4) (* v (- v))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (+ (- (* (* v v) (sqrt 2))) (* (/ (sqrt 2) 4) 4)))))) (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (27 enodes) * * [misc]simplify: iters left: 2 (36 enodes) * * [misc]simplify: iters left: 1 (53 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 4 (* v (* 12 v)))) (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (sqrt (+ 1 (* 3 (* v v)))) (* (sqrt 2) (sqrt (+ (* -3 (* v v)) 1)))) (* (* (* (/ (sqrt 2) 4) 4) (* v (- v))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (+ (- (* (* v v) (sqrt 2))) (* (/ (sqrt 2) 4) 4)))))) (* (sqrt (+ 4 (* v (* 12 v)))) (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 4))))) * * * * [misc]progress: [ 655 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (375 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (/ (sqrt 2) 4) (* v v)) (sqrt (+ 1 (* (* 3 v) v))))))) (sqrt (+ (* (* (sqrt (+ (* (* -3 v) v) 1)) (sqrt 2)) (sqrt (+ 1 (* (* 3 v) v)))) (* (* 4 (* (/ (sqrt 2) 4) (* v (- v)))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (/ (sqrt 2) 4) (* v v)) (sqrt (+ 1 (* (* 3 v) v))))))) (sqrt (+ (* (* (sqrt (+ (* (* -3 v) v) 1)) (sqrt 2)) (sqrt (+ 1 (* (* 3 v) v)))) (* (* 4 (* (/ (sqrt 2) 4) (* v (- v)))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))))) (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (131 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (255 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) 1) (* v (* 3 v)))) (sqrt (+ (* v (* 3 v)) 1)))) (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (/ (sqrt 2) 4) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (/ (sqrt 2) 4) (* v v)) (sqrt (+ 1 (* (* 3 v) v))))))) (sqrt (+ (* (* (sqrt (+ (* (* -3 v) v) 1)) (sqrt 2)) (sqrt (+ 1 (* (* 3 v) v)))) (* (* 4 (* (/ (sqrt 2) 4) (* v (- v)))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))))) (* (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) 1) (* v (* 3 v)))) (sqrt (+ (* v (* 3 v)) 1)))) (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) 4))))) * * * * [misc]progress: [ 656 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (77 enodes) * * [misc]simplify: iters left: 4 (219 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (sqrt 2) (sqrt (+ 1 (* (* v -3) v)))) (sqrt (+ 1 (* 3 (* v v))))) (* (* (* v (- v)) (* (/ (sqrt 2) 4) 4)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (sqrt (+ 1 (* 3 (* v v)))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt 2) (sqrt (+ 1 (* (* v -3) v)))) (sqrt (+ 1 (* 3 (* v v))))) (* (* (* v (- v)) (* (/ (sqrt 2) 4) 4)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (sqrt (+ 1 (* 3 (* v v)))) (* v v)))))) (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt 2) (sqrt (+ 1 (* (* v -3) v)))) (sqrt (+ 1 (* 3 (* v v))))) (* (* (* v (- v)) (* (/ (sqrt 2) 4) 4)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (sqrt (+ 1 (* 3 (* v v)))) (* v v)))))) (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) 4))))) * * * * [misc]progress: [ 657 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (33 enodes) * * [misc]simplify: iters left: 5 (83 enodes) * * [misc]simplify: iters left: 4 (252 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (sqrt 2) (sqrt (+ (* v (* -3 v)) 1))) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (* (/ (sqrt 2) 4) (* (- v) v))) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))))) (sqrt (- (* (/ (* 4 (sqrt 2)) 4) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* -3 v)) 1))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt 2) (sqrt (+ (* v (* -3 v)) 1))) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (* (/ (sqrt 2) 4) (* (- v) v))) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))))) (sqrt (- (* (/ (* 4 (sqrt 2)) 4) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* -3 v)) 1))))))) (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* (* 3 v) v))) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (sqrt 2) (sqrt (+ (* v (* -3 v)) 1))) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (* (/ (sqrt 2) 4) (* (- v) v))) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))))) (sqrt (- (* (/ (* 4 (sqrt 2)) 4) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* v (* -3 v)) 1))))))) (* (sqrt (+ 1 (* (* 3 v) v))) 4))) * * * * [misc]progress: [ 658 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (353 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ 1 (* (* 3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ 1 (* (* 3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (85 enodes) * * [misc]simplify: iters left: 3 (154 enodes) * * [misc]simplify: iters left: 2 (256 enodes) * * [misc]simplify: iters left: 1 (294 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) 4)) (sqrt (* (sqrt (+ (+ (* 3 (* v v)) 1) (* 9 (pow v 4)))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* 3 v) v)))) (sqrt (+ 1 (* (* 3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) 4)) (sqrt (* (sqrt (+ (+ (* 3 (* v v)) 1) (* 9 (pow v 4)))) 16))))) * * * * [misc]progress: [ 659 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (85 enodes) * * [misc]simplify: iters left: 4 (252 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt 2) (* (sqrt (+ (* v (* -3 v)) 1)) (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (- (* (* (sqrt (+ (* v (* -3 v)) 1)) (sqrt 2)) (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (* (* v v) (sqrt 2)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt 2) (* (sqrt (+ (* v (* -3 v)) 1)) (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (- (* (* (sqrt (+ (* v (* -3 v)) 1)) (sqrt 2)) (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ 1 (* (* v v) 3))))) (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt 2) (* (sqrt (+ (* v (* -3 v)) 1)) (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (- (* (* (sqrt (+ (* v (* -3 v)) 1)) (sqrt 2)) (* (sqrt (+ 1 (* 3 (* v v)))) 4)) (* (sqrt (- 1 (* (* 9 (* v v)) (* v v)))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* 16 (sqrt (+ 1 (* (* v v) 3))))) (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 4))))) * * * * [misc]progress: [ 660 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (112 enodes) * * [misc]simplify: iters left: 4 (345 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt 2) (* (sqrt (- 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* (* (sqrt (- 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt 2) (* (sqrt (- 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* (* (sqrt (- 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (131 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (255 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) 1) (* v (* 3 v)))) 4)) (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt 2) (* (sqrt (- 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (/ (* (sqrt 2) (* v v)) 4) 4)))) (sqrt (- (* (* (sqrt (- 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) (* (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) 1) (* v (* 3 v)))) 4)) (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) 4))))) * * * * [misc]progress: [ 661 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (63 enodes) * * [misc]simplify: iters left: 4 (177 enodes) * [exit]simplify: Simplified to (- (* (sqrt (+ 1 (* 3 (* v v)))) (* (sqrt (+ 1 (* (* v v) -3))) (sqrt 2))) (* (sqrt (- 1 (* (* v v) (* (* v v) 9)))) (* (* (/ (sqrt 2) 4) (* v v)) 4))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (* (sqrt (+ 1 (* 3 (* v v)))) (* (sqrt (+ 1 (* (* v v) -3))) (sqrt 2))) (* (sqrt (- 1 (* (* v v) (* (* v v) 9)))) (* (* (/ (sqrt 2) 4) (* v v)) 4))) (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* (* v v) 3))) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (* (sqrt (+ 1 (* 3 (* v v)))) (* (sqrt (+ 1 (* (* v v) -3))) (sqrt 2))) (* (sqrt (- 1 (* (* v v) (* (* v v) 9)))) (* (* (/ (sqrt 2) 4) (* v v)) 4))) (* (sqrt (+ 1 (* (* v v) 3))) 4))) * * * * [misc]progress: [ 662 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (80 enodes) * * [misc]simplify: iters left: 4 (245 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (+ (* -3 (* v v)) 1))) (* (sqrt (+ (* (* (* v v) -9) (* v v)) 1)) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (* (* (sqrt 2) (sqrt (+ (* -3 (* v v)) 1))) (+ 4 (* (- v) (* v 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (+ (* -3 (* v v)) 1))) (* (sqrt (+ (* (* (* v v) -9) (* v v)) 1)) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (* (* (sqrt 2) (sqrt (+ (* -3 (* v v)) 1))) (+ 4 (* (- v) (* v 4)))))) (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 4))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* 4 4))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * [exit]simplify: Simplified to (* 4 (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (+ (* -3 (* v v)) 1))) (* (sqrt (+ (* (* (* v v) -9) (* v v)) 1)) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (* (* (sqrt 2) (sqrt (+ (* -3 (* v v)) 1))) (+ 4 (* (- v) (* v 4)))))) (* 4 (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) 4))))) * * * * [misc]progress: [ 663 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3)))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (92 enodes) * * [misc]simplify: iters left: 4 (326 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ 1 (* 3 (* v v)))) (* (sqrt (+ (* v (* v -3)) 1)) (sqrt 2))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (* (pow (* (sqrt (+ (* v (* v -3)) 1)) (/ (sqrt 2) 4)) 3) (+ 1 (* (* v (- v)) (* (* v v) (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ 1 (* 3 (* v v)))) (* (sqrt (+ (* v (* v -3)) 1)) (sqrt 2))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (* (pow (* (sqrt (+ (* v (* v -3)) 1)) (/ (sqrt 2) 4)) 3) (+ 1 (* (* v (- v)) (* (* v v) (* v v))))))) (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (69 enodes) * * [misc]simplify: iters left: 4 (227 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 4)) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (+ (* -3 (* v v)) 1))) (* (/ (sqrt 2) 4) (sqrt (+ (* -3 (* v v)) 1)))) (* (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (+ (* -3 (* v v)) 1))) (* (sqrt (+ (* -3 (* v v)) 1)) (- (* (/ (sqrt 2) 4) (- (* v v))) (/ (sqrt 2) 4))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ 1 (* 3 (* v v)))) (* (sqrt (+ (* v (* v -3)) 1)) (sqrt 2))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (* (pow (* (sqrt (+ (* v (* v -3)) 1)) (/ (sqrt 2) 4)) 3) (+ 1 (* (* v (- v)) (* (* v v) (* v v))))))) (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 4)) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (+ (* -3 (* v v)) 1))) (* (/ (sqrt 2) 4) (sqrt (+ (* -3 (* v v)) 1)))) (* (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (+ (* -3 (* v v)) 1))) (* (sqrt (+ (* -3 (* v v)) 1)) (- (* (/ (sqrt 2) 4) (- (* v v))) (/ (sqrt 2) 4))))))))) * * * * [misc]progress: [ 664 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (93 enodes) * * [misc]simplify: iters left: 4 (322 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ 1 (* 3 (* v v)))) (* (sqrt 2) (sqrt (+ (* -3 (* v v)) 1)))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* -3 (* v v)) 1))) (* (sqrt (+ (* -3 (* v v)) 1)) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ 1 (* 3 (* v v)))) (* (sqrt 2) (sqrt (+ (* -3 (* v v)) 1)))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* -3 (* v v)) 1))) (* (sqrt (+ (* -3 (* v v)) 1)) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4))))))) (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (129 enodes) * * [misc]simplify: iters left: 3 (424 enodes) * [exit]simplify: Simplified to (* (sqrt (* (/ (* (+ (* v v) 1) (sqrt 2)) 4) (sqrt (+ (* v (* -3 v)) 1)))) (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ 1 (* 3 (* v v)))) (* (sqrt 2) (sqrt (+ (* -3 (* v v)) 1)))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* -3 (* v v)) 1))) (* (sqrt (+ (* -3 (* v v)) 1)) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4))))))) (* (sqrt (* (/ (* (+ (* v v) 1) (sqrt 2)) 4) (sqrt (+ (* v (* -3 v)) 1)))) (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) 4))))) * * * * [misc]progress: [ 665 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (37 enodes) * * [misc]simplify: iters left: 5 (106 enodes) * * [misc]simplify: iters left: 4 (343 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) 4) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))))) (sqrt (* (* (sqrt 2) (sqrt (- 1 (* (* 3 v) v)))) (+ 4 (* (* 4 v) (- v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) 4) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))))) (sqrt (* (* (sqrt 2) (sqrt (- 1 (* (* 3 v) v)))) (+ 4 (* (* 4 v) (- v)))))) (* (sqrt (* 4 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (98 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (285 enodes) * [exit]simplify: Simplified to (* 4 (sqrt (* (+ (+ 4 (* (* v v) 12)) (* (* (* v v) (* 9 v)) (* v 4))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) 4) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2))))) (sqrt (* (* (sqrt 2) (sqrt (- 1 (* (* 3 v) v)))) (+ 4 (* (* 4 v) (- v)))))) (* 4 (sqrt (* (+ (+ 4 (* (* v v) 12)) (* (* (* v v) (* 9 v)) (* v 4))) 4))))) * * * * [misc]progress: [ 666 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (366 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) 4) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* v v) (sqrt 2)))))) (sqrt (* (* (sqrt 2) (sqrt (+ (* v (* -3 v)) 1))) (+ (* (* 4 v) (- v)) 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) 4) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* v v) (sqrt 2)))))) (sqrt (* (* (sqrt 2) (sqrt (+ (* v (* -3 v)) 1))) (+ (* (* 4 v) (- v)) 4)))) (* (sqrt (* 4 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (104 enodes) * * [misc]simplify: iters left: 3 (175 enodes) * * [misc]simplify: iters left: 2 (261 enodes) * * [misc]simplify: iters left: 1 (309 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 16 (sqrt (+ (* (* 3 v) v) 1))) (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))))) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) 4) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* v v) (sqrt 2)))))) (sqrt (* (* (sqrt 2) (sqrt (+ (* v (* -3 v)) 1))) (+ (* (* 4 v) (- v)) 4)))) (* (sqrt (* (* 16 (sqrt (+ (* (* 3 v) v) 1))) (sqrt (+ 1 (+ (* (* 3 v) v) (* (pow v 4) 9)))))) 4))) * * * * [misc]progress: [ 667 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (109 enodes) * * [misc]simplify: iters left: 4 (371 enodes) * [exit]simplify: Simplified to (* (sqrt (* (+ (* v (- v)) 1) (* (* 4 (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))))) (sqrt (- (* (sqrt 2) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (/ (sqrt 2) 4))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (+ (* v (- v)) 1) (* (* 4 (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))))) (sqrt (- (* (sqrt 2) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (/ (sqrt 2) 4))))))) (* (sqrt (* 4 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (169 enodes) * * [misc]simplify: iters left: 2 (340 enodes) * [exit]simplify: Simplified to (* 4 (sqrt (+ (+ (* (* v v) 12) 4) (* (* (* v v) 12) (* (* v v) 3))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (+ (* v (- v)) 1) (* (* 4 (sqrt 2)) (sqrt (- 1 (* 3 (* v v))))))) (sqrt (- (* (sqrt 2) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (/ (sqrt 2) 4))))))) (* 4 (sqrt (+ (+ (* (* v v) 12) 4) (* (* (* v v) 12) (* (* v v) 3))))))) * * * * [misc]progress: [ 668 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (117 enodes) * * [misc]simplify: iters left: 4 (365 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (/ (sqrt 2) 4) (* v v))) (* 4 (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))))))) (sqrt (* (* (sqrt 2) (sqrt (+ 1 (* (* v -3) v)))) (+ 4 (* (* 4 v) (- v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (/ (sqrt 2) 4) (* v v))) (* 4 (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))))))) (sqrt (* (* (sqrt 2) (sqrt (+ 1 (* (* v -3) v)))) (+ 4 (* (* 4 v) (- v)))))) (* (sqrt (* 4 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (95 enodes) * * [misc]simplify: iters left: 3 (151 enodes) * * [misc]simplify: iters left: 2 (250 enodes) * * [misc]simplify: iters left: 1 (326 enodes) * [exit]simplify: Simplified to (* 4 (sqrt (* (sqrt (+ 1 (+ (* (* 3 v) v) (* 9 (pow v 4))))) (* 4 (sqrt (+ (* (* 3 v) v) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* 3 (* v v)) 1)) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (/ (sqrt 2) 4) (* v v))) (* 4 (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))))))) (sqrt (* (* (sqrt 2) (sqrt (+ 1 (* (* v -3) v)))) (+ 4 (* (* 4 v) (- v)))))) (* 4 (sqrt (* (sqrt (+ 1 (+ (* (* 3 v) v) (* 9 (pow v 4))))) (* 4 (sqrt (+ (* (* 3 v) v) 1)))))))) * * * * [misc]progress: [ 669 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (36 enodes) * * [misc]simplify: iters left: 5 (98 enodes) * * [misc]simplify: iters left: 4 (301 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* (* v -3) v) 1)) (sqrt 2)) (+ 4 (* (* 4 v) (- v))))) (sqrt (+ (* (* (* (* (* 4 v) (- v)) (sqrt 2)) (sqrt (+ (* (* v -3) v) 1))) (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v)))))) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (sqrt 2) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* (* v -3) v) 1)) (sqrt 2)) (+ 4 (* (* 4 v) (- v))))) (sqrt (+ (* (* (* (* (* 4 v) (- v)) (sqrt 2)) (sqrt (+ (* (* v -3) v) 1))) (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v)))))) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (sqrt 2) 4))))) (* (sqrt (* 4 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* 4 4)) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (227 enodes) * * [misc]simplify: iters left: 1 (287 enodes) * [exit]simplify: Simplified to (* 4 (sqrt (* 16 (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* (* v -3) v) 1)) (sqrt 2)) (+ 4 (* (* 4 v) (- v))))) (sqrt (+ (* (* (* (* (* 4 v) (- v)) (sqrt 2)) (sqrt (+ (* (* v -3) v) 1))) (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v)))))) (* (sqrt (- 1 (pow (* v (* 3 v)) 3))) (* (sqrt 2) 4))))) (* 4 (sqrt (* 16 (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9))))))))) * * * * [misc]progress: [ 670 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (368 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4)) (* (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* v v) (sqrt 2))))) (sqrt (* (* (sqrt 2) (sqrt (+ 1 (* (* v -3) v)))) (+ (* (* 4 v) (- v)) 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4)) (* (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* v v) (sqrt 2))))) (sqrt (* (* (sqrt 2) (sqrt (+ 1 (* (* v -3) v)))) (+ (* (* 4 v) (- v)) 4)))) (* (sqrt (* 4 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (105 enodes) * * [misc]simplify: iters left: 3 (198 enodes) * * [misc]simplify: iters left: 2 (311 enodes) * * [misc]simplify: iters left: 1 (378 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* 9 (pow v 4)) (+ 1 (* v (* 3 v))))) (* (sqrt (+ 1 (* v (* 3 v)))) 16))) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4)) (* (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* v v) (sqrt 2))))) (sqrt (* (* (sqrt 2) (sqrt (+ 1 (* (* v -3) v)))) (+ (* (* 4 v) (- v)) 4)))) (* (sqrt (* (sqrt (+ (* 9 (pow v 4)) (+ 1 (* v (* 3 v))))) (* (sqrt (+ 1 (* v (* 3 v)))) 16))) 4))) * * * * [misc]progress: [ 671 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (33 enodes) * * [misc]simplify: iters left: 5 (86 enodes) * * [misc]simplify: iters left: 4 (262 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* (* v v) -3) 1)) (sqrt 2)) (+ (* (* 4 v) (- v)) 4))) (sqrt (* (+ (* (- v) v) 1) (* (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt 2))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* (* v v) -3) 1)) (sqrt 2)) (+ (* (* 4 v) (- v)) 4))) (sqrt (* (+ (* (- v) v) 1) (* (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt 2))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))))) (* (sqrt (* 4 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * * [misc]simplify: iters left: 2 (51 enodes) * * [misc]simplify: iters left: 1 (76 enodes) * [exit]simplify: Simplified to (* 4 (sqrt (+ 16 (* (* v v) 48)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* (* v v) -3) 1)) (sqrt 2)) (+ (* (* 4 v) (- v)) 4))) (sqrt (* (+ (* (- v) v) 1) (* (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt 2))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))))))) (* 4 (sqrt (+ 16 (* (* v v) 48)))))) * * * * [misc]progress: [ 672 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (117 enodes) * * [misc]simplify: iters left: 4 (369 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* v v))))) (sqrt (* (+ (* (- v) v) 1) (* (sqrt (+ 1 (* v (* -3 v)))) (* (sqrt 2) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* v v))))) (sqrt (* (+ (* (- v) v) 1) (* (sqrt (+ 1 (* v (* -3 v)))) (* (sqrt 2) 4))))) (* (sqrt (* 4 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (239 enodes) * * [misc]simplify: iters left: 1 (299 enodes) * [exit]simplify: Simplified to (* 4 (sqrt (* (sqrt (+ (* (pow v 4) 9) (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) 4)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* v v))))) (sqrt (* (+ (* (- v) v) 1) (* (sqrt (+ 1 (* v (* -3 v)))) (* (sqrt 2) 4))))) (* 4 (sqrt (* (sqrt (+ (* (pow v 4) 9) (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) 4)))))) * * * * [misc]progress: [ 673 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (89 enodes) * * [misc]simplify: iters left: 4 (292 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 9) (* v v))))) (* (* (sqrt (- 1 (* (* (* v v) 9) (* v v)))) (/ (sqrt 2) 4)) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* v v))))) (sqrt (* (+ (* v (- v)) 1) (* (sqrt (+ (* (* v v) -3) 1)) (* 4 (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 9) (* v v))))) (* (* (sqrt (- 1 (* (* (* v v) 9) (* v v)))) (/ (sqrt 2) 4)) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* v v))))) (sqrt (* (+ (* v (- v)) 1) (* (sqrt (+ (* (* v v) -3) 1)) (* 4 (sqrt 2)))))) (* (sqrt (* 4 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (66 enodes) * [exit]simplify: Simplified to (* 4 (sqrt (+ (* v (* 12 v)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 9) (* v v))))) (* (* (sqrt (- 1 (* (* (* v v) 9) (* v v)))) (/ (sqrt 2) 4)) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* v v))))) (sqrt (* (+ (* v (- v)) 1) (* (sqrt (+ (* (* v v) -3) 1)) (* 4 (sqrt 2)))))) (* 4 (sqrt (+ (* v (* 12 v)) 4))))) * * * * [misc]progress: [ 674 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (78 enodes) * * [misc]simplify: iters left: 4 (220 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt 2) (sqrt (+ 1 (* v (* -3 v))))) (+ 4 (* (* 4 v) (- v))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* -3 v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt 2) (sqrt (+ 1 (* v (* -3 v))))) (+ 4 (* (* 4 v) (- v))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* -3 v))))))))) (* (sqrt (* 4 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* 4 4)) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * [exit]simplify: Simplified to (* 4 (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt 2) (sqrt (+ 1 (* v (* -3 v))))) (+ 4 (* (* 4 v) (- v))))) (sqrt (- (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (* (sqrt (+ 1 (* 3 (* v v)))) 4) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* -3 v))))))))) (* 4 (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 16))))) * * * * [misc]progress: [ 675 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (109 enodes) * * [misc]simplify: iters left: 4 (360 enodes) * [exit]simplify: Simplified to (* (sqrt (* (+ (* v (- v)) 1) (* (sqrt (+ 1 (* (* v v) -3))) (* 4 (sqrt 2))))) (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (+ (* v (- v)) 1) (* (sqrt (+ 1 (* (* v v) -3))) (* 4 (sqrt 2))))) (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* v v) (sqrt 2))))))) (* (sqrt (* 4 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (255 enodes) * * [misc]simplify: iters left: 1 (447 enodes) * [exit]simplify: Simplified to (* 4 (sqrt (+ 4 (+ (* v (* v 12)) (* (* 36 v) (pow v 3)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (+ (* v (- v)) 1) (* (sqrt (+ 1 (* (* v v) -3))) (* 4 (sqrt 2))))) (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* v v) (sqrt 2))))))) (* 4 (sqrt (+ 4 (+ (* v (* v 12)) (* (* 36 v) (pow v 3)))))))) * * * * [misc]progress: [ 676 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (117 enodes) * * [misc]simplify: iters left: 4 (362 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (* (* (sqrt 2) (sqrt (+ 1 (* v (* v -3))))) (+ (* (* 4 v) (- v)) 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (* (* (sqrt 2) (sqrt (+ 1 (* v (* v -3))))) (+ (* (* 4 v) (- v)) 4)))) (* (sqrt (* 4 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * * [misc]simplify: iters left: 2 (252 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (* 4 (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) (* (sqrt (+ (* v (* 3 v)) 1)) 4)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))))) (sqrt (* (* (sqrt 2) (sqrt (+ 1 (* v (* v -3))))) (+ (* (* 4 v) (- v)) 4)))) (* 4 (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) (* (sqrt (+ (* v (* 3 v)) 1)) 4)))))) * * * * [misc]progress: [ 677 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (37 enodes) * * [misc]simplify: iters left: 5 (103 enodes) * * [misc]simplify: iters left: 4 (327 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* v (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* v (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))))))) (sqrt (* (+ (* v (- v)) 1) (* (* 4 (sqrt 2)) (sqrt (+ (* (* v -3) v) 1)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* v (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* v (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))))))) (sqrt (* (+ (* v (- v)) 1) (* (* 4 (sqrt 2)) (sqrt (+ (* (* v -3) v) 1)))))) (* (sqrt (* 4 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (223 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (+ (* 3 (* v v)) (* 9 (pow v 4))))) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* v (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* v (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))))))) (sqrt (* (+ (* v (- v)) 1) (* (* 4 (sqrt 2)) (sqrt (+ (* (* v -3) v) 1)))))) (* (sqrt (+ 1 (+ (* 3 (* v v)) (* 9 (pow v 4))))) 4))) * * * * [misc]progress: [ 678 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (362 enodes) * [exit]simplify: Simplified to (* (sqrt (* (+ (* v (- v)) 1) (* (sqrt (+ (* (* v -3) v) 1)) (* (sqrt 2) 4)))) (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (/ (sqrt 2) 4) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (+ (* v (- v)) 1) (* (sqrt (+ (* (* v -3) v) 1)) (* (sqrt 2) 4)))) (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (/ (sqrt 2) 4) (* v v)))))) (* (sqrt (* 4 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (148 enodes) * * [misc]simplify: iters left: 2 (241 enodes) * * [misc]simplify: iters left: 1 (314 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) (sqrt (+ (* v (* 3 v)) 1)))) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (+ (* v (- v)) 1) (* (sqrt (+ (* (* v -3) v) 1)) (* (sqrt 2) 4)))) (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (/ (sqrt 2) 4) (* v v)))))) (* (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) (sqrt (+ (* v (* 3 v)) 1)))) 4))) * * * * [misc]progress: [ 679 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (36 enodes) * * [misc]simplify: iters left: 5 (97 enodes) * * [misc]simplify: iters left: 4 (289 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* (* v -3) v) 1)) (sqrt 2)) (+ (* (* 4 v) (- v)) 4))) (sqrt (- (* (/ (* 4 (sqrt 2)) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* v -3) v) 1))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* (* v -3) v) 1)) (sqrt 2)) (+ (* (* 4 v) (- v)) 4))) (sqrt (- (* (/ (* 4 (sqrt 2)) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* v -3) v) 1))))))) (* (sqrt (* 4 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* 4 4)) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (133 enodes) * * [misc]simplify: iters left: 2 (213 enodes) * * [misc]simplify: iters left: 1 (248 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) 4)) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* (* v -3) v) 1)) (sqrt 2)) (+ (* (* 4 v) (- v)) 4))) (sqrt (- (* (/ (* 4 (sqrt 2)) 4) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* v -3) v) 1))))))) (* (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) 4)) 4))) * * * * [misc]progress: [ 680 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (117 enodes) * * [misc]simplify: iters left: 4 (366 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (* (+ (* (- v) v) 1) (* (* (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (* (+ (* (- v) v) 1) (* (* (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))))) (* (sqrt (* 4 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (167 enodes) * * [misc]simplify: iters left: 2 (288 enodes) * * [misc]simplify: iters left: 1 (340 enodes) * [exit]simplify: Simplified to (* 4 (sqrt (* (sqrt (+ 1 (+ (* 3 (* v v)) (* 9 (pow v 4))))) (* (sqrt (+ 1 (* 3 (* v v)))) 4)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (* (+ (* (- v) v) 1) (* (* (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))))) (* 4 (sqrt (* (sqrt (+ 1 (+ (* 3 (* v v)) (* 9 (pow v 4))))) (* (sqrt (+ 1 (* 3 (* v v)))) 4)))))) * * * * [misc]progress: [ 681 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (89 enodes) * * [misc]simplify: iters left: 4 (283 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (/ (sqrt 2) 4))) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (sqrt (+ (* (* (* v v) -9) (* v v)) 1)) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (* (* (sqrt 2) (sqrt (+ (* -3 (* v v)) 1))) (+ 4 (* (* 4 v) (- v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (/ (sqrt 2) 4))) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (sqrt (+ (* (* (* v v) -9) (* v v)) 1)) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (* (* (sqrt 2) (sqrt (+ (* -3 (* v v)) 1))) (+ 4 (* (* 4 v) (- v)))))) (* (sqrt (* 4 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * * [misc]simplify: iters left: 2 (39 enodes) * * [misc]simplify: iters left: 1 (56 enodes) * [exit]simplify: Simplified to (* 4 (sqrt (+ (* v (* 12 v)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (/ (sqrt 2) 4))) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (sqrt (+ (* (* (* v v) -9) (* v v)) 1)) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (* (* (sqrt 2) (sqrt (+ (* -3 (* v v)) 1))) (+ 4 (* (* 4 v) (- v)))))) (* 4 (sqrt (+ (* v (* 12 v)) 4))))) * * * * [misc]progress: [ 682 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (364 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2)) (+ (* (* 4 v) (- v)) 4))) (sqrt (+ (* (* (sqrt (+ 1 (* (* 3 v) v))) (* (/ (sqrt 2) 4) (* v (- v)))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2)) (+ (* (* 4 v) (- v)) 4))) (sqrt (+ (* (* (sqrt (+ 1 (* (* 3 v) v))) (* (/ (sqrt 2) 4) (* v (- v)))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))))) (* (sqrt (* 4 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (127 enodes) * * [misc]simplify: iters left: 2 (213 enodes) * * [misc]simplify: iters left: 1 (247 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))))) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* (* 3 v) v))) (sqrt 2)) (+ (* (* 4 v) (- v)) 4))) (sqrt (+ (* (* (sqrt (+ 1 (* (* 3 v) v))) (* (/ (sqrt 2) 4) (* v (- v)))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))))) (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))))) 4))) * * * * [misc]progress: [ 683 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (33 enodes) * * [misc]simplify: iters left: 5 (83 enodes) * * [misc]simplify: iters left: 4 (250 enodes) * [exit]simplify: Simplified to (* (sqrt (* (+ (* (- v) v) 1) (* (sqrt (+ 1 (* (* -3 v) v))) (* 4 (sqrt 2))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* (/ (sqrt 2) 4) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (sqrt (+ 1 (* 3 (* v v)))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (+ (* (- v) v) 1) (* (sqrt (+ 1 (* (* -3 v) v))) (* 4 (sqrt 2))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* (/ (sqrt 2) 4) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (sqrt (+ 1 (* 3 (* v v)))) (* v v)))))) (* (sqrt (* 4 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* (* v v) 3))) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (+ (* (- v) v) 1) (* (sqrt (+ 1 (* (* -3 v) v))) (* 4 (sqrt 2))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* (/ (sqrt 2) 4) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (sqrt (+ 1 (* 3 (* v v)))) (* v v)))))) (* (sqrt (+ 1 (* (* v v) 3))) 4))) * * * * [misc]progress: [ 684 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (77 enodes) * * [misc]simplify: iters left: 4 (218 enodes) * [exit]simplify: Simplified to (* (sqrt (* (+ (* v (- v)) 1) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* v v) -3)))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v v) -3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (+ (* v (- v)) 1) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* v v) -3)))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v v) -3)))))))) (* (sqrt (* 4 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))))) * [enter]simplify: Simplifying (* (sqrt (* 4 4)) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 4)) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (+ (* v (- v)) 1) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* v v) -3)))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) (* v v)) 9)))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v v) -3)))))))) (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 4)) 4))) * * * * [misc]progress: [ 685 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (36 enodes) * * [misc]simplify: iters left: 5 (100 enodes) * * [misc]simplify: iters left: 4 (317 enodes) * [exit]simplify: Simplified to (* (sqrt (* (+ (- (* v v)) 1) (* (* 4 (sqrt 2)) (sqrt (+ (* (* -3 v) v) 1))))) (sqrt (+ (* (* (* 4 (sqrt 2)) (sqrt (+ (* (* -3 v) v) 1))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* 4 (sqrt 2)) (- (* v v))) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (+ (- (* v v)) 1) (* (* 4 (sqrt 2)) (sqrt (+ (* (* -3 v) v) 1))))) (sqrt (+ (* (* (* 4 (sqrt 2)) (sqrt (+ (* (* -3 v) v) 1))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* 4 (sqrt 2)) (- (* v v))) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (* (sqrt (* 4 4)) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 4)) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (225 enodes) * * [misc]simplify: iters left: 1 (287 enodes) * [exit]simplify: Simplified to (* 4 (sqrt (* 16 (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (+ (- (* v v)) 1) (* (* 4 (sqrt 2)) (sqrt (+ (* (* -3 v) v) 1))))) (sqrt (+ (* (* (* 4 (sqrt 2)) (sqrt (+ (* (* -3 v) v) 1))) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* 4 (sqrt 2)) (- (* v v))) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (* 4 (sqrt (* 16 (sqrt (+ 1 (+ (* (* v v) 3) (* (pow v 4) 9))))))))) * * * * [misc]progress: [ 686 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (80 enodes) * * [misc]simplify: iters left: 4 (242 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt 2) (sqrt (+ 1 (* v (* -3 v))))) (+ (* (- v) (* v 4)) 4))) (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (+ 1 (* v (* -3 v))))) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (* (* (* v v) (sqrt 2)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt 2) (sqrt (+ 1 (* v (* -3 v))))) (+ (* (- v) (* v 4)) 4))) (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (+ 1 (* v (* -3 v))))) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (* (* (* v v) (sqrt 2)) 4))))) (* (sqrt (* 4 4)) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 4)) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * [exit]simplify: Simplified to (* 4 (sqrt (* 16 (sqrt (+ 1 (* (* v v) 3)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt 2) (sqrt (+ 1 (* v (* -3 v))))) (+ (* (- v) (* v 4)) 4))) (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (+ 1 (* v (* -3 v))))) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* (* v v) (* v v)) 9))) (* (* (* v v) (sqrt 2)) 4))))) (* 4 (sqrt (* 16 (sqrt (+ 1 (* (* v v) 3)))))))) * * * * [misc]progress: [ 687 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (36 enodes) * * [misc]simplify: iters left: 5 (100 enodes) * * [misc]simplify: iters left: 4 (320 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* (* -3 v) v) 1)) (sqrt 2)) (+ 4 (* (* 4 v) (- v))))) (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (+ (* (* -3 v) v) 1)) (sqrt 2))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* (* -3 v) v) 1)) (sqrt 2)) (+ 4 (* (* 4 v) (- v))))) (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (+ (* (* -3 v) v) 1)) (sqrt 2))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) (* (sqrt (* 4 4)) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 4)) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (133 enodes) * * [misc]simplify: iters left: 2 (213 enodes) * * [misc]simplify: iters left: 1 (248 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) 4)) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* (* -3 v) v) 1)) (sqrt 2)) (+ 4 (* (* 4 v) (- v))))) (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt (+ (* (* -3 v) v) 1)) (sqrt 2))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) (* (sqrt (* (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))) 4)) 4))) * * * * [misc]progress: [ 688 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (80 enodes) * * [misc]simplify: iters left: 4 (245 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* -3 (* v v)) 1)) (sqrt 2)) (+ 4 (* (- v) (* v 4))))) (sqrt (- (* (sqrt (+ 1 (* 3 (* v v)))) (* (sqrt (+ (* -3 (* v v)) 1)) (sqrt 2))) (* (sqrt (- 1 (* (* v v) (* 9 (* v v))))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* -3 (* v v)) 1)) (sqrt 2)) (+ 4 (* (- v) (* v 4))))) (sqrt (- (* (sqrt (+ 1 (* 3 (* v v)))) (* (sqrt (+ (* -3 (* v v)) 1)) (sqrt 2))) (* (sqrt (- 1 (* (* v v) (* 9 (* v v))))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) (* (sqrt (* 4 4)) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 4)) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 4)) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* -3 (* v v)) 1)) (sqrt 2)) (+ 4 (* (- v) (* v 4))))) (sqrt (- (* (sqrt (+ 1 (* 3 (* v v)))) (* (sqrt (+ (* -3 (* v v)) 1)) (sqrt 2))) (* (sqrt (- 1 (* (* v v) (* 9 (* v v))))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) (* (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 4)) 4))) * * * * [misc]progress: [ 689 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (294 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* v (* -3 v)))) (* (sqrt 2) (- 4 (* (* 4 v) v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ 1 (* v (* -3 v)))) (* (sqrt 2) (- 4 (* (* 4 v) v)))) (* (sqrt (* 4 4)) (sqrt (* 4 4))))) * [enter]simplify: Simplifying (* (sqrt (* 4 4)) (sqrt (* 4 4))) * * [misc]simplify: iters left: 5 (4 enodes) * * [misc]simplify: iters left: 4 (6 enodes) * [exit]simplify: Simplified to 16 * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ 1 (* v (* -3 v)))) (* (sqrt 2) (- 4 (* (* 4 v) v)))) 16)) * * * * [misc]progress: [ 690 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3)))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (73 enodes) * * [misc]simplify: iters left: 4 (254 enodes) * [exit]simplify: Simplified to (* (sqrt (- (pow (* (sqrt (+ 1 (* v (* v -3)))) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* v -3))))) 3))) (sqrt (* (* (sqrt (+ 1 (* v (* v -3)))) (sqrt 2)) (+ 4 (* (* 4 v) (- v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (pow (* (sqrt (+ 1 (* v (* v -3)))) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* v -3))))) 3))) (sqrt (* (* (sqrt (+ 1 (* v (* v -3)))) (sqrt 2)) (+ 4 (* (* 4 v) (- v)))))) (* (sqrt (* 4 4)) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 4)) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (67 enodes) * * [misc]simplify: iters left: 4 (225 enodes) * [exit]simplify: Simplified to (* 4 (sqrt (- (* (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (- 1 (* (* 3 v) v)))) (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (- 1 (* (* 3 v) v))))) (* (* (sqrt (- 1 (* (* 3 v) v))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* 3 v) v))) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (pow (* (sqrt (+ 1 (* v (* v -3)))) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* v -3))))) 3))) (sqrt (* (* (sqrt (+ 1 (* v (* v -3)))) (sqrt 2)) (+ 4 (* (* 4 v) (- v)))))) (* 4 (sqrt (- (* (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (- 1 (* (* 3 v) v)))) (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (- 1 (* (* 3 v) v))))) (* (* (sqrt (- 1 (* (* 3 v) v))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* 3 v) v))) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))))))))) * * * * [misc]progress: [ 691 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (74 enodes) * * [misc]simplify: iters left: 4 (250 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ 1 (* (* v v) -3))) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* (- v) v)))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v v) -3)))))) (sqrt (* (* 4 (sqrt 2)) (* (sqrt (+ 1 (* (* v v) -3))) (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ 1 (* (* v v) -3))) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* (- v) v)))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v v) -3)))))) (sqrt (* (* 4 (sqrt 2)) (* (sqrt (+ 1 (* (* v v) -3))) (- 1 (* v v)))))) (* (sqrt (* 4 4)) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * [enter]simplify: Simplifying (* (sqrt (* 4 4)) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (127 enodes) * * [misc]simplify: iters left: 3 (411 enodes) * [exit]simplify: Simplified to (* 4 (sqrt (* (sqrt (+ (* (* v v) -3) 1)) (+ (* (* v v) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ 1 (* (* v v) -3))) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* (- v) v)))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v v) -3)))))) (sqrt (* (* 4 (sqrt 2)) (* (sqrt (+ 1 (* (* v v) -3))) (- 1 (* v v)))))) (* 4 (sqrt (* (sqrt (+ (* (* v v) -3) 1)) (+ (* (* v v) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))))))) * * * * [misc]progress: [ 692 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (38 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (418 enodes) * [exit]simplify: Simplified to (* (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* 3 (* v v))))) 3))) (sqrt (* (* 4 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (sqrt 2) (- (* (* v v) (sqrt 2)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* 3 (* v v))))) 3))) (sqrt (* (* 4 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (sqrt 2) (- (* (* v v) (sqrt 2)))))))) (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (31 enodes) * * [misc]simplify: iters left: 5 (92 enodes) * * [misc]simplify: iters left: 4 (299 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (sqrt (+ 1 (* (* -3 v) v))) (- (* (* v (- v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (* v (- v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* -3 v) v))))) (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* -3 v) v)))) (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* -3 v) v))))))) (sqrt (* (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v)))) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* 3 (* v v))))) 3))) (sqrt (* (* 4 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (+ (sqrt 2) (- (* (* v v) (sqrt 2)))))))) (* (sqrt (+ (* (* (sqrt (+ 1 (* (* -3 v) v))) (- (* (* v (- v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (* v (- v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* -3 v) v))))) (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* -3 v) v)))) (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* -3 v) v))))))) (sqrt (* (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v)))) 16))))) * * * * [misc]progress: [ 693 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (126 enodes) * * [misc]simplify: iters left: 4 (446 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* 4 (sqrt (+ (* 3 (* v v)) 1)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4)))) (sqrt (- (pow (* (sqrt (+ (* v (* v -3)) 1)) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1))) 3)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* 4 (sqrt (+ (* 3 (* v v)) 1)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4)))) (sqrt (- (pow (* (sqrt (+ (* v (* v -3)) 1)) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1))) 3)))) (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (97 enodes) * * [misc]simplify: iters left: 4 (306 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (sqrt (+ (* v (* v -3)) 1)) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (- (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1)))) (* (* (sqrt (+ (* v (* v -3)) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* v (* v -3)) 1)) (/ (sqrt 2) 4))))) (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (+ 1 (* (* v v) 3))) 16)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt 2) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* 4 (sqrt (+ (* 3 (* v v)) 1)))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4)))) (sqrt (- (pow (* (sqrt (+ (* v (* v -3)) 1)) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1))) 3)))) (* (sqrt (+ (* (* (sqrt (+ (* v (* v -3)) 1)) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (- (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1)))) (* (* (sqrt (+ (* v (* v -3)) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* v (* v -3)) 1)) (/ (sqrt 2) 4))))) (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt (+ 1 (* (* v v) 3))) 16)))))) * * * * [misc]progress: [ 694 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (447 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt 2) (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt (- 1 (pow (* (* 3 v) v) 3))))) (* (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))) 4) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (/ (sqrt 2) 4) (* v v)))))) (sqrt (- (pow (* (sqrt (- 1 (* (* 3 v) v))) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 v) v)))) 3)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt 2) (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt (- 1 (pow (* (* 3 v) v) 3))))) (* (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))) 4) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (/ (sqrt 2) 4) (* v v)))))) (sqrt (- (pow (* (sqrt (- 1 (* (* 3 v) v))) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 v) v)))) 3)))) (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (31 enodes) * * [misc]simplify: iters left: 5 (90 enodes) * * [misc]simplify: iters left: 4 (290 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* (* (- v) v) (/ (sqrt 2) 4)) (sqrt (+ (* (* -3 v) v) 1))) (* (sqrt (+ (* (* -3 v) v) 1)) (- (* (* (- v) v) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))) (* (* (/ (sqrt 2) 4) (sqrt (+ (* (* -3 v) v) 1))) (* (/ (sqrt 2) 4) (sqrt (+ (* (* -3 v) v) 1)))))) (sqrt (* (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt 2) (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt (- 1 (pow (* (* 3 v) v) 3))))) (* (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))) 4) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (/ (sqrt 2) 4) (* v v)))))) (sqrt (- (pow (* (sqrt (- 1 (* (* 3 v) v))) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 v) v)))) 3)))) (* (sqrt (+ (* (* (* (* (- v) v) (/ (sqrt 2) 4)) (sqrt (+ (* (* -3 v) v) 1))) (* (sqrt (+ (* (* -3 v) v) 1)) (- (* (* (- v) v) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))) (* (* (/ (sqrt 2) 4) (sqrt (+ (* (* -3 v) v) 1))) (* (/ (sqrt 2) 4) (sqrt (+ (* (* -3 v) v) 1)))))) (sqrt (* (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v))) 4))))) * * * * [misc]progress: [ 695 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (124 enodes) * * [misc]simplify: iters left: 4 (441 enodes) * [exit]simplify: Simplified to (* (sqrt (- (pow (* (sqrt (+ 1 (* v (* v -3)))) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* v -3))))) 3))) (sqrt (- (* (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (pow (* (sqrt (+ 1 (* v (* v -3)))) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* v -3))))) 3))) (sqrt (- (* (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* v v)))))) (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (33 enodes) * * [misc]simplify: iters left: 5 (93 enodes) * * [misc]simplify: iters left: 4 (293 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt (+ 1 (* v (* 3 v)))) 4))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (+ (* (* v -3) v) 1))) (* (sqrt (+ (* (* v -3) v) 1)) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))) (* (* (sqrt (+ (* (* v -3) v) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* v -3) v) 1)) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (pow (* (sqrt (+ 1 (* v (* v -3)))) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* v -3))))) 3))) (sqrt (- (* (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* v v)))))) (* (sqrt (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v (* 3 v)) (* v (* 3 v))))) (* (sqrt (+ 1 (* v (* 3 v)))) 4))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (+ (* (* v -3) v) 1))) (* (sqrt (+ (* (* v -3) v) 1)) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))) (* (* (sqrt (+ (* (* v -3) v) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* v -3) v) 1)) (/ (sqrt 2) 4)))))))) * * * * [misc]progress: [ 696 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (113 enodes) * * [misc]simplify: iters left: 4 (408 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (* 4 (* v (* (- v) (sqrt 2)))) (sqrt (+ (* (* -3 v) v) 1)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))))) (sqrt (- (pow (* (sqrt (+ (* (* -3 v) v) 1)) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* -3 v) v) 1))) 3)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (* 4 (* v (* (- v) (sqrt 2)))) (sqrt (+ (* (* -3 v) v) 1)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))))) (sqrt (- (pow (* (sqrt (+ (* (* -3 v) v) 1)) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* -3 v) v) 1))) 3)))) (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))) * * [misc]simplify: iters left: 6 (31 enodes) * * [misc]simplify: iters left: 5 (88 enodes) * * [misc]simplify: iters left: 4 (290 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* (- (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))) (* (sqrt (+ (* (* v -3) v) 1)) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))) (* (* (/ (sqrt 2) 4) (sqrt (+ (* (* v -3) v) 1))) (* (/ (sqrt 2) 4) (sqrt (+ (* (* v -3) v) 1)))))) (sqrt (* 16 (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (* 4 (* v (* (- v) (sqrt 2)))) (sqrt (+ (* (* -3 v) v) 1)))) (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))))) (sqrt (- (pow (* (sqrt (+ (* (* -3 v) v) 1)) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* -3 v) v) 1))) 3)))) (* (sqrt (+ (* (* (* (- (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))) (* (sqrt (+ (* (* v -3) v) 1)) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))) (* (* (/ (sqrt 2) 4) (sqrt (+ (* (* v -3) v) 1))) (* (/ (sqrt 2) 4) (sqrt (+ (* (* v -3) v) 1)))))) (sqrt (* 16 (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v))))))))) * * * * [misc]progress: [ 697 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (126 enodes) * * [misc]simplify: iters left: 4 (448 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v (* 3 v)) (* v (* 3 v))))) 4) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (sqrt 2))) (* (* v v) (* (* (sqrt (+ 1 (* v (* 3 v)))) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* v (* 3 v)) 3))))))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ (* v (* v -3)) 1))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1))) 3)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v (* 3 v)) (* v (* 3 v))))) 4) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (sqrt 2))) (* (* v v) (* (* (sqrt (+ 1 (* v (* 3 v)))) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* v (* 3 v)) 3))))))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ (* v (* v -3)) 1))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1))) 3)))) (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (97 enodes) * * [misc]simplify: iters left: 4 (308 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (sqrt (+ (* v (* -3 v)) 1)) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (+ (* v (* -3 v)) 1)))) (* (* (sqrt (+ (* v (* -3 v)) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* v (* -3 v)) 1)) (/ (sqrt 2) 4))))) (sqrt (* (* (sqrt (+ (* (* v v) 3) 1)) 16) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v (* 3 v)) (* v (* 3 v))))) 4) (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (sqrt 2))) (* (* v v) (* (* (sqrt (+ 1 (* v (* 3 v)))) (* 4 (sqrt 2))) (sqrt (- 1 (pow (* v (* 3 v)) 3))))))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ (* v (* v -3)) 1))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1))) 3)))) (* (sqrt (+ (* (* (sqrt (+ (* v (* -3 v)) 1)) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (+ (* v (* -3 v)) 1)))) (* (* (sqrt (+ (* v (* -3 v)) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* v (* -3 v)) 1)) (/ (sqrt 2) 4))))) (sqrt (* (* (sqrt (+ (* (* v v) 3) 1)) 16) (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))))))) * * * * [misc]progress: [ 698 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (95 enodes) * * [misc]simplify: iters left: 4 (343 enodes) * [exit]simplify: Simplified to (* (sqrt (- (pow (* (sqrt (+ 1 (* (* v v) -3))) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v v) -3)))) 3))) (sqrt (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* (sqrt (+ (* (* v v) (* (* v v) -9)) 1)) (+ (sqrt 2) (* (- v) (* v (sqrt 2)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (pow (* (sqrt (+ 1 (* (* v v) -3))) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v v) -3)))) 3))) (sqrt (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* (sqrt (+ (* (* v v) (* (* v v) -9)) 1)) (+ (sqrt 2) (* (- v) (* v (sqrt 2)))))))) (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (75 enodes) * * [misc]simplify: iters left: 4 (241 enodes) * [exit]simplify: Simplified to (* (fabs (* 4 (sqrt (+ (* (* 3 v) v) 1)))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (* v (- v))) (sqrt (+ (* -3 (* v v)) 1))) (* (sqrt (+ (* -3 (* v v)) 1)) (- (* (* v (- v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))) (* (* (sqrt (+ (* -3 (* v v)) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* -3 (* v v)) 1)) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (pow (* (sqrt (+ 1 (* (* v v) -3))) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v v) -3)))) 3))) (sqrt (* (* (sqrt (+ (* (* 3 v) v) 1)) 4) (* (sqrt (+ (* (* v v) (* (* v v) -9)) 1)) (+ (sqrt 2) (* (- v) (* v (sqrt 2)))))))) (* (fabs (* 4 (sqrt (+ (* (* 3 v) v) 1)))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (* v (- v))) (sqrt (+ (* -3 (* v v)) 1))) (* (sqrt (+ (* -3 (* v v)) 1)) (- (* (* v (- v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))) (* (* (sqrt (+ (* -3 (* v v)) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* -3 (* v v)) 1)) (/ (sqrt 2) 4)))))))) * * * * [misc]progress: [ 699 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (124 enodes) * * [misc]simplify: iters left: 4 (446 enodes) * [exit]simplify: Simplified to (* (sqrt (- (pow (* (sqrt (+ (* v (* v -3)) 1)) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1))) 3))) (sqrt (- (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2))) (* (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (/ (sqrt 2) 4) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (pow (* (sqrt (+ (* v (* v -3)) 1)) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1))) 3))) (sqrt (- (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2))) (* (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (/ (sqrt 2) 4) (* v v)))))) (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (33 enodes) * * [misc]simplify: iters left: 5 (93 enodes) * * [misc]simplify: iters left: 4 (293 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* 4 (sqrt (+ (* (* 3 v) v) 1))))) (sqrt (+ (* (* (* (* (- v) v) (/ (sqrt 2) 4)) (sqrt (+ (* (* -3 v) v) 1))) (* (sqrt (+ (* (* -3 v) v) 1)) (- (* (* (- v) v) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))) (* (* (/ (sqrt 2) 4) (sqrt (+ (* (* -3 v) v) 1))) (* (/ (sqrt 2) 4) (sqrt (+ (* (* -3 v) v) 1))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (pow (* (sqrt (+ (* v (* v -3)) 1)) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1))) 3))) (sqrt (- (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt 2))) (* (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (/ (sqrt 2) 4) (* v v)))))) (* (sqrt (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* 4 (sqrt (+ (* (* 3 v) v) 1))))) (sqrt (+ (* (* (* (* (- v) v) (/ (sqrt 2) 4)) (sqrt (+ (* (* -3 v) v) 1))) (* (sqrt (+ (* (* -3 v) v) 1)) (- (* (* (- v) v) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))) (* (* (/ (sqrt 2) 4) (sqrt (+ (* (* -3 v) v) 1))) (* (/ (sqrt 2) 4) (sqrt (+ (* (* -3 v) v) 1))))))))) * * * * [misc]progress: [ 700 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (97 enodes) * * [misc]simplify: iters left: 4 (368 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt 2)) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* (/ (sqrt 2) 4) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* v v) (* 4 (sqrt (+ (* v (* 3 v)) 1))))))) (sqrt (- (pow (* (sqrt (+ 1 (* v (* v -3)))) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* v -3))))) 3)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt 2)) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* (/ (sqrt 2) 4) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* v v) (* 4 (sqrt (+ (* v (* 3 v)) 1))))))) (sqrt (- (pow (* (sqrt (+ 1 (* v (* v -3)))) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* v -3))))) 3)))) (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (73 enodes) * * [misc]simplify: iters left: 4 (232 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 4 (* 4 (* (* 3 v) v)))) (sqrt (+ (* (* (sqrt (+ (* (* v v) -3) 1)) (- (* (* v (- v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (/ (sqrt 2) 4) (* v (- v))) (sqrt (+ (* (* v v) -3) 1)))) (* (* (sqrt (+ (* (* v v) -3) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* v v) -3) 1)) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt 2)) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* (/ (sqrt 2) 4) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* v v) (* 4 (sqrt (+ (* v (* 3 v)) 1))))))) (sqrt (- (pow (* (sqrt (+ 1 (* v (* v -3)))) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* v -3))))) 3)))) (* (sqrt (+ 4 (* 4 (* (* 3 v) v)))) (sqrt (+ (* (* (sqrt (+ (* (* v v) -3) 1)) (- (* (* v (- v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (/ (sqrt 2) 4) (* v (- v))) (sqrt (+ (* (* v v) -3) 1)))) (* (* (sqrt (+ (* (* v v) -3) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* v v) -3) 1)) (/ (sqrt 2) 4)))))))) * * * * [misc]progress: [ 701 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (94 enodes) * * [misc]simplify: iters left: 4 (335 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* 4 (sqrt 2))) (* (* 4 (sqrt (+ (* v (* 3 v)) 1))) (* (sqrt (+ 1 (* (* v -3) v))) (* (sqrt 2) (* v v)))))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* v -3) v)))) 3) (pow (/ (sqrt (+ 1 (* (* v -3) v))) (/ 4 (* (sqrt 2) (* v v)))) 3)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* 4 (sqrt 2))) (* (* 4 (sqrt (+ (* v (* 3 v)) 1))) (* (sqrt (+ 1 (* (* v -3) v))) (* (sqrt 2) (* v v)))))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* v -3) v)))) 3) (pow (/ (sqrt (+ 1 (* (* v -3) v))) (/ 4 (* (sqrt 2) (* v v)))) 3)))) (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (71 enodes) * * [misc]simplify: iters left: 4 (232 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) 16)) (sqrt (+ (* (* (sqrt (+ (* v (* v -3)) 1)) (- (* (* v (- v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (/ (sqrt 2) 4) (* v (- v))) (sqrt (+ (* v (* v -3)) 1)))) (* (* (sqrt (+ (* v (* v -3)) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* v (* v -3)) 1)) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* 4 (sqrt 2))) (* (* 4 (sqrt (+ (* v (* 3 v)) 1))) (* (sqrt (+ 1 (* (* v -3) v))) (* (sqrt 2) (* v v)))))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* v -3) v)))) 3) (pow (/ (sqrt (+ 1 (* (* v -3) v))) (/ 4 (* (sqrt 2) (* v v)))) 3)))) (* (sqrt (* (sqrt (+ (* 3 (* v v)) 1)) 16)) (sqrt (+ (* (* (sqrt (+ (* v (* v -3)) 1)) (- (* (* v (- v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (/ (sqrt 2) 4) (* v (- v))) (sqrt (+ (* v (* v -3)) 1)))) (* (* (sqrt (+ (* v (* v -3)) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* v (* v -3)) 1)) (/ (sqrt 2) 4)))))))) * * * * [misc]progress: [ 702 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (440 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 v) v)))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 v) v)))) 3)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 v) v)))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 v) v)))) 3)))) (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (31 enodes) * * [misc]simplify: iters left: 5 (88 enodes) * * [misc]simplify: iters left: 4 (289 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (+ (* (* -3 v) v) 1))) (* (sqrt (+ (* (* -3 v) v) 1)) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))) (* (* (sqrt (+ (* (* -3 v) v) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* -3 v) v) 1)) (/ (sqrt 2) 4))))) (sqrt (* (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v))) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* v v) (sqrt 2)))))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 v) v)))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 v) v)))) 3)))) (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (+ (* (* -3 v) v) 1))) (* (sqrt (+ (* (* -3 v) v) 1)) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))) (* (* (sqrt (+ (* (* -3 v) v) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* -3 v) v) 1)) (/ (sqrt 2) 4))))) (sqrt (* (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v))) 4))))) * * * * [misc]progress: [ 703 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (124 enodes) * * [misc]simplify: iters left: 4 (437 enodes) * [exit]simplify: Simplified to (* (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ (* (* v v) -3) 1))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1))) 3))) (sqrt (- (* (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) 4) (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ (* (* v v) -3) 1))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1))) 3))) (sqrt (- (* (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) 4) (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))))) (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (33 enodes) * * [misc]simplify: iters left: 5 (93 enodes) * * [misc]simplify: iters left: 4 (291 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (* (- v) v)) (sqrt (+ (* (* v -3) v) 1))) (* (sqrt (+ (* (* v -3) v) 1)) (- (* (* (- v) v) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))) (* (* (sqrt (+ (* (* v -3) v) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* v -3) v) 1)) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ (* (* v v) -3) 1))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1))) 3))) (sqrt (- (* (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) 4) (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))))) (* (sqrt (* (* 4 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (* (- v) v)) (sqrt (+ (* (* v -3) v) 1))) (* (sqrt (+ (* (* v -3) v) 1)) (- (* (* (- v) v) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))) (* (* (sqrt (+ (* (* v -3) v) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* v -3) v) 1)) (/ (sqrt 2) 4)))))))) * * * * [misc]progress: [ 704 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (37 enodes) * * [misc]simplify: iters left: 5 (110 enodes) * * [misc]simplify: iters left: 4 (403 enodes) * [exit]simplify: Simplified to (* (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 v) v)))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 v) v)))) 3))) (sqrt (- (/ (* (sqrt 2) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (/ 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 v) v)))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 v) v)))) 3))) (sqrt (- (/ (* (sqrt 2) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (/ 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))))))) (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (30 enodes) * * [misc]simplify: iters left: 5 (87 enodes) * * [misc]simplify: iters left: 4 (283 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt (+ (* (* (* (- (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))) (* (sqrt (+ (* (* v -3) v) 1)) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))) (* (* (sqrt (+ (* (* v -3) v) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* v -3) v) 1)) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* 3 v) v)))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 v) v)))) 3))) (sqrt (- (/ (* (sqrt 2) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (/ 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))))) (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))))))) (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt (+ (* (* (* (- (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))) (* (sqrt (+ (* (* v -3) v) 1)) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))) (* (* (sqrt (+ (* (* v -3) v) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* v -3) v) 1)) (/ (sqrt 2) 4)))))))) * * * * [misc]progress: [ 705 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (122 enodes) * * [misc]simplify: iters left: 4 (424 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* v (* 3 v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) (/ (sqrt 2) 4)) (* (* v v) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))))))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ (* (* v -3) v) 1))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))) 3)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* v (* 3 v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) (/ (sqrt 2) 4)) (* (* v v) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))))))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ (* (* v -3) v) 1))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))) 3)))) (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (89 enodes) * * [misc]simplify: iters left: 4 (282 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v (* 3 v)) (* v (* 3 v))))))) (sqrt (+ (* (* (sqrt (+ 1 (* (* v -3) v))) (- (* (* v (- v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (* v (- v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v))))) (* (* (sqrt (+ 1 (* (* v -3) v))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* (* v -3) v))) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* v (* 3 v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) (/ (sqrt 2) 4)) (* (* v v) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))))))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ (* (* v -3) v) 1))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))) 3)))) (* (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ (+ 1 (* v (* 3 v))) (* (* v (* 3 v)) (* v (* 3 v))))))) (sqrt (+ (* (* (sqrt (+ 1 (* (* v -3) v))) (- (* (* v (- v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (* v (- v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v))))) (* (* (sqrt (+ 1 (* (* v -3) v))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* (* v -3) v))) (/ (sqrt 2) 4)))))))) * * * * [misc]progress: [ 706 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (38 enodes) * * [misc]simplify: iters left: 5 (111 enodes) * * [misc]simplify: iters left: 4 (397 enodes) * [exit]simplify: Simplified to (* (sqrt (- (pow (* (sqrt (+ (* v (* -3 v)) 1)) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* v (* -3 v)) 1))) 3))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (sqrt (+ (* v (* -3 v)) 1)) (* (sqrt 2) (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (pow (* (sqrt (+ (* v (* -3 v)) 1)) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* v (* -3 v)) 1))) 3))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (sqrt (+ (* v (* -3 v)) 1)) (* (sqrt 2) (* v v))))))) (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))) * * [misc]simplify: iters left: 6 (30 enodes) * * [misc]simplify: iters left: 5 (86 enodes) * * [misc]simplify: iters left: 4 (285 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) 4)) (sqrt (+ (* (* (sqrt (+ 1 (* (* v -3) v))) (- (* (* (- v) v) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (* (- v) v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v))))) (* (* (sqrt (+ 1 (* (* v -3) v))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* (* v -3) v))) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (pow (* (sqrt (+ (* v (* -3 v)) 1)) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* v (* -3 v)) 1))) 3))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (sqrt (+ (* v (* -3 v)) 1)) (* (sqrt 2) (* v v))))))) (* (sqrt (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) 4)) (sqrt (+ (* (* (sqrt (+ 1 (* (* v -3) v))) (- (* (* (- v) v) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (* (- v) v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v))))) (* (* (sqrt (+ 1 (* (* v -3) v))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* (* v -3) v))) (/ (sqrt 2) 4)))))))) * * * * [misc]progress: [ 707 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (124 enodes) * * [misc]simplify: iters left: 4 (441 enodes) * [exit]simplify: Simplified to (* (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ (* v (* -3 v)) 1))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* v (* -3 v)) 1))) 3))) (sqrt (- (* (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))) 4) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (sqrt 2) (* v v)) (sqrt (+ 1 (* (* 3 v) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ (* v (* -3 v)) 1))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* v (* -3 v)) 1))) 3))) (sqrt (- (* (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))) 4) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (sqrt 2) (* v v)) (sqrt (+ 1 (* (* 3 v) v)))))))) (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (33 enodes) * * [misc]simplify: iters left: 5 (93 enodes) * * [misc]simplify: iters left: 4 (294 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))) (* 4 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (+ (* (* (* (* (- v) v) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))) (* (sqrt (+ (* (* v -3) v) 1)) (- (* (* (- v) v) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))) (* (* (sqrt (+ (* (* v -3) v) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* v -3) v) 1)) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ (* v (* -3 v)) 1))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* v (* -3 v)) 1))) 3))) (sqrt (- (* (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))) 4) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (sqrt 2) (* v v)) (sqrt (+ 1 (* (* 3 v) v)))))))) (* (sqrt (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))) (* 4 (sqrt (+ 1 (* (* 3 v) v)))))) (sqrt (+ (* (* (* (* (- v) v) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))) (* (sqrt (+ (* (* v -3) v) 1)) (- (* (* (- v) v) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))) (* (* (sqrt (+ (* (* v -3) v) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* v -3) v) 1)) (/ (sqrt 2) 4)))))))) * * * * [misc]progress: [ 708 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (97 enodes) * * [misc]simplify: iters left: 4 (361 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (sqrt (+ (* (* (* v v) -9) (* v v)) 1)) (* (sqrt 2) (* v v)))))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ 1 (* v (* v -3))))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* v -3))))) 3)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (sqrt (+ (* (* (* v v) -9) (* v v)) 1)) (* (sqrt 2) (* v v)))))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ 1 (* v (* v -3))))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* v -3))))) 3)))) (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (71 enodes) * * [misc]simplify: iters left: 4 (231 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (+ (* 3 (* v v)) 1))) (sqrt (+ (* (* (sqrt (+ (* v (* v -3)) 1)) (- (* (* v (- v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (/ (sqrt 2) 4) (* v (- v))) (sqrt (+ (* v (* v -3)) 1)))) (* (* (sqrt (+ (* v (* v -3)) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* v (* v -3)) 1)) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (sqrt (+ (* (* (* v v) -9) (* v v)) 1)) (* (sqrt 2) (* v v)))))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ 1 (* v (* v -3))))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* v -3))))) 3)))) (* (sqrt (* 4 (+ (* 3 (* v v)) 1))) (sqrt (+ (* (* (sqrt (+ (* v (* v -3)) 1)) (- (* (* v (- v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (/ (sqrt 2) 4) (* v (- v))) (sqrt (+ (* v (* v -3)) 1)))) (* (* (sqrt (+ (* v (* v -3)) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* v (* v -3)) 1)) (/ (sqrt 2) 4)))))))) * * * * [misc]progress: [ 709 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (122 enodes) * * [misc]simplify: iters left: 4 (435 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (/ (sqrt 2) 4) (* v v)) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ (* (* v -3) v) 1))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))) 3)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (/ (sqrt 2) 4) (* v v)) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ (* (* v -3) v) 1))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))) 3)))) (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (89 enodes) * * [misc]simplify: iters left: 4 (282 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt (+ 1 (* (* 3 v) v))))) (sqrt (+ (* (* (sqrt (- 1 (* (* 3 v) v))) (- (* (* v (- v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (* v (- v)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 v) v))))) (* (* (sqrt (- 1 (* (* 3 v) v))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* 3 v) v))) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (/ (sqrt 2) 4) (* v v)) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ (* (* v -3) v) 1))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))) 3)))) (* (sqrt (* (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))) (sqrt (+ 1 (* (* 3 v) v))))) (sqrt (+ (* (* (sqrt (- 1 (* (* 3 v) v))) (- (* (* v (- v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (* v (- v)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 v) v))))) (* (* (sqrt (- 1 (* (* 3 v) v))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* 3 v) v))) (/ (sqrt 2) 4)))))))) * * * * [misc]progress: [ 710 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (33 enodes) * * [misc]simplify: iters left: 5 (91 enodes) * * [misc]simplify: iters left: 4 (324 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (+ (* v (* 3 v)) 1))) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (- (* v v)) (* (* (/ (sqrt 2) 4) (sqrt (+ (* v (* 3 v)) 1))) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))))))) (sqrt (- (pow (* (sqrt (+ 1 (* v (* -3 v)))) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* -3 v))))) 3)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (+ (* v (* 3 v)) 1))) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (- (* v v)) (* (* (/ (sqrt 2) 4) (sqrt (+ (* v (* 3 v)) 1))) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))))))) (sqrt (- (pow (* (sqrt (+ 1 (* v (* -3 v)))) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* -3 v))))) 3)))) (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (70 enodes) * * [misc]simplify: iters left: 4 (228 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* v v) 3) 1)) (sqrt (+ (* (* (sqrt (+ 1 (* (* v -3) v))) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (+ 1 (* (* v -3) v))))) (* (* (sqrt (+ 1 (* (* v -3) v))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* (* v -3) v))) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (+ (* v (* 3 v)) 1))) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v)))))) (* (- (* v v)) (* (* (/ (sqrt 2) 4) (sqrt (+ (* v (* 3 v)) 1))) (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))))))) (sqrt (- (pow (* (sqrt (+ 1 (* v (* -3 v)))) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* -3 v))))) 3)))) (* (sqrt (+ (* (* v v) 3) 1)) (sqrt (+ (* (* (sqrt (+ 1 (* (* v -3) v))) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (/ (sqrt 2) 4) (- (* v v))) (sqrt (+ 1 (* (* v -3) v))))) (* (* (sqrt (+ 1 (* (* v -3) v))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* (* v -3) v))) (/ (sqrt 2) 4)))))))) * * * * [misc]progress: [ 711 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (92 enodes) * * [misc]simplify: iters left: 4 (326 enodes) * [exit]simplify: Simplified to (* (sqrt (- (pow (* (sqrt (+ (* v (* -3 v)) 1)) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* v (* -3 v)) 1))) 3))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (+ (* v (* -3 v)) 1)) (* (sqrt 2) (* v v))) (sqrt (+ (* (* 3 v) v) 1)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (pow (* (sqrt (+ (* v (* -3 v)) 1)) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* v (* -3 v)) 1))) 3))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (+ (* v (* -3 v)) 1)) (* (sqrt 2) (* v v))) (sqrt (+ (* (* 3 v) v) 1)))))) (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))))) * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (69 enodes) * * [misc]simplify: iters left: 4 (227 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ (* 3 (* v v)) 1)))) (sqrt (+ (* (* (sqrt (+ 1 (* v (* v -3)))) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (- (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* v -3)))))) (* (* (sqrt (+ 1 (* v (* v -3)))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* v (* v -3)))) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (pow (* (sqrt (+ (* v (* -3 v)) 1)) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* v (* -3 v)) 1))) 3))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (sqrt (+ (* v (* -3 v)) 1)) (* (sqrt 2) (* v v))) (sqrt (+ (* (* 3 v) v) 1)))))) (* (sqrt (* 4 (sqrt (+ (* 3 (* v v)) 1)))) (sqrt (+ (* (* (sqrt (+ 1 (* v (* v -3)))) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (- (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* v -3)))))) (* (* (sqrt (+ 1 (* v (* v -3)))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* v (* v -3)))) (/ (sqrt 2) 4)))))))) * * * * [misc]progress: [ 712 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (113 enodes) * * [misc]simplify: iters left: 4 (409 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* v (* -3 v)))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (pow (* (sqrt (+ 1 (* v (* -3 v)))) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* -3 v))))) 3)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* v (* -3 v)))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (pow (* (sqrt (+ 1 (* v (* -3 v)))) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* -3 v))))) 3)))) (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (31 enodes) * * [misc]simplify: iters left: 5 (91 enodes) * * [misc]simplify: iters left: 4 (291 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* (- (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))) (* (sqrt (+ (* (* v -3) v) 1)) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))) (* (* (sqrt (+ (* (* v -3) v) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* v -3) v) 1)) (/ (sqrt 2) 4))))) (sqrt (* 16 (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* v (* -3 v)))))) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (- (pow (* (sqrt (+ 1 (* v (* -3 v)))) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* -3 v))))) 3)))) (* (sqrt (+ (* (* (* (- (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))) (* (sqrt (+ (* (* v -3) v) 1)) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))) (* (* (sqrt (+ (* (* v -3) v) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* v -3) v) 1)) (/ (sqrt 2) 4))))) (sqrt (* 16 (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v))))))))) * * * * [misc]progress: [ 713 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (94 enodes) * * [misc]simplify: iters left: 4 (330 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* (sqrt (+ 1 (* -3 (* v v)))) (sqrt 2))) (* (sqrt (+ 1 (* (* (* v v) -9) (* v v)))) (* (* (sqrt 2) (* v v)) 4)))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ 1 (* -3 (* v v))))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* -3 (* v v))))) 3)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* (sqrt (+ 1 (* -3 (* v v)))) (sqrt 2))) (* (sqrt (+ 1 (* (* (* v v) -9) (* v v)))) (* (* (sqrt 2) (* v v)) 4)))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ 1 (* -3 (* v v))))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* -3 (* v v))))) 3)))) (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (74 enodes) * * [misc]simplify: iters left: 4 (233 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* v v) 3) 1)) 16)) (sqrt (+ (* (* (sqrt (+ (* -3 (* v v)) 1)) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (- (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* -3 (* v v)) 1)))) (* (* (sqrt (+ (* -3 (* v v)) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* -3 (* v v)) 1)) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* (sqrt (+ 1 (* -3 (* v v)))) (sqrt 2))) (* (sqrt (+ 1 (* (* (* v v) -9) (* v v)))) (* (* (sqrt 2) (* v v)) 4)))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ 1 (* -3 (* v v))))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* -3 (* v v))))) 3)))) (* (sqrt (* (sqrt (+ (* (* v v) 3) 1)) 16)) (sqrt (+ (* (* (sqrt (+ (* -3 (* v v)) 1)) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (- (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* -3 (* v v)) 1)))) (* (* (sqrt (+ (* -3 (* v v)) 1)) (/ (sqrt 2) 4)) (* (sqrt (+ (* -3 (* v v)) 1)) (/ (sqrt 2) 4)))))))) * * * * [misc]progress: [ 714 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (38 enodes) * * [misc]simplify: iters left: 5 (111 enodes) * * [misc]simplify: iters left: 4 (403 enodes) * [exit]simplify: Simplified to (* (sqrt (- (pow (* (sqrt (+ (* v (* -3 v)) 1)) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* v (* -3 v)) 1))) 3))) (sqrt (- (* (* (sqrt 2) (sqrt (+ (* v (* -3 v)) 1))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (pow (* (sqrt (+ (* v (* -3 v)) 1)) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* v (* -3 v)) 1))) 3))) (sqrt (- (* (* (sqrt 2) (sqrt (+ (* v (* -3 v)) 1))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (30 enodes) * * [misc]simplify: iters left: 5 (86 enodes) * * [misc]simplify: iters left: 4 (285 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) 4)) (sqrt (+ (* (* (sqrt (+ 1 (* (* v -3) v))) (- (* (* (- v) v) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (* (- v) v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v))))) (* (* (sqrt (+ 1 (* (* v -3) v))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* (* v -3) v))) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (pow (* (sqrt (+ (* v (* -3 v)) 1)) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* v (* -3 v)) 1))) 3))) (sqrt (- (* (* (sqrt 2) (sqrt (+ (* v (* -3 v)) 1))) (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (* (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v))))) 4)) (sqrt (+ (* (* (sqrt (+ 1 (* (* v -3) v))) (- (* (* (- v) v) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (* (- v) v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v))))) (* (* (sqrt (+ 1 (* (* v -3) v))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* (* v -3) v))) (/ (sqrt 2) 4)))))))) * * * * [misc]progress: [ 715 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (92 enodes) * * [misc]simplify: iters left: 4 (326 enodes) * [exit]simplify: Simplified to (* (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ (* v (* -3 v)) 1))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* v (* -3 v)) 1))) 3))) (sqrt (- (* (sqrt (+ (* (* 3 v) v) 1)) (* (sqrt 2) (sqrt (+ (* v (* -3 v)) 1)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ (* v (* -3 v)) 1))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* v (* -3 v)) 1))) 3))) (sqrt (- (* (sqrt (+ (* (* 3 v) v) 1)) (* (sqrt 2) (sqrt (+ (* v (* -3 v)) 1)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (69 enodes) * * [misc]simplify: iters left: 4 (227 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ (* 3 (* v v)) 1)))) (sqrt (+ (* (* (sqrt (+ 1 (* v (* v -3)))) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (- (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* v -3)))))) (* (* (sqrt (+ 1 (* v (* v -3)))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* v (* v -3)))) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ (* v (* -3 v)) 1))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* v (* -3 v)) 1))) 3))) (sqrt (- (* (sqrt (+ (* (* 3 v) v) 1)) (* (sqrt 2) (sqrt (+ (* v (* -3 v)) 1)))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (* 4 (sqrt (+ (* 3 (* v v)) 1)))) (sqrt (+ (* (* (sqrt (+ 1 (* v (* v -3)))) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (- (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* v -3)))))) (* (* (sqrt (+ 1 (* v (* v -3)))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* v (* v -3)))) (/ (sqrt 2) 4)))))))) * * * * [misc]progress: [ 716 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (73 enodes) * * [misc]simplify: iters left: 4 (254 enodes) * [exit]simplify: Simplified to (* (sqrt (* (+ (* (- v) v) 1) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* -3 (* v v))))))) (sqrt (- (pow (* (sqrt (+ 1 (* -3 (* v v)))) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* -3 (* v v))))) 3)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (+ (* (- v) v) 1) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* -3 (* v v))))))) (sqrt (- (pow (* (sqrt (+ 1 (* -3 (* v v)))) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* -3 (* v v))))) 3)))) (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* 4 4))))) * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* 4 4))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (67 enodes) * * [misc]simplify: iters left: 4 (225 enodes) * [exit]simplify: Simplified to (* 4 (sqrt (+ (* (* (* (* (- v) v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* v -3))))) (* (sqrt (+ 1 (* v (* v -3)))) (- (* (* (- v) v) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))) (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* v (* v -3))))) (* (/ (sqrt 2) 4) (sqrt (+ 1 (* v (* v -3))))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (+ (* (- v) v) 1) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* -3 (* v v))))))) (sqrt (- (pow (* (sqrt (+ 1 (* -3 (* v v)))) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* -3 (* v v))))) 3)))) (* 4 (sqrt (+ (* (* (* (* (- v) v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* v -3))))) (* (sqrt (+ 1 (* v (* v -3)))) (- (* (* (- v) v) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))) (* (* (/ (sqrt 2) 4) (sqrt (+ 1 (* v (* v -3))))) (* (/ (sqrt 2) 4) (sqrt (+ 1 (* v (* v -3))))))))))) * * * * [misc]progress: [ 717 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3))) (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (53 enodes) * * [misc]simplify: iters left: 4 (194 enodes) * [exit]simplify: Simplified to (- (pow (* (sqrt (+ (* v (* v -3)) 1)) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1))) 3)) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (pow (* (sqrt (+ (* v (* v -3)) 1)) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1))) 3)) (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (62 enodes) * * [misc]simplify: iters left: 4 (221 enodes) * [exit]simplify: Simplified to (+ (* (* (* (- (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))) (* (sqrt (+ (* (* v -3) v) 1)) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))) (* (* (/ (sqrt 2) 4) (sqrt (+ (* (* v -3) v) 1))) (* (/ (sqrt 2) 4) (sqrt (+ (* (* v -3) v) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (- (pow (* (sqrt (+ (* v (* v -3)) 1)) (/ (sqrt 2) 4)) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1))) 3)) (+ (* (* (* (- (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))) (* (sqrt (+ (* (* v -3) v) 1)) (- (* (- (* v v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))) (* (* (/ (sqrt 2) 4) (sqrt (+ (* (* v -3) v) 1))) (* (/ (sqrt 2) 4) (sqrt (+ (* (* v -3) v) 1))))))) * * * * [misc]progress: [ 718 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3))) (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (69 enodes) * * [misc]simplify: iters left: 4 (264 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* -3 (* v v)) 1))) (* (sqrt (+ (* -3 (* v v)) 1)) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))))) (sqrt (+ (pow (* (/ (sqrt 2) 4) (sqrt (+ (* -3 (* v v)) 1))) 3) (pow (* (sqrt (+ (* -3 (* v v)) 1)) (* (* (- v) v) (/ (sqrt 2) 4))) 3)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* -3 (* v v)) 1))) (* (sqrt (+ (* -3 (* v v)) 1)) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))))) (sqrt (+ (pow (* (/ (sqrt 2) 4) (sqrt (+ (* -3 (* v v)) 1))) 3) (pow (* (sqrt (+ (* -3 (* v v)) 1)) (* (* (- v) v) (/ (sqrt 2) 4))) 3)))) (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (69 enodes) * * [misc]simplify: iters left: 4 (231 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1)))) (sqrt (+ (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1))) (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1)))) (* (* (/ (sqrt 2) 4) (sqrt (+ (* v (* v -3)) 1))) (* (/ (sqrt 2) 4) (sqrt (+ (* v (* v -3)) 1))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* -3 (* v v)) 1))) (* (sqrt (+ (* -3 (* v v)) 1)) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))))) (sqrt (+ (pow (* (/ (sqrt 2) 4) (sqrt (+ (* -3 (* v v)) 1))) 3) (pow (* (sqrt (+ (* -3 (* v v)) 1)) (* (* (- v) v) (/ (sqrt 2) 4))) 3)))) (* (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1)))) (sqrt (+ (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1))) (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1)))) (* (* (/ (sqrt 2) 4) (sqrt (+ (* v (* v -3)) 1))) (* (/ (sqrt 2) 4) (sqrt (+ (* v (* v -3)) 1))))))))) * * * * [misc]progress: [ 719 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (38 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (421 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (- 1 (* (* 3 v) v))) (+ (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))) (* (sqrt (- 1 (* (* 3 v) v))) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))))) (sqrt (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) 4) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* (* 3 v) v))) (+ (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))) (* (sqrt (- 1 (* (* 3 v) v))) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))))) (sqrt (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) 4) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2)))))) (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (73 enodes) * * [misc]simplify: iters left: 4 (202 enodes) * [exit]simplify: Simplified to (* (fabs (* 4 (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))))) (sqrt (* (* (+ (* v v) 1) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* (* 3 v) v))) (+ (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))) (* (sqrt (- 1 (* (* 3 v) v))) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))))) (sqrt (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) 4) (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (+ (- (* (* v v) (sqrt 2))) (sqrt 2)))))) (* (fabs (* 4 (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))))) (sqrt (* (* (+ (* v v) 1) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1))))))) * * * * [misc]progress: [ 720 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (128 enodes) * * [misc]simplify: iters left: 4 (439 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* 4 (* (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) 4)))) (sqrt (* (* (sqrt (+ 1 (* v (* v -3)))) (- (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4)))) (* (* (+ 1 (- (* v v))) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* v -3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* 4 (* (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) 4)))) (sqrt (* (* (sqrt (+ 1 (* v (* v -3)))) (- (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4)))) (* (* (+ 1 (- (* v v))) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* v -3)))))))) (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (30 enodes) * * [misc]simplify: iters left: 5 (78 enodes) * * [misc]simplify: iters left: 4 (209 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) (* (sqrt (+ (* (* 3 v) v) 1)) 16))) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* 4 (* (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3))))) (* (* (* (* v v) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) 4)))) (sqrt (* (* (sqrt (+ 1 (* v (* v -3)))) (- (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4)))) (* (* (+ 1 (- (* v v))) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* v -3)))))))) (* (sqrt (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ (* (* 3 v) v) 1))) (* (sqrt (+ (* (* 3 v) v) 1)) 16))) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))))))) * * * * [misc]progress: [ 721 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (444 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (* (* (sqrt (- 1 (* (* v v) 3))) (- (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4)))) (* (* (+ 1 (- (* v v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) 3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (* (* (sqrt (- 1 (* (* v v) 3))) (- (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4)))) (* (* (+ 1 (- (* v v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) 3))))))) (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (71 enodes) * * [misc]simplify: iters left: 4 (191 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ (* v (* 3 v)) 1)))) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (+ (* (* 4 (* (- (* v v)) (/ (sqrt 2) 4))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt 2) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (* (* (sqrt (- 1 (* (* v v) 3))) (- (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4)))) (* (* (+ 1 (- (* v v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) 3))))))) (* (sqrt (* 4 (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ (* v (* 3 v)) 1)))) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v)))))))) * * * * [misc]progress: [ 722 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (126 enodes) * * [misc]simplify: iters left: 4 (433 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ 1 (* v (* v -3)))) (+ (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))) (* (sqrt (+ 1 (* v (* v -3)))) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))))) (sqrt (- (* (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ 1 (* v (* v -3)))) (+ (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))) (* (sqrt (+ 1 (* v (* v -3)))) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))))) (sqrt (- (* (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* v v)))))) (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (29 enodes) * * [misc]simplify: iters left: 5 (74 enodes) * * [misc]simplify: iters left: 4 (195 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v))))) (sqrt (* (* (sqrt (+ (* 3 (* v v)) 1)) 4) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ 1 (* v (* v -3)))) (+ (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))) (* (sqrt (+ 1 (* v (* v -3)))) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))))) (sqrt (- (* (* (sqrt (+ 1 (* (* 3 v) v))) (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))) (* v v)))))) (* (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v))))) (sqrt (* (* (sqrt (+ (* 3 (* v v)) 1)) 4) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1)))))))) * * * * [misc]progress: [ 723 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (405 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* 4 (* v (* (- v) (sqrt 2)))) (sqrt (+ (* (* v -3) v) 1))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))))) (sqrt (* (* (sqrt (+ (* (* v -3) v) 1)) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))) (* (sqrt (+ (* (* v -3) v) 1)) (+ (* (* v (- v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* (* 4 (* v (* (- v) (sqrt 2)))) (sqrt (+ (* (* v -3) v) 1))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))))) (sqrt (* (* (sqrt (+ (* (* v -3) v) 1)) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))) (* (sqrt (+ (* (* v -3) v) 1)) (+ (* (* v (- v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))))) (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (69 enodes) * * [misc]simplify: iters left: 4 (191 enodes) * [exit]simplify: Simplified to (* (sqrt (* 16 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))))) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (* 4 (* v (* (- v) (sqrt 2)))) (sqrt (+ (* (* v -3) v) 1))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* v v) 3) 3)))))) (sqrt (* (* (sqrt (+ (* (* v -3) v) 1)) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))) (* (sqrt (+ (* (* v -3) v) 1)) (+ (* (* v (- v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))))) (* (sqrt (* 16 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))))) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v)))))))) * * * * [misc]progress: [ 724 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (44 enodes) * * [misc]simplify: iters left: 5 (128 enodes) * * [misc]simplify: iters left: 4 (448 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2))) (* (sqrt (+ 1 (* 3 (* v v)))) 4)))) (sqrt (* (* (sqrt (+ 1 (* (* v -3) v))) (- (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4)))) (* (sqrt (+ 1 (* (* v -3) v))) (+ (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2))) (* (sqrt (+ 1 (* 3 (* v v)))) 4)))) (sqrt (* (* (sqrt (+ 1 (* (* v -3) v))) (- (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4)))) (* (sqrt (+ 1 (* (* v -3) v))) (+ (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4))))))) (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (30 enodes) * * [misc]simplify: iters left: 5 (78 enodes) * * [misc]simplify: iters left: 4 (211 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* 16 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))))) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt 2))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2))) (* (sqrt (+ 1 (* 3 (* v v)))) 4)))) (sqrt (* (* (sqrt (+ 1 (* (* v -3) v))) (- (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4)))) (* (sqrt (+ 1 (* (* v -3) v))) (+ (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4))))))) (* (sqrt (* (* 16 (sqrt (+ 1 (* (* 3 v) v)))) (sqrt (+ (+ 1 (* (* 3 v) v)) (* (* (* 3 v) v) (* (* 3 v) v)))))) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1))))))) * * * * [misc]progress: [ 725 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (96 enodes) * * [misc]simplify: iters left: 4 (339 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v v) -3)))) (* (sqrt (+ 1 (* (* v v) -3))) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))))) (sqrt (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (+ (* (* (- v) v) (sqrt 2)) (sqrt 2))) (* (sqrt (+ (* 3 (* v v)) 1)) 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v v) -3)))) (* (sqrt (+ 1 (* (* v v) -3))) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))))) (sqrt (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (+ (* (* (- v) v) (sqrt 2)) (sqrt 2))) (* (sqrt (+ (* 3 (* v v)) 1)) 4)))) (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (56 enodes) * * [misc]simplify: iters left: 4 (143 enodes) * * [misc]simplify: iters left: 3 (430 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* v v) -3) 1)) (* (+ 1 (* v v)) (/ (sqrt 2) 4)))) (sqrt (* 16 (+ (* (* v v) 3) 1)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v v) -3)))) (* (sqrt (+ 1 (* (* v v) -3))) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))))) (sqrt (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (+ (* (* (- v) v) (sqrt 2)) (sqrt 2))) (* (sqrt (+ (* 3 (* v v)) 1)) 4)))) (* (sqrt (* (sqrt (+ (* (* v v) -3) 1)) (* (+ 1 (* v v)) (/ (sqrt 2) 4)))) (sqrt (* 16 (+ (* (* v v) 3) 1)))))) * * * * [misc]progress: [ 726 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (126 enodes) * * [misc]simplify: iters left: 4 (446 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (* (+ 1 (* v (- v))) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))) (* (sqrt (+ (* (* v -3) v) 1)) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))))) (sqrt (- (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (/ (* (sqrt 2) (* v v)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (* (+ 1 (* v (- v))) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))) (* (sqrt (+ (* (* v -3) v) 1)) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))))) (sqrt (- (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (/ (* (sqrt 2) (* v v)) 4))))) (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (29 enodes) * * [misc]simplify: iters left: 5 (74 enodes) * * [misc]simplify: iters left: 4 (196 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (- 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (* (+ 1 (* v (- v))) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))) (* (sqrt (+ (* (* v -3) v) 1)) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))))) (sqrt (- (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (sqrt 2)) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))) (* (* (* 4 (sqrt (+ 1 (* (* v v) 3)))) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (/ (* (sqrt 2) (* v v)) 4))))) (* (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (- 1 (* 3 (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))))))) * * * * [misc]progress: [ 727 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (98 enodes) * * [misc]simplify: iters left: 4 (364 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))))) (sqrt (* (* (sqrt (+ 1 (* (* v v) -3))) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v v) -3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))))) (sqrt (* (* (sqrt (+ 1 (* (* v v) -3))) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v v) -3))))))) (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (54 enodes) * * [misc]simplify: iters left: 4 (134 enodes) * * [misc]simplify: iters left: 3 (426 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (/ (sqrt 2) 4) (+ 1 (* v v))) (sqrt (+ (* (* v -3) v) 1)))) (sqrt (+ 4 (* 12 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt 2)) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* v v)) (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v)))))))) (sqrt (* (* (sqrt (+ 1 (* (* v v) -3))) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v v) -3))))))) (* (sqrt (* (* (/ (sqrt 2) 4) (+ 1 (* v v))) (sqrt (+ (* (* v -3) v) 1)))) (sqrt (+ 4 (* 12 (* v v))))))) * * * * [misc]progress: [ 728 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (95 enodes) * * [misc]simplify: iters left: 4 (331 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* (* v v) -9) (* v v))))) (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* (sqrt (+ 1 (* (* v v) -3))) (* (sqrt 2) (* v v)))))) (sqrt (* (* (sqrt (+ 1 (* (* v v) -3))) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v v) -3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* (* v v) -9) (* v v))))) (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* (sqrt (+ 1 (* (* v v) -3))) (* (sqrt 2) (* v v)))))) (sqrt (* (* (sqrt (+ 1 (* (* v v) -3))) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v v) -3))))))) (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (134 enodes) * * [misc]simplify: iters left: 3 (413 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (/ (sqrt 2) 4) (+ (* v v) 1)) (sqrt (+ (* -3 (* v v)) 1)))) (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) 16))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* (* v v) -9) (* v v))))) (* (* 4 (sqrt (+ (* (* 3 v) v) 1))) (* (sqrt (+ 1 (* (* v v) -3))) (* (sqrt 2) (* v v)))))) (sqrt (* (* (sqrt (+ 1 (* (* v v) -3))) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v v) -3))))))) (* (sqrt (* (* (/ (sqrt 2) 4) (+ (* v v) 1)) (sqrt (+ (* -3 (* v v)) 1)))) (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) 16))))) * * * * [misc]progress: [ 729 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (437 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* v v) (sqrt 2)))))) (sqrt (* (* (sqrt (- 1 (* (* v v) 3))) (- (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4)))) (* (* (+ 1 (- (* v v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) 3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* v v) (sqrt 2)))))) (sqrt (* (* (sqrt (- 1 (* (* v v) 3))) (- (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4)))) (* (* (+ 1 (- (* v v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) 3))))))) (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (69 enodes) * * [misc]simplify: iters left: 4 (190 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* v v) (sqrt 2)))))) (sqrt (* (* (sqrt (- 1 (* (* v v) 3))) (- (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4)))) (* (* (+ 1 (- (* v v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) 3))))))) (* (sqrt (* 4 (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1)))) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v)))))))) * * * * [misc]progress: [ 730 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (126 enodes) * * [misc]simplify: iters left: 4 (430 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* (* v -3) v) 1)) (+ (* (* v (- v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (sqrt (+ (* (* v -3) v) 1)) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))))) (sqrt (- (/ (* (sqrt 2) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (/ 4 (* 4 (sqrt (+ (* (* 3 v) v) 1))))) (* (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* (* v -3) v) 1)) (+ (* (* v (- v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (sqrt (+ (* (* v -3) v) 1)) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))))) (sqrt (- (/ (* (sqrt 2) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (/ 4 (* 4 (sqrt (+ (* (* 3 v) v) 1))))) (* (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* v v)))))) (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (29 enodes) * * [misc]simplify: iters left: 5 (74 enodes) * * [misc]simplify: iters left: 4 (194 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v))))) (sqrt (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* (* v -3) v) 1)) (+ (* (* v (- v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (sqrt (+ (* (* v -3) v) 1)) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))))) (sqrt (- (/ (* (sqrt 2) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (/ 4 (* 4 (sqrt (+ (* (* 3 v) v) 1))))) (* (* (sqrt 2) (sqrt (- 1 (* (* (* 3 v) v) (* (* 3 v) v))))) (* (sqrt (+ (+ (* (* 3 v) v) 1) (* (* (* 3 v) v) (* (* 3 v) v)))) (* v v)))))) (* (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v))))) (sqrt (* (* 4 (sqrt (+ (* 3 (* v v)) 1))) (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v)))))))))) * * * * [misc]progress: [ 731 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (37 enodes) * * [misc]simplify: iters left: 5 (112 enodes) * * [misc]simplify: iters left: 4 (400 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (- 1 (* 3 (* v v)))) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))) (* (* (+ 1 (* (- v) v)) (/ (sqrt 2) 4)) (sqrt (- 1 (* 3 (* v v))))))) (sqrt (- (/ (* (sqrt 2) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v)))))) (/ 4 (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* 3 (* v v)))) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))) (* (* (+ 1 (* (- v) v)) (/ (sqrt 2) 4)) (sqrt (- 1 (* 3 (* v v))))))) (sqrt (- (/ (* (sqrt 2) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v)))))) (/ 4 (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* v v)))))) (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (68 enodes) * * [misc]simplify: iters left: 4 (183 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* 3 (* v v)))) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))) (* (* (+ 1 (* (- v) v)) (/ (sqrt 2) 4)) (sqrt (- 1 (* 3 (* v v))))))) (sqrt (- (/ (* (sqrt 2) (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v)))))) (/ 4 (sqrt (- 1 (pow (* 3 (* v v)) 3))))) (* (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) (* v v)))))) (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1))))))) * * * * [misc]progress: [ 732 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (124 enodes) * * [misc]simplify: iters left: 4 (421 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ 1 (* v (* 3 v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (/ (sqrt 2) 4) (* v v))) (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v)))))))) (sqrt (* (* (sqrt (+ (* v (* v -3)) 1)) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))) (* (* (+ 1 (* v (- v))) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* v (* 3 v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (/ (sqrt 2) 4) (* v v))) (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v)))))))) (sqrt (* (* (sqrt (+ (* v (* v -3)) 1)) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))) (* (* (+ 1 (* v (- v))) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1)))))) (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (28 enodes) * * [misc]simplify: iters left: 5 (70 enodes) * * [misc]simplify: iters left: 4 (185 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))))) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* -3 v) v) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ 1 (* v (* 3 v)))) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* v (* 3 v)) 3)))) (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (* (/ (sqrt 2) 4) (* v v))) (sqrt (+ (* (* v (* 3 v)) (* v (* 3 v))) (+ 1 (* v (* 3 v)))))))) (sqrt (* (* (sqrt (+ (* v (* v -3)) 1)) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))) (* (* (+ 1 (* v (- v))) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1)))))) (* (sqrt (* (sqrt (+ (* v (* 3 v)) 1)) (sqrt (+ (+ (* v (* 3 v)) 1) (* (* v (* 3 v)) (* v (* 3 v))))))) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* -3 v) v) 1))))))) * * * * [misc]progress: [ 733 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (38 enodes) * * [misc]simplify: iters left: 5 (113 enodes) * * [misc]simplify: iters left: 4 (398 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ 1 (* v (* v -3)))) (+ (* (* (- v) v) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (sqrt (+ 1 (* v (* v -3)))) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v -3))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ 1 (* v (* v -3)))) (+ (* (* (- v) v) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (sqrt (+ 1 (* v (* v -3)))) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v -3))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))))) (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))))) * [enter]simplify: Simplifying (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (67 enodes) * * [misc]simplify: iters left: 4 (186 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))))) (sqrt (* (* (+ (* v v) 1) (/ (sqrt 2) 4)) (sqrt (+ (* (* -3 v) v) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ 1 (* v (* v -3)))) (+ (* (* (- v) v) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (sqrt (+ 1 (* v (* v -3)))) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* v (* v -3))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))))) (* (sqrt (* 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))))) (sqrt (* (* (+ (* v v) 1) (/ (sqrt 2) 4)) (sqrt (+ (* (* -3 v) v) 1))))))) * * * * [misc]progress: [ 734 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (126 enodes) * * [misc]simplify: iters left: 4 (443 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (+ (* v (* v -3)) 1)) (+ (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))) (* (sqrt (+ (* v (* v -3)) 1)) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))))) (sqrt (- (* (* 4 (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v v) 3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* v (* v -3)) 1)) (+ (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))) (* (sqrt (+ (* v (* v -3)) 1)) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))))) (sqrt (- (* (* 4 (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v v) 3)))))))) (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (29 enodes) * * [misc]simplify: iters left: 5 (74 enodes) * * [misc]simplify: iters left: 4 (196 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (sqrt (+ (* v (* v -3)) 1)) (+ (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))) (* (sqrt (+ (* v (* v -3)) 1)) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))))) (sqrt (- (* (* 4 (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v v) 3)))))))) (* (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))))))) * * * * [misc]progress: [ 735 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (98 enodes) * * [misc]simplify: iters left: 4 (357 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 9) (* v v))))) (* (sqrt (- 1 (* (* (* v v) 9) (* v v)))) (* (sqrt 2) (* v v)))))) (sqrt (* (* (sqrt (+ 1 (* v (* v -3)))) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* v -3)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 9) (* v v))))) (* (sqrt (- 1 (* (* (* v v) 9) (* v v)))) (* (sqrt 2) (* v v)))))) (sqrt (* (* (sqrt (+ 1 (* v (* v -3)))) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* v -3)))))))) (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (133 enodes) * * [misc]simplify: iters left: 3 (412 enodes) * [exit]simplify: Simplified to (* (sqrt (* (/ (* (+ (* v v) 1) (sqrt 2)) 4) (sqrt (+ (* -3 (* v v)) 1)))) (sqrt (+ 4 (* (* (* 3 v) v) 4)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (sqrt (+ (* (* 3 v) v) 1)) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 9) (* v v))))) (* (sqrt (- 1 (* (* (* v v) 9) (* v v)))) (* (sqrt 2) (* v v)))))) (sqrt (* (* (sqrt (+ 1 (* v (* v -3)))) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* v -3)))))))) (* (sqrt (* (/ (* (+ (* v v) 1) (sqrt 2)) 4) (sqrt (+ (* -3 (* v v)) 1)))) (sqrt (+ 4 (* (* (* 3 v) v) 4)))))) * * * * [misc]progress: [ 736 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (124 enodes) * * [misc]simplify: iters left: 4 (433 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (/ (sqrt 2) 4) (* v v)) (sqrt (+ 1 (* (* v v) 3))))))) (sqrt (* (* (sqrt (- 1 (* (* v v) 3))) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))) (* (* (+ 1 (* v (- v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) 3))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (/ (sqrt 2) 4) (* v v)) (sqrt (+ 1 (* (* v v) 3))))))) (sqrt (* (* (sqrt (- 1 (* (* v v) 3))) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))) (* (* (+ 1 (* v (- v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) 3))))))) (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (28 enodes) * * [misc]simplify: iters left: 5 (70 enodes) * * [misc]simplify: iters left: 4 (184 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* -3 v) v) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (/ (sqrt 2) 4) (* v v)) (sqrt (+ 1 (* (* v v) 3))))))) (sqrt (* (* (sqrt (- 1 (* (* v v) 3))) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))) (* (* (+ 1 (* v (- v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) 3))))))) (* (sqrt (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (* (* (+ 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* -3 v) v) 1))))))) * * * * [misc]progress: [ 737 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (33 enodes) * * [misc]simplify: iters left: 5 (92 enodes) * * [misc]simplify: iters left: 4 (320 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* (* v v) -9) (* v v))))) (* (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* (* v v) -9) (* v v))))) (* v v)))) (sqrt (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* -3 v) v)))) (* (sqrt (+ 1 (* (* -3 v) v))) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* (* v v) -9) (* v v))))) (* (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* (* v v) -9) (* v v))))) (* v v)))) (sqrt (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* -3 v) v)))) (* (sqrt (+ 1 (* (* -3 v) v))) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4))))))) (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (130 enodes) * * [misc]simplify: iters left: 3 (395 enodes) * [exit]simplify: Simplified to (* (sqrt (* (/ (* (+ (* v v) 1) (sqrt 2)) 4) (sqrt (+ (* v (* -3 v)) 1)))) (sqrt (+ (* (* 3 v) v) 1))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* (* v v) -9) (* v v))))) (* (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* (* v v) -9) (* v v))))) (* v v)))) (sqrt (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* -3 v) v)))) (* (sqrt (+ 1 (* (* -3 v) v))) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4))))))) (* (sqrt (* (/ (* (+ (* v v) 1) (sqrt 2)) 4) (sqrt (+ (* v (* -3 v)) 1)))) (sqrt (+ (* (* 3 v) v) 1))))) * * * * [misc]progress: [ 738 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (93 enodes) * * [misc]simplify: iters left: 4 (322 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* -3 (* v v)) 1))) (* (sqrt (+ (* -3 (* v v)) 1)) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* (sqrt 2) (sqrt (+ (* (* v v) 3) 1))) (* (sqrt (+ (* -3 (* v v)) 1)) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* -3 (* v v)) 1))) (* (sqrt (+ (* -3 (* v v)) 1)) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* (sqrt 2) (sqrt (+ (* (* v v) 3) 1))) (* (sqrt (+ (* -3 (* v v)) 1)) (* v v)))))) (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))))) * [enter]simplify: Simplifying (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (129 enodes) * * [misc]simplify: iters left: 3 (413 enodes) * [exit]simplify: Simplified to (* (sqrt (* (/ (* (sqrt 2) (+ 1 (* v v))) 4) (sqrt (+ 1 (* (* v -3) v))))) (sqrt (* 4 (sqrt (+ (* (* v v) 3) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* -3 (* v v)) 1))) (* (sqrt (+ (* -3 (* v v)) 1)) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* (sqrt 2) (sqrt (+ (* (* v v) 3) 1))) (* (sqrt (+ (* -3 (* v v)) 1)) (* v v)))))) (* (sqrt (* (/ (* (sqrt 2) (+ 1 (* v v))) 4) (sqrt (+ 1 (* (* v -3) v))))) (sqrt (* 4 (sqrt (+ (* (* v v) 3) 1))))))) * * * * [misc]progress: [ 739 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (115 enodes) * * [misc]simplify: iters left: 4 (406 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* v v) 3)))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (sqrt 2) (* v v)) 4)))) (sqrt (* (* (sqrt (- 1 (* (* v v) 3))) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))) (* (sqrt (- 1 (* (* v v) 3))) (+ (* (* v (- v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* v v) 3)))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (sqrt 2) (* v v)) 4)))) (sqrt (* (* (sqrt (- 1 (* (* v v) 3))) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))) (* (sqrt (- 1 (* (* v v) 3))) (+ (* (* v (- v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))))) (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * [enter]simplify: Simplifying (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (72 enodes) * * [misc]simplify: iters left: 4 (192 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) 16)) (sqrt (* (* (+ (* v v) 1) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* v -3))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (* (* 4 (sqrt 2)) (sqrt (- 1 (* (* v v) 3)))) (sqrt (+ (+ 1 (* (* v v) 3)) (* (* (* v v) 3) (* (* v v) 3))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (sqrt 2) (* v v)) 4)))) (sqrt (* (* (sqrt (- 1 (* (* v v) 3))) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))) (* (sqrt (- 1 (* (* v v) 3))) (+ (* (* v (- v)) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)))))) (* (sqrt (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) 16)) (sqrt (* (* (+ (* v v) 1) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* v -3))))))))) * * * * [misc]progress: [ 740 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (95 enodes) * * [misc]simplify: iters left: 4 (326 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (* v (* 3 v)) 1)) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* v -3) v))))) (* (sqrt (+ 1 (* (* (* v v) -9) (* v v)))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (* (* (sqrt (+ 1 (* (* v -3) v))) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* v (* 3 v)) 1)) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* v -3) v))))) (* (sqrt (+ 1 (* (* (* v v) -9) (* v v)))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (* (* (sqrt (+ 1 (* (* v -3) v))) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v))))))) (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (55 enodes) * * [misc]simplify: iters left: 4 (135 enodes) * * [misc]simplify: iters left: 3 (423 enodes) * [exit]simplify: Simplified to (* (sqrt (* (sqrt (+ (* (* v v) -3) 1)) (* (+ 1 (* v v)) (/ (sqrt 2) 4)))) (sqrt (* 16 (sqrt (+ (* (* 3 v) v) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (* v (* 3 v)) 1)) (* (* 4 (sqrt 2)) (sqrt (+ 1 (* (* v -3) v))))) (* (sqrt (+ 1 (* (* (* v v) -9) (* v v)))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (* (* (sqrt (+ 1 (* (* v -3) v))) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v))))))) (* (sqrt (* (sqrt (+ (* (* v v) -3) 1)) (* (+ 1 (* v v)) (/ (sqrt 2) 4)))) (sqrt (* 16 (sqrt (+ (* (* 3 v) v) 1))))))) * * * * [misc]progress: [ 741 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (38 enodes) * * [misc]simplify: iters left: 5 (113 enodes) * * [misc]simplify: iters left: 4 (402 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (* (+ 1 (- (* v v))) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* -3 v))))) (* (sqrt (+ 1 (* v (* -3 v)))) (- (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4)))))) (sqrt (- (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (sqrt 2) (sqrt (+ 1 (* v (* -3 v)))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (* (+ 1 (- (* v v))) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* -3 v))))) (* (sqrt (+ 1 (* v (* -3 v)))) (- (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4)))))) (sqrt (- (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (sqrt 2) (sqrt (+ 1 (* v (* -3 v)))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * [enter]simplify: Simplifying (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (67 enodes) * * [misc]simplify: iters left: 4 (186 enodes) * [exit]simplify: Simplified to (* (sqrt (* 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))))) (sqrt (* (* (+ (* v v) 1) (/ (sqrt 2) 4)) (sqrt (+ (* (* -3 v) v) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (* (+ 1 (- (* v v))) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* -3 v))))) (* (sqrt (+ 1 (* v (* -3 v)))) (- (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4)))))) (sqrt (- (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ 1 (* (* v v) 3)))) (* (sqrt 2) (sqrt (+ 1 (* v (* -3 v)))))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (* 4 (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))))) (sqrt (* (* (+ (* v v) 1) (/ (sqrt 2) 4)) (sqrt (+ (* (* -3 v) v) 1))))))) * * * * [misc]progress: [ 742 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (93 enodes) * * [misc]simplify: iters left: 4 (322 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1))) (* (sqrt (+ (* (* v v) -3) 1)) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))))) (sqrt (- (* (sqrt 2) (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt (+ (* (* v v) -3) 1)))) (* (sqrt (- 1 (* (* (* v v) 9) (* v v)))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1))) (* (sqrt (+ (* (* v v) -3) 1)) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))))) (sqrt (- (* (sqrt 2) (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt (+ (* (* v v) -3) 1)))) (* (sqrt (- 1 (* (* (* v v) 9) (* v v)))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * [enter]simplify: Simplifying (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (129 enodes) * * [misc]simplify: iters left: 3 (413 enodes) * [exit]simplify: Simplified to (* (sqrt (* (/ (* (sqrt 2) (+ 1 (* v v))) 4) (sqrt (+ 1 (* (* v -3) v))))) (sqrt (* 4 (sqrt (+ (* (* v v) 3) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1))) (* (sqrt (+ (* (* v v) -3) 1)) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))))) (sqrt (- (* (sqrt 2) (* (sqrt (+ (* (* 3 v) v) 1)) (sqrt (+ (* (* v v) -3) 1)))) (* (sqrt (- 1 (* (* (* v v) 9) (* v v)))) (* (* (/ (sqrt 2) 4) (* v v)) 4))))) (* (sqrt (* (/ (* (sqrt 2) (+ 1 (* v v))) 4) (sqrt (+ 1 (* (* v -3) v))))) (sqrt (* 4 (sqrt (+ (* (* v v) 3) 1))))))) * * * * [misc]progress: [ 743 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (74 enodes) * * [misc]simplify: iters left: 4 (250 enodes) * [exit]simplify: Simplified to (* (sqrt (* (- 1 (* v v)) (* (sqrt (+ (* -3 (* v v)) 1)) (* 4 (sqrt 2))))) (sqrt (* (* (sqrt (+ (* -3 (* v v)) 1)) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* -3 (* v v)) 1)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (- 1 (* v v)) (* (sqrt (+ (* -3 (* v v)) 1)) (* 4 (sqrt 2))))) (sqrt (* (* (sqrt (+ (* -3 (* v v)) 1)) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* -3 (* v v)) 1)))))) (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* 4 4))))) * [enter]simplify: Simplifying (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* 4 4))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (127 enodes) * * [misc]simplify: iters left: 3 (428 enodes) * [exit]simplify: Simplified to (* (sqrt (* (/ (* (sqrt 2) (+ 1 (* v v))) 4) (sqrt (+ (* -3 (* v v)) 1)))) 4) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (* (- 1 (* v v)) (* (sqrt (+ (* -3 (* v v)) 1)) (* 4 (sqrt 2))))) (sqrt (* (* (sqrt (+ (* -3 (* v v)) 1)) (- (/ (sqrt 2) 4) (* (* (- v) v) (/ (sqrt 2) 4)))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* -3 (* v v)) 1)))))) (* (sqrt (* (/ (* (sqrt 2) (+ 1 (* v v))) 4) (sqrt (+ (* -3 (* v v)) 1)))) 4))) * * * * [misc]progress: [ 744 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3)))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (69 enodes) * * [misc]simplify: iters left: 4 (267 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (* (- v) v)) (sqrt (+ (* (* v v) -3) 1))) 3) (pow (* (/ (sqrt 2) 4) (sqrt (+ (* (* v v) -3) 1))) 3))) (sqrt (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1))) (* (sqrt (+ (* (* v v) -3) 1)) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* (- v) v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (* (- v) v)) (sqrt (+ (* (* v v) -3) 1))) 3) (pow (* (/ (sqrt 2) 4) (sqrt (+ (* (* v v) -3) 1))) 3))) (sqrt (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1))) (* (sqrt (+ (* (* v v) -3) 1)) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* (- v) v))))))) (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))))) * [enter]simplify: Simplifying (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (69 enodes) * * [misc]simplify: iters left: 4 (231 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1)))) (* (* (sqrt (+ (* v (* v -3)) 1)) (/ (sqrt 2) 4)) (* (* (+ (* v v) 1) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1)))))) (sqrt (* (* (+ (* v v) 1) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (* (- v) v)) (sqrt (+ (* (* v v) -3) 1))) 3) (pow (* (/ (sqrt 2) 4) (sqrt (+ (* (* v v) -3) 1))) 3))) (sqrt (* (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1))) (* (sqrt (+ (* (* v v) -3) 1)) (- (/ (sqrt 2) 4) (* (/ (sqrt 2) 4) (* (- v) v))))))) (* (sqrt (+ (* (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1)))) (* (* (sqrt (+ (* v (* v -3)) 1)) (/ (sqrt 2) 4)) (* (* (+ (* v v) 1) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1)))))) (sqrt (* (* (+ (* v v) 1) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1))))))) * * * * [misc]progress: [ 745 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (54 enodes) * * [misc]simplify: iters left: 4 (189 enodes) * [exit]simplify: Simplified to (* (* (sqrt (+ 1 (* (* -3 v) v))) (- (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4)))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* -3 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (* (sqrt (+ 1 (* (* -3 v) v))) (- (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4)))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* -3 v) v))))) (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * [enter]simplify: Simplifying (* (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (122 enodes) * * [misc]simplify: iters left: 3 (402 enodes) * [exit]simplify: Simplified to (* (/ (* (sqrt 2) (+ 1 (* v v))) 4) (sqrt (+ 1 (* (* v -3) v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (* (sqrt (+ 1 (* (* -3 v) v))) (- (/ (sqrt 2) 4) (* (- (* v v)) (/ (sqrt 2) 4)))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* -3 v) v))))) (* (/ (* (sqrt 2) (+ 1 (* v v))) 4) (sqrt (+ 1 (* (* v -3) v)))))) * * * * [misc]progress: [ 746 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 747 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (cbrt (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (116 enodes) * * [misc]simplify: iters left: 3 (339 enodes) * [exit]simplify: Simplified to (cbrt (sqrt (* (/ (* (- 1 (* v v)) (sqrt 2)) 4) (sqrt (+ 1 (* -3 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (* (cbrt (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (cbrt (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) (cbrt (sqrt (* (/ (* (- 1 (* v v)) (sqrt 2)) 4) (sqrt (+ 1 (* -3 (* v v))))))))) * * * * [misc]progress: [ 748 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (cbrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (116 enodes) * * [misc]simplify: iters left: 3 (339 enodes) * [exit]simplify: Simplified to (sqrt (cbrt (* (/ (* (- 1 (* v v)) (sqrt 2)) 4) (sqrt (+ 1 (* -3 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (cbrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (cbrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) (sqrt (cbrt (* (/ (* (- 1 (* v v)) (sqrt 2)) 4) (sqrt (+ 1 (* -3 (* v v))))))))) * * * * [misc]progress: [ 749 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (116 enodes) * * [misc]simplify: iters left: 3 (339 enodes) * [exit]simplify: Simplified to (sqrt (sqrt (* (/ (* (- 1 (* v v)) (sqrt 2)) 4) (sqrt (+ 1 (* -3 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (sqrt (* (/ (* (- 1 (* v v)) (sqrt 2)) 4) (sqrt (+ 1 (* -3 (* v v))))))))) * * * * [misc]progress: [ 750 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (115 enodes) * * [misc]simplify: iters left: 3 (327 enodes) * [exit]simplify: Simplified to (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt 1)) (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1)))))) * * * * [misc]progress: [ 751 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (+ 1 (- (* v v)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * [exit]simplify: Simplified to (sqrt (- 1 (* v v))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))))) (sqrt (- 1 (* v v))))) * * * * [misc]progress: [ 752 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (116 enodes) * * [misc]simplify: iters left: 3 (339 enodes) * [exit]simplify: Simplified to (sqrt (sqrt (* (/ (* (- 1 (* v v)) (sqrt 2)) 4) (sqrt (+ 1 (* -3 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (sqrt (* (/ (* (- 1 (* v v)) (sqrt 2)) 4) (sqrt (+ 1 (* -3 (* v v))))))))) * * * * [misc]progress: [ 753 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (115 enodes) * * [misc]simplify: iters left: 3 (327 enodes) * [exit]simplify: Simplified to (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) 1) (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1)))))) * * * * [misc]progress: [ 754 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (cbrt (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (117 enodes) * * [misc]simplify: iters left: 3 (335 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (* (/ (* (- 1 (* v v)) (sqrt 2)) 4) (sqrt (- 1 (* (* 3 v) v)))))) (cbrt (sqrt (* (/ (* (- 1 (* v v)) (sqrt 2)) 4) (sqrt (- 1 (* (* 3 v) v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (sqrt (* (/ (* (- 1 (* v v)) (sqrt 2)) 4) (sqrt (- 1 (* (* 3 v) v)))))) (cbrt (sqrt (* (/ (* (- 1 (* v v)) (sqrt 2)) 4) (sqrt (- 1 (* (* 3 v) v))))))) (* (cbrt (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * * * * [misc]progress: [ 755 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (cbrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (cbrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (343 enodes) * [exit]simplify: Simplified to (fabs (cbrt (* (/ (* (sqrt 2) (- 1 (* v v))) 4) (sqrt (+ 1 (* (* v v) -3)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (fabs (cbrt (* (/ (* (sqrt 2) (- 1 (* v v))) 4) (sqrt (+ 1 (* (* v v) -3)))))) (* (sqrt (cbrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * * * * [misc]progress: [ 756 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (116 enodes) * * [misc]simplify: iters left: 3 (339 enodes) * [exit]simplify: Simplified to (sqrt (sqrt (* (/ (* (- 1 (* v v)) (sqrt 2)) 4) (sqrt (+ 1 (* -3 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (sqrt (sqrt (* (/ (* (- 1 (* v v)) (sqrt 2)) 4) (sqrt (+ 1 (* -3 (* v v))))))) (* (sqrt (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * * * * [misc]progress: [ 757 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt 1) * * [misc]simplify: iters left: 1 (2 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 1) to (λ (v) (* 1 (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * * * * [misc]progress: [ 758 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * [exit]simplify: Simplified to (sqrt (* (sqrt (+ (* (* v v) -3) 1)) (/ (sqrt 2) 4))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (sqrt (* (sqrt (+ (* (* v v) -3) 1)) (/ (sqrt 2) 4))) (* (sqrt (+ 1 (- (* v v)))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * * * * [misc]progress: [ 759 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (116 enodes) * * [misc]simplify: iters left: 3 (339 enodes) * [exit]simplify: Simplified to (sqrt (sqrt (* (/ (* (- 1 (* v v)) (sqrt 2)) 4) (sqrt (+ 1 (* -3 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (sqrt (sqrt (* (/ (* (- 1 (* v v)) (sqrt 2)) 4) (sqrt (+ 1 (* -3 (* v v))))))) (* (sqrt (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))))) * * * * [misc]progress: [ 760 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 761 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * * [misc]simplify: iters left: 2 (262 enodes) * [exit]simplify: Simplified to (sqrt (* (+ (+ 4 (* (* v v) 12)) (* (* (* v v) 12) (* (* v v) 3))) 4)) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) (sqrt (* (+ (+ 4 (* (* v v) 12)) (* (* (* v v) 12) (* (* v v) 3))) 4)))) * * * * [misc]progress: [ 762 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (170 enodes) * * [misc]simplify: iters left: 2 (274 enodes) * * [misc]simplify: iters left: 1 (346 enodes) * [exit]simplify: Simplified to (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* 9 (pow v 4)) 1))) (* 16 (sqrt (+ 1 (* v (* 3 v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) (sqrt (* (sqrt (+ (* v (* 3 v)) (+ (* 9 (pow v 4)) 1))) (* 16 (sqrt (+ 1 (* v (* 3 v))))))))) * * * * [misc]progress: [ 763 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (164 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * [exit]simplify: Simplified to (sqrt (+ (* (* (* 12 v) (* 3 v)) (* v v)) (+ (* (* 12 v) v) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) (sqrt (+ (* (* (* 12 v) (* 3 v)) (* v v)) (+ (* (* 12 v) v) 4))))) * * * * [misc]progress: [ 764 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (148 enodes) * * [misc]simplify: iters left: 2 (245 enodes) * * [misc]simplify: iters left: 1 (321 enodes) * [exit]simplify: Simplified to (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (pow v 4) 9))) (* 4 (sqrt (+ 1 (* (* v v) 3)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) (sqrt (* (sqrt (+ (+ 1 (* (* v v) 3)) (* (pow v 4) 9))) (* 4 (sqrt (+ 1 (* (* v v) 3)))))))) * * * * [misc]progress: [ 765 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (213 enodes) * * [misc]simplify: iters left: 1 (243 enodes) * [exit]simplify: Simplified to (sqrt (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (pow v 4) 9))) 16)) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (pow v 4) 9))) 16)))) * * * * [misc]progress: [ 766 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (99 enodes) * * [misc]simplify: iters left: 3 (169 enodes) * * [misc]simplify: iters left: 2 (274 enodes) * * [misc]simplify: iters left: 1 (292 enodes) * [exit]simplify: Simplified to (sqrt (* (* (sqrt (+ (* (* v v) 3) 1)) 16) (sqrt (+ (+ (* (* v v) 3) (* 9 (pow v 4))) 1)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) (sqrt (* (* (sqrt (+ (* (* v v) 3) 1)) 16) (sqrt (+ (+ (* (* v v) 3) (* 9 (pow v 4))) 1)))))) * * * * [misc]progress: [ 767 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * * [misc]simplify: iters left: 1 (72 enodes) * [exit]simplify: Simplified to (sqrt (+ 16 (* 48 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) (sqrt (+ 16 (* 48 (* v v)))))) * * * * [misc]progress: [ 768 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (85 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (233 enodes) * * [misc]simplify: iters left: 1 (290 enodes) * [exit]simplify: Simplified to (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) (sqrt (* (sqrt (+ (+ (* v (* 3 v)) (* (pow v 4) 9)) 1)) (* (sqrt (+ (* v (* 3 v)) 1)) 4))))) * * * * [misc]progress: [ 769 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * * [misc]simplify: iters left: 2 (50 enodes) * * [misc]simplify: iters left: 1 (59 enodes) * [exit]simplify: Simplified to (sqrt (+ 4 (* 12 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) (sqrt (+ 4 (* 12 (* v v)))))) * * * * [misc]progress: [ 770 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (sqrt (* 16 (sqrt (+ 1 (* (* v v) 3))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* 16 (sqrt (+ 1 (* (* v v) 3))))))) * * * * [misc]progress: [ 771 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (166 enodes) * * [misc]simplify: iters left: 2 (310 enodes) * [exit]simplify: Simplified to (sqrt (+ 4 (+ (* (pow v 4) 36) (* (* v v) 12)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) (sqrt (+ 4 (+ (* (pow v 4) 36) (* (* v v) 12)))))) * * * * [misc]progress: [ 772 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (230 enodes) * * [misc]simplify: iters left: 1 (275 enodes) * [exit]simplify: Simplified to (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* v (* 3 v))))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))))))) * * * * [misc]progress: [ 773 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (133 enodes) * * [misc]simplify: iters left: 2 (213 enodes) * * [misc]simplify: iters left: 1 (249 enodes) * [exit]simplify: Simplified to (sqrt (+ 1 (+ (* 3 (* v v)) (* 9 (pow v 4))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) (sqrt (+ 1 (+ (* 3 (* v v)) (* 9 (pow v 4))))))) * * * * [misc]progress: [ 774 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (126 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (269 enodes) * [exit]simplify: Simplified to (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) (sqrt (* (sqrt (+ 1 (* v (* 3 v)))) (sqrt (+ 1 (+ (* v (* 3 v)) (* (pow v 4) 9)))))))) * * * * [misc]progress: [ 775 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (79 enodes) * * [misc]simplify: iters left: 3 (166 enodes) * * [misc]simplify: iters left: 2 (285 enodes) * * [misc]simplify: iters left: 1 (351 enodes) * [exit]simplify: Simplified to (sqrt (* (sqrt (+ 1 (+ (* 3 (* v v)) (* 9 (pow v 4))))) 4)) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (sqrt (+ 1 (+ (* 3 (* v v)) (* 9 (pow v 4))))) 4)))) * * * * [misc]progress: [ 776 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (152 enodes) * * [misc]simplify: iters left: 2 (250 enodes) * * [misc]simplify: iters left: 1 (294 enodes) * [exit]simplify: Simplified to (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (+ 1 (* (pow v 4) 9)) (* 3 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (+ 1 (* (pow v 4) 9)) (* 3 (* v v)))))))) * * * * [misc]progress: [ 777 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * * [misc]simplify: iters left: 2 (33 enodes) * * [misc]simplify: iters left: 1 (50 enodes) * [exit]simplify: Simplified to (sqrt (+ (* 12 (* v v)) 4)) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) (sqrt (+ (* 12 (* v v)) 4)))) * * * * [misc]progress: [ 778 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (134 enodes) * * [misc]simplify: iters left: 2 (235 enodes) * * [misc]simplify: iters left: 1 (319 enodes) * [exit]simplify: Simplified to (sqrt (* (sqrt (+ (+ 1 (* (pow v 4) 9)) (* v (* v 3)))) (sqrt (+ 1 (* v (* v 3)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) (sqrt (* (sqrt (+ (+ 1 (* (pow v 4) 9)) (* v (* v 3)))) (sqrt (+ 1 (* v (* v 3)))))))) * * * * [misc]progress: [ 779 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * [exit]simplify: Simplified to (sqrt (+ 1 (* (* v v) 3))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) (sqrt (+ 1 (* (* v v) 3))))) * * * * [misc]progress: [ 780 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * [exit]simplify: Simplified to (sqrt (* 4 (sqrt (+ 1 (* (* v v) 3))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* 4 (sqrt (+ 1 (* (* v v) 3))))))) * * * * [misc]progress: [ 781 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (138 enodes) * * [misc]simplify: iters left: 2 (214 enodes) * * [misc]simplify: iters left: 1 (248 enodes) * [exit]simplify: Simplified to (sqrt (* 16 (sqrt (+ (+ 1 (* 3 (* v v))) (* 9 (pow v 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) (sqrt (* 16 (sqrt (+ (+ 1 (* 3 (* v v))) (* 9 (pow v 4)))))))) * * * * [misc]progress: [ 782 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * [exit]simplify: Simplified to (sqrt (* 16 (sqrt (+ 1 (* (* v v) 3))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) (sqrt (* 16 (sqrt (+ 1 (* (* v v) 3))))))) * * * * [misc]progress: [ 783 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (77 enodes) * * [misc]simplify: iters left: 3 (131 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (274 enodes) * [exit]simplify: Simplified to (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) (* v (* 3 v))) 1)) 4)) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))))))) (sqrt (* (sqrt (+ (+ (* (pow v 4) 9) (* v (* 3 v))) 1)) 4)))) * * * * [misc]progress: [ 784 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * [exit]simplify: Simplified to (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 4)) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))))))) (sqrt (* (sqrt (+ 1 (* (* v v) 3))) 4)))) * * * * [misc]progress: [ 785 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* 4 4)) * * [misc]simplify: iters left: 3 (3 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to 4 * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) 4)) * * * * [misc]progress: [ 786 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (61 enodes) * * [misc]simplify: iters left: 4 (219 enodes) * [exit]simplify: Simplified to (sqrt (+ (* (* (sqrt (+ 1 (* (* v v) -3))) (- (* (* (- v) v) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (* (- v) v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v v) -3))))) (* (* (sqrt (+ 1 (* (* v v) -3))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* (* v v) -3))) (/ (sqrt 2) 4))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3)))) (sqrt (+ (* (* (sqrt (+ 1 (* (* v v) -3))) (- (* (* (- v) v) (/ (sqrt 2) 4)) (/ (sqrt 2) 4))) (* (* (* (- v) v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v v) -3))))) (* (* (sqrt (+ 1 (* (* v v) -3))) (/ (sqrt 2) 4)) (* (sqrt (+ 1 (* (* v v) -3))) (/ (sqrt 2) 4))))))) * * * * [misc]progress: [ 787 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (121 enodes) * * [misc]simplify: iters left: 3 (410 enodes) * [exit]simplify: Simplified to (sqrt (* (* (/ (sqrt 2) 4) (+ (* v v) 1)) (sqrt (+ (* v (* v -3)) 1)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) (sqrt (* (* (/ (sqrt 2) 4) (+ (* v v) 1)) (sqrt (+ (* v (* v -3)) 1)))))) * * * * [misc]progress: [ 788 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (36 enodes) * * [misc]simplify: iters left: 5 (104 enodes) * * [misc]simplify: iters left: 4 (341 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (sqrt 2) (* (sqrt 2) (* (- v) v)))) (* 4 (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (+ (sqrt 2) (* (sqrt 2) (* (- v) v)))) (* 4 (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3))))))) (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * * * * [misc]progress: [ 789 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (370 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (* (sqrt (+ (* 3 (* v v)) 1)) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) 4) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt 2) (* v v))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4)))) (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (* (sqrt (+ (* 3 (* v v)) 1)) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) 4) (* (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt 2) (* v v))) (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) 4)))) (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * * * * [misc]progress: [ 790 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (37 enodes) * * [misc]simplify: iters left: 5 (106 enodes) * * [misc]simplify: iters left: 4 (368 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* -3 v) v))))) (sqrt (- (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (sqrt 2) (sqrt (- 1 (pow (* (* 3 v) v) 3))))) (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* v v) (/ (sqrt 2) 4))) (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* -3 v) v))))) (sqrt (- (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (sqrt 2) (sqrt (- 1 (pow (* (* 3 v) v) 3))))) (* (* (sqrt (- 1 (pow (* (* 3 v) v) 3))) (* (* v v) (/ (sqrt 2) 4))) (* 4 (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v))))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * * * [misc]progress: [ 791 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (365 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (- 1 (* 3 (* v v)))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (/ (sqrt 2) 4))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (- 1 (* 3 (* v v)))))) (sqrt (- (* (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt 2)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ 1 (* 3 (* v v))))) 4) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* v v) (/ (sqrt 2) 4))))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (sqrt (+ 1 (* 3 (* v v)))))))) * * * * [misc]progress: [ 792 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (37 enodes) * * [misc]simplify: iters left: 5 (103 enodes) * * [misc]simplify: iters left: 4 (337 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (sqrt (- 1 (* (* 3 v) v))) (* (* (sqrt 2) (- (* v v))) 4))))) (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 v) v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (+ (* (* 4 (sqrt 2)) (sqrt (- 1 (pow (* (* 3 v) v) 3)))) (* (sqrt (+ (* (* (* 3 v) v) (* (* 3 v) v)) (+ 1 (* (* 3 v) v)))) (* (sqrt (- 1 (* (* 3 v) v))) (* (* (sqrt 2) (- (* v v))) 4))))) (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 v) v)))))) (sqrt (* (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) 4)))) * * * * [misc]progress: [ 793 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (42 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (373 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) 4) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2))) (* (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (sqrt 2)) (* (* v v) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) 4) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (sqrt 2))) (* (* (* 4 (sqrt (+ (* (* v v) 3) 1))) (sqrt 2)) (* (* v v) (sqrt (- 1 (pow (* (* v v) 3) 3))))))) (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * * * * [misc]progress: [ 794 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (84 enodes) * * [misc]simplify: iters left: 4 (266 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (+ (sqrt 2) (* v (* (- v) (sqrt 2))))) (* 4 (sqrt (+ (* v (* 3 v)) 1))))) (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (sqrt (- 1 (* (* v (* 3 v)) (* v (* 3 v))))) (+ (sqrt 2) (* v (* (- v) (sqrt 2))))) (* 4 (sqrt (+ (* v (* 3 v)) 1))))) (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * * * * [misc]progress: [ 795 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (368 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) 3))))) (sqrt (- (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) 3))))) (sqrt (- (* (sqrt (+ (+ (* (* v v) 3) 1) (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))))) (* (* (sqrt (+ (* (* v v) 3) 1)) (* 4 (/ (sqrt 2) 4))) (* (sqrt (- 1 (pow (* (* v v) 3) 3))) (* v v)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * * * [misc]progress: [ 796 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (33 enodes) * * [misc]simplify: iters left: 5 (86 enodes) * * [misc]simplify: iters left: 4 (291 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* -3 v) v) 1)))) (sqrt (* (sqrt (+ (* (* v v) 3) 1)) (+ (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4)) (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* -3 v) v) 1)))) (sqrt (* (sqrt (+ (* (* v v) 3) 1)) (+ (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (* (- (* v v)) (/ (sqrt 2) 4)) 4)) (* (sqrt 2) (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3))))))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (sqrt (+ 1 (* 3 (* v v)))))))) * * * * [misc]progress: [ 797 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (33 enodes) * * [misc]simplify: iters left: 5 (83 enodes) * * [misc]simplify: iters left: 4 (257 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt 2) 4)) (* (* (sqrt (+ 1 (* (* v v) -3))) (* (sqrt 2) (* v v))) (* 4 (sqrt (+ (* (* v v) 3) 1)))))) (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v v) -3)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* (sqrt 2) 4)) (* (* (sqrt (+ 1 (* (* v v) -3))) (* (sqrt 2) (* v v))) (* 4 (sqrt (+ (* (* v v) 3) 1)))))) (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v v) -3)))))) (sqrt (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) 4)))) * * * * [misc]progress: [ 798 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (37 enodes) * * [misc]simplify: iters left: 5 (106 enodes) * * [misc]simplify: iters left: 4 (364 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* v -3)))))) (sqrt (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* v (* v -3)))))) (sqrt (* (sqrt (+ (* (* 3 (* v v)) (* 3 (* v v))) (+ (* 3 (* v v)) 1))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* v v) (sqrt 2))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * * * * [misc]progress: [ 799 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (365 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v))))) (sqrt (- (* (* (/ (sqrt 2) 4) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* v v) (sqrt 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v))))) (sqrt (- (* (* (/ (sqrt 2) 4) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (* (* v v) (sqrt 2)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * * * * [misc]progress: [ 800 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (35 enodes) * * [misc]simplify: iters left: 5 (100 enodes) * * [misc]simplify: iters left: 4 (327 enodes) * [exit]simplify: Simplified to (* (sqrt (- (/ (* (sqrt 2) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1)))) (/ 4 (sqrt (- 1 (pow (* (* v 3) v) 3))))) (* (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (* v v))))) (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* -3 v) v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (/ (* (sqrt 2) (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1)))) (/ 4 (sqrt (- 1 (pow (* (* v 3) v) 3))))) (* (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (/ (sqrt 2) 4)) (* (sqrt (+ (* (* (* v 3) v) (* (* v 3) v)) (+ (* (* v 3) v) 1))) (* v v))))) (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* -3 v) v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * * * [misc]progress: [ 801 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (112 enodes) * * [misc]simplify: iters left: 4 (362 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) 3))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* v v) 3))))) (sqrt (- (* (* (sqrt (+ (* (* v v) 3) 1)) (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* (* v v) 3) 3)))) (* (* (sqrt (+ (* (* (* v v) 3) (* (* v v) 3)) (+ (* (* v v) 3) 1))) (/ (sqrt 2) 4)) (* (sqrt (- 1 (* (* (* v v) 3) (* (* v v) 3)))) (* v v)))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (sqrt (+ 1 (* 3 (* v v)))))))) * * * * [misc]progress: [ 802 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) 1) 4) (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (36 enodes) * * [misc]simplify: iters left: 5 (101 enodes) * * [misc]simplify: iters left: 4 (331 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v -3) v)))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v))))) (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (pow (* 3 (* v v)) 3)))) (* (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* (* v -3) v)))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v))))))))) (sqrt (* (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))) 4)))) * * * * [misc]progress: [ 803 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (355 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* -3 (* v v)))))) (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v))))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* -3 (* v v)))))) (sqrt (- (* (* (* 4 (/ (sqrt 2) 4)) (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v)))))) (sqrt (+ (+ 1 (* 3 (* v v))) (* (* 3 (* v v)) (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v))))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * * * * [misc]progress: [ 804 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (33 enodes) * * [misc]simplify: iters left: 5 (86 enodes) * * [misc]simplify: iters left: 4 (284 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1)))) (sqrt (* (sqrt (+ 1 (* v (* v 3)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* v (* v -3)) 1)))) (sqrt (* (sqrt (+ 1 (* v (* v 3)))) (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* (* v v) (sqrt 2)) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * * * * [misc]progress: [ 805 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (112 enodes) * * [misc]simplify: iters left: 4 (351 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1)))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v 3) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1)))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* (* v 3) v) (* (* v 3) v))))) (sqrt (+ (+ 1 (* (* v 3) v)) (* (* (* v 3) v) (* (* v 3) v))))) (* (sqrt (- 1 (pow (* (* v 3) v) 3))) (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v 3) v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * * * [misc]progress: [ 806 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (31 enodes) * * [misc]simplify: iters left: 5 (80 enodes) * * [misc]simplify: iters left: 4 (247 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1)))) (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 9) (* v v))))) (* (* (sqrt (- 1 (* (* (* v v) 9) (* v v)))) (/ (sqrt 2) 4)) (* (* v v) (sqrt (+ 1 (* (* v 3) v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1)))) (sqrt (- (* (* (sqrt (+ 1 (* (* v 3) v))) (/ (sqrt 2) 4)) (sqrt (- 1 (* (* (* v v) 9) (* v v))))) (* (* (sqrt (- 1 (* (* (* v v) 9) (* v v)))) (/ (sqrt 2) 4)) (* (* v v) (sqrt (+ 1 (* (* v 3) v)))))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) (sqrt (+ 1 (* 3 (* v v)))))))) * * * * [misc]progress: [ 807 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) 1) 4) (* (sqrt (+ 1 (* 3 (* v v)))) (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (81 enodes) * * [misc]simplify: iters left: 4 (248 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* (sqrt (+ (* (* v v) -3) 1)) (sqrt 2)) (* (* v v) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (/ (sqrt 2) 4)) (sqrt (+ (* (* (* v v) -9) (* v v)) 1))) (* (* (sqrt (+ (* (* v v) -3) 1)) (sqrt 2)) (* (* v v) (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1))))) (sqrt (* (sqrt (+ 1 (* 3 (* v v)))) 4)))) * * * * [misc]progress: [ 808 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))) (* 4 (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (37 enodes) * * [misc]simplify: iters left: 5 (103 enodes) * * [misc]simplify: iters left: 4 (332 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (+ (* (* v v) -3) 1)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (* 4 (sqrt 2)) (sqrt (+ (* (* v v) -3) 1)))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1))))) (sqrt (* 4 (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * * * * [misc]progress: [ 809 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (* 4 (sqrt (+ 1 (* 3 (* v v)))))) (* 4 (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (33 enodes) * * [misc]simplify: iters left: 5 (83 enodes) * * [misc]simplify: iters left: 4 (253 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* -3 (* v v)))) (sqrt 2))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* -3 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* 4 (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ 1 (* -3 (* v v)))) (sqrt 2))) (* (sqrt (- 1 (* (* 3 (* v v)) (* 3 (* v v))))) (* (* (* v v) (sqrt 2)) 4)))) (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* -3 (* v v))))))) (sqrt (* 4 (* 4 (sqrt (+ 1 (* 3 (* v v))))))))) * * * * [misc]progress: [ 810 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (36 enodes) * * [misc]simplify: iters left: 5 (101 enodes) * * [misc]simplify: iters left: 4 (328 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (- 1 (* 3 (* v v)))))) (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt 2) (sqrt (- 1 (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (- 1 (* 3 (* v v)))))) (sqrt (- (* (sqrt (+ (+ (* 3 (* v v)) 1) (* (* 3 (* v v)) (* 3 (* v v))))) (* (sqrt 2) (sqrt (- 1 (* 3 (* v v)))))) (* (sqrt (- 1 (pow (* 3 (* v v)) 3))) (* (/ (* (sqrt 2) (* v v)) 4) 4))))) (sqrt (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) * * * * [misc]progress: [ 811 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) (sqrt (+ 1 (* 3 (* v v))))) (* 4 (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (81 enodes) * * [misc]simplify: iters left: 4 (249 enodes) * [exit]simplify: Simplified to (* (sqrt (- (* (* (sqrt (+ (* (* -3 v) v) 1)) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* (* v v) (* (* v v) -9)) 1)) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* -3 v) v) 1))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (- (* (* (sqrt (+ (* (* -3 v) v) 1)) (sqrt 2)) (sqrt (+ 1 (* 3 (* v v))))) (* (sqrt (+ (* (* v v) (* (* v v) -9)) 1)) (* (* (/ (sqrt 2) 4) (* v v)) 4)))) (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* -3 v) v) 1))))) (sqrt (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) * * * * [misc]progress: [ 812 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (* (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) 1) 4) (* 4 (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (62 enodes) * * [misc]simplify: iters left: 4 (177 enodes) * [exit]simplify: Simplified to (* (sqrt (* (- 1 (* v v)) (* (* (sqrt 2) 4) (sqrt (+ (* (* v v) -3) 1))))) (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (- 1 (* v v)) (* (* (sqrt 2) 4) (sqrt (+ (* (* v v) -3) 1))))) (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v v) -3) 1))))) (sqrt (* 4 4)))) * * * * [misc]progress: [ 813 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) 3) (pow (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) 3))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (59 enodes) * * [misc]simplify: iters left: 4 (213 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v))))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* v -3) v)))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v)))) 3)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v))))) (sqrt (- (pow (* (/ (sqrt 2) 4) (sqrt (+ 1 (* (* v -3) v)))) 3) (pow (* (* (* v v) (/ (sqrt 2) 4)) (sqrt (+ 1 (* (* v -3) v)))) 3)))) (sqrt (+ (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))))) * * * * [misc]progress: [ 814 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (- (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1)) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (59 enodes) * * [misc]simplify: iters left: 4 (202 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1)))) (sqrt (* (* (sqrt (+ (* (* v -3) v) 1)) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (sqrt (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1)))) (sqrt (* (* (sqrt (+ (* (* v -3) v) 1)) (- (/ (sqrt 2) 4) (* (* v (- v)) (/ (sqrt 2) 4)))) (* (* (- 1 (* v v)) (/ (sqrt 2) 4)) (sqrt (+ (* (* v -3) v) 1)))))) (sqrt (- (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * * * [misc]progress: [ 815 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 816 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (207 enodes) * * [misc]simplify: iters left: 2 (387 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (* -3 (* v v)))) (/ (/ 4 (* v v)) (- (sqrt 2)))) * [misc]simplify: Simplified (2 2 1 2 1) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (pow (/ (sqrt (+ 1 (* -3 (* v v)))) (/ (/ 4 (* v v)) (- (sqrt 2)))) 1))))) * * * * [misc]progress: [ 817 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (207 enodes) * * [misc]simplify: iters left: 2 (387 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (* -3 (* v v)))) (/ (/ 4 (* v v)) (- (sqrt 2)))) * [misc]simplify: Simplified (2 2 1 2 1) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (pow (/ (sqrt (+ 1 (* -3 (* v v)))) (/ (/ 4 (* v v)) (- (sqrt 2)))) 1))))) * * * * [misc]progress: [ 818 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 819 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (+ (log (/ (sqrt 2) 4)) (log (sqrt (- 1 (* 3 (* v v)))))) (log (- (* v v)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (125 enodes) * * [misc]simplify: iters left: 2 (274 enodes) * [exit]simplify: Simplified to (+ (log (sqrt (+ 1 (* -3 (* v v))))) (+ (log (/ (sqrt 2) 4)) (log (* (- v) v)))) * [misc]simplify: Simplified (2 2 1 2 1) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (exp (+ (log (sqrt (+ 1 (* -3 (* v v))))) (+ (log (/ (sqrt 2) 4)) (log (* (- v) v))))))))) * * * * [misc]progress: [ 820 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))) (log (- (* v v)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (102 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (391 enodes) * [exit]simplify: Simplified to (+ (log (sqrt (+ 1 (* v (* v -3))))) (+ (log (/ (sqrt 2) 4)) (log (* v (- v))))) * [misc]simplify: Simplified (2 2 1 2 1) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (exp (+ (log (sqrt (+ 1 (* v (* v -3))))) (+ (log (/ (sqrt 2) 4)) (log (* v (- v)))))))))) * * * * [misc]progress: [ 821 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 822 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 823 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (* (/ (sqrt 2) 4) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)) (* (* (sqrt (- 1 (* 3 (* v v)))) (sqrt (- 1 (* 3 (* v v))))) (sqrt (- 1 (* 3 (* v v)))))) (* (* (- (* v v)) (- (* v v))) (- (* v v)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (56 enodes) * * [misc]simplify: iters left: 4 (234 enodes) * [exit]simplify: Simplified to (* (* (* (/ (* (sqrt 2) 1/2) 16) (* (- (* v v)) (* (* v v) (* v v)))) (+ (* v (* -3 v)) 1)) (sqrt (+ (* v (* -3 v)) 1))) * [misc]simplify: Simplified (2 2 1 2 1) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (cbrt (* (* (* (/ (* (sqrt 2) 1/2) 16) (* (- (* v v)) (* (* v v) (* v v)))) (+ (* v (* -3 v)) 1)) (sqrt (+ (* v (* -3 v)) 1)))))))) * * * * [misc]progress: [ 824 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))) (* (* (- (* v v)) (- (* v v))) (- (* v v)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (200 enodes) * [exit]simplify: Simplified to (* (* (sqrt (+ (* -3 (* v v)) 1)) (* (/ (sqrt 2) 4) (* v (- v)))) (* (* (/ (sqrt 2) 4) (+ (* -3 (* v v)) 1)) (* (/ (sqrt 2) 4) (* (* v v) (* v v))))) * [misc]simplify: Simplified (2 2 1 2 1) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (cbrt (* (* (sqrt (+ (* -3 (* v v)) 1)) (* (/ (sqrt 2) 4) (* v (- v)))) (* (* (/ (sqrt 2) 4) (+ (* -3 (* v v)) 1)) (* (/ (sqrt 2) 4) (* (* v v) (* v v)))))))))) * * * * [misc]progress: [ 825 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 826 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 827 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 828 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 829 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 830 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (cbrt (- (* v v))) * * [misc]simplify: iters left: 5 (4 enodes) * * [misc]simplify: iters left: 4 (7 enodes) * [exit]simplify: Simplified to (cbrt (* (- v) v)) * [misc]simplify: Simplified (2 2 1 2 2) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* (cbrt (- (* v v))) (cbrt (- (* v v))))) (cbrt (* (- v) v))))))) * * * * [misc]progress: [ 831 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (- (* v v))) * * [misc]simplify: iters left: 5 (4 enodes) * * [misc]simplify: iters left: 4 (7 enodes) * [exit]simplify: Simplified to (sqrt (* (- v) v)) * [misc]simplify: Simplified (2 2 1 2 2) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (sqrt (- (* v v)))) (sqrt (* (- v) v))))))) * * * * [misc]progress: [ 832 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* v v)) * * [misc]simplify: iters left: 4 (3 enodes) * * [misc]simplify: iters left: 3 (6 enodes) * [exit]simplify: Simplified to (* (- v) v) * [misc]simplify: Simplified (2 2 1 2 2) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (- v) v)))))) * * * * [misc]progress: [ 833 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* v v) * * [misc]simplify: iters left: 2 (2 enodes) * [exit]simplify: Simplified to (* v v) * [misc]simplify: Simplified (2 2 1 2 2) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) -1) (* v v)))))) * * * * [misc]progress: [ 834 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 835 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (- v) * * [misc]simplify: iters left: 2 (2 enodes) * [exit]simplify: Simplified to (- v) * [misc]simplify: Simplified (2 2 1 2 2) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) v) (- v)))))) * * * * [misc]progress: [ 836 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt 2) 4) * * [misc]simplify: iters left: 3 (4 enodes) * [exit]simplify: Simplified to (/ (sqrt 2) 4) * [misc]simplify: Simplified (2 2 1 2 1) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (/ (sqrt 2) 4) (* (sqrt (- 1 (* 3 (* v v)))) (- (* v v)))))))) * * * * [misc]progress: [ 837 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (108 enodes) * * [misc]simplify: iters left: 3 (353 enodes) * [exit]simplify: Simplified to (* (- (* (* v v) (sqrt 2))) (sqrt (+ 1 (* (* (* v v) (* -3 v)) (* (* v v) (* 9 v)))))) * [misc]simplify: Simplified (2 2 1 2 1) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (/ (* (- (* (* v v) (sqrt 2))) (sqrt (+ 1 (* (* (* v v) (* -3 v)) (* (* v v) (* 9 v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))))) * * * * [misc]progress: [ 838 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (229 enodes) * * [misc]simplify: iters left: 2 (392 enodes) * * [misc]simplify: iters left: 1 (447 enodes) * [exit]simplify: Simplified to (* (* (- v) (* v (sqrt 2))) (sqrt (+ (* -9 (pow v 4)) 1))) * [misc]simplify: Simplified (2 2 1 2 1) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (/ (* (* (- v) (* v (sqrt 2))) (sqrt (+ (* -9 (pow v 4)) 1))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))))) * * * * [misc]progress: [ 839 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (124 enodes) * * [misc]simplify: iters left: 3 (427 enodes) * [exit]simplify: Simplified to (* (sqrt (- 1 (* (* (* v v) (* v 3)) (* (* 9 v) (* v v))))) (* (* (- v) v) (/ (sqrt 2) 4))) * [misc]simplify: Simplified (2 2 1 2 1) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (/ (* (sqrt (- 1 (* (* (* v v) (* v 3)) (* (* 9 v) (* v v))))) (* (* (- v) v) (/ (sqrt 2) 4))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))))) * * * * [misc]progress: [ 840 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (109 enodes) * * [misc]simplify: iters left: 3 (305 enodes) * [exit]simplify: Simplified to (* (* (* v (- v)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (pow v 3) (* 9 v))))) * [misc]simplify: Simplified (2 2 1 2 1) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (/ (* (* (* v (- v)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (pow v 3) (* 9 v))))) (sqrt (+ 1 (* 3 (* v v))))))))) * * * * [misc]progress: [ 841 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (128 enodes) * * [misc]simplify: iters left: 2 (177 enodes) * * [misc]simplify: iters left: 1 (188 enodes) * [exit]simplify: Simplified to (* (* (* (sqrt 2) (- v)) v) (sqrt (+ (* v (* -3 v)) 1))) * [misc]simplify: Simplified (2 2 1 2 1) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (/ (* (* (* (sqrt 2) (- v)) v) (sqrt (+ (* v (* -3 v)) 1))) 4))))) * * * * [misc]progress: [ 842 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 843 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (207 enodes) * * [misc]simplify: iters left: 2 (387 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (* -3 (* v v)))) (/ (/ 4 (* v v)) (- (sqrt 2)))) * [misc]simplify: Simplified (2 1 1 2 1) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (pow (/ (sqrt (+ 1 (* -3 (* v v)))) (/ (/ 4 (* v v)) (- (sqrt 2)))) 1))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * * * [misc]progress: [ 844 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (207 enodes) * * [misc]simplify: iters left: 2 (387 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (* -3 (* v v)))) (/ (/ 4 (* v v)) (- (sqrt 2)))) * [misc]simplify: Simplified (2 1 1 2 1) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (pow (/ (sqrt (+ 1 (* -3 (* v v)))) (/ (/ 4 (* v v)) (- (sqrt 2)))) 1))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * * * [misc]progress: [ 845 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 846 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (+ (log (/ (sqrt 2) 4)) (log (sqrt (- 1 (* 3 (* v v)))))) (log (- (* v v)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (125 enodes) * * [misc]simplify: iters left: 2 (274 enodes) * [exit]simplify: Simplified to (+ (log (sqrt (+ 1 (* -3 (* v v))))) (+ (log (/ (sqrt 2) 4)) (log (* (- v) v)))) * [misc]simplify: Simplified (2 1 1 2 1) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (exp (+ (log (sqrt (+ 1 (* -3 (* v v))))) (+ (log (/ (sqrt 2) 4)) (log (* (- v) v))))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * * * [misc]progress: [ 847 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))) (log (- (* v v)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (102 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (391 enodes) * [exit]simplify: Simplified to (+ (log (sqrt (+ 1 (* v (* v -3))))) (+ (log (/ (sqrt 2) 4)) (log (* v (- v))))) * [misc]simplify: Simplified (2 1 1 2 1) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (exp (+ (log (sqrt (+ 1 (* v (* v -3))))) (+ (log (/ (sqrt 2) 4)) (log (* v (- v)))))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * * * [misc]progress: [ 848 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 849 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 850 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (* (/ (sqrt 2) 4) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)) (* (* (sqrt (- 1 (* 3 (* v v)))) (sqrt (- 1 (* 3 (* v v))))) (sqrt (- 1 (* 3 (* v v)))))) (* (* (- (* v v)) (- (* v v))) (- (* v v)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (56 enodes) * * [misc]simplify: iters left: 4 (234 enodes) * [exit]simplify: Simplified to (* (* (* (/ (* (sqrt 2) 1/2) 16) (* (- (* v v)) (* (* v v) (* v v)))) (+ (* v (* -3 v)) 1)) (sqrt (+ (* v (* -3 v)) 1))) * [misc]simplify: Simplified (2 1 1 2 1) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (cbrt (* (* (* (/ (* (sqrt 2) 1/2) 16) (* (- (* v v)) (* (* v v) (* v v)))) (+ (* v (* -3 v)) 1)) (sqrt (+ (* v (* -3 v)) 1)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * * * [misc]progress: [ 851 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))) (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))) (* (* (- (* v v)) (- (* v v))) (- (* v v)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (200 enodes) * [exit]simplify: Simplified to (* (* (sqrt (+ (* -3 (* v v)) 1)) (* (/ (sqrt 2) 4) (* v (- v)))) (* (* (/ (sqrt 2) 4) (+ (* -3 (* v v)) 1)) (* (/ (sqrt 2) 4) (* (* v v) (* v v))))) * [misc]simplify: Simplified (2 1 1 2 1) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (cbrt (* (* (sqrt (+ (* -3 (* v v)) 1)) (* (/ (sqrt 2) 4) (* v (- v)))) (* (* (/ (sqrt 2) 4) (+ (* -3 (* v v)) 1)) (* (/ (sqrt 2) 4) (* (* v v) (* v v)))))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * * * [misc]progress: [ 852 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 853 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 854 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 855 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 856 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 857 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (cbrt (- (* v v))) * * [misc]simplify: iters left: 5 (4 enodes) * * [misc]simplify: iters left: 4 (7 enodes) * [exit]simplify: Simplified to (cbrt (* (- v) v)) * [misc]simplify: Simplified (2 1 1 2 2) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (* (cbrt (- (* v v))) (cbrt (- (* v v))))) (cbrt (* (- v) v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * * * [misc]progress: [ 858 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (- (* v v))) * * [misc]simplify: iters left: 5 (4 enodes) * * [misc]simplify: iters left: 4 (7 enodes) * [exit]simplify: Simplified to (sqrt (* (- v) v)) * [misc]simplify: Simplified (2 1 1 2 2) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (sqrt (- (* v v)))) (sqrt (* (- v) v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * * * [misc]progress: [ 859 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* v v)) * * [misc]simplify: iters left: 4 (3 enodes) * * [misc]simplify: iters left: 3 (6 enodes) * [exit]simplify: Simplified to (* (- v) v) * [misc]simplify: Simplified (2 1 1 2 2) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (- v) v)))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * * * [misc]progress: [ 860 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* v v) * * [misc]simplify: iters left: 2 (2 enodes) * [exit]simplify: Simplified to (* v v) * [misc]simplify: Simplified (2 1 1 2 2) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) -1) (* v v)))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * * * [misc]progress: [ 861 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 862 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (- v) * * [misc]simplify: iters left: 2 (2 enodes) * [exit]simplify: Simplified to (- v) * [misc]simplify: Simplified (2 1 1 2 2) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) v) (- v)))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * * * [misc]progress: [ 863 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt 2) 4) * * [misc]simplify: iters left: 3 (4 enodes) * [exit]simplify: Simplified to (/ (sqrt 2) 4) * [misc]simplify: Simplified (2 1 1 2 1) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (/ (sqrt 2) 4) (* (sqrt (- 1 (* 3 (* v v)))) (- (* v v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * * * [misc]progress: [ 864 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (sqrt 2) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (108 enodes) * * [misc]simplify: iters left: 3 (353 enodes) * [exit]simplify: Simplified to (* (- (* (* v v) (sqrt 2))) (sqrt (+ 1 (* (* (* v v) (* -3 v)) (* (* v v) (* 9 v)))))) * [misc]simplify: Simplified (2 1 1 2 1) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (/ (* (- (* (* v v) (sqrt 2))) (sqrt (+ 1 (* (* (* v v) (* -3 v)) (* (* v v) (* 9 v)))))) (* 4 (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v)))))))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * * * [misc]progress: [ 865 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (sqrt 2) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (229 enodes) * * [misc]simplify: iters left: 2 (392 enodes) * * [misc]simplify: iters left: 1 (447 enodes) * [exit]simplify: Simplified to (* (* (- v) (* v (sqrt 2))) (sqrt (+ (* -9 (pow v 4)) 1))) * [misc]simplify: Simplified (2 1 1 2 1) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (/ (* (* (- v) (* v (sqrt 2))) (sqrt (+ (* -9 (pow v 4)) 1))) (* 4 (sqrt (+ 1 (* 3 (* v v)))))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * * * [misc]progress: [ 866 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (sqrt 2) 4) (sqrt (- (pow 1 3) (pow (* 3 (* v v)) 3)))) (- (* v v))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (124 enodes) * * [misc]simplify: iters left: 3 (427 enodes) * [exit]simplify: Simplified to (* (sqrt (- 1 (* (* (* v v) (* v 3)) (* (* 9 v) (* v v))))) (* (* (- v) v) (/ (sqrt 2) 4))) * [misc]simplify: Simplified (2 1 1 2 1) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (/ (* (sqrt (- 1 (* (* (* v v) (* v 3)) (* (* 9 v) (* v v))))) (* (* (- v) v) (/ (sqrt 2) 4))) (sqrt (+ (* 1 1) (+ (* (* 3 (* v v)) (* 3 (* v v))) (* 1 (* 3 (* v v))))))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * * * [misc]progress: [ 867 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (sqrt 2) 4) (sqrt (- (* 1 1) (* (* 3 (* v v)) (* 3 (* v v)))))) (- (* v v))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (109 enodes) * * [misc]simplify: iters left: 3 (305 enodes) * [exit]simplify: Simplified to (* (* (* v (- v)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (pow v 3) (* 9 v))))) * [misc]simplify: Simplified (2 1 1 2 1) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (/ (* (* (* v (- v)) (/ (sqrt 2) 4)) (sqrt (- 1 (* (pow v 3) (* 9 v))))) (sqrt (+ 1 (* 3 (* v v))))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * * * [misc]progress: [ 868 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (sqrt 2) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (128 enodes) * * [misc]simplify: iters left: 2 (177 enodes) * * [misc]simplify: iters left: 1 (188 enodes) * [exit]simplify: Simplified to (* (* (* (sqrt 2) (- v)) v) (sqrt (+ (* v (* -3 v)) 1))) * [misc]simplify: Simplified (2 1 1 2 1) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (/ (* (* (* (sqrt 2) (- v)) v) (sqrt (+ (* v (* -3 v)) 1))) 4))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * * * [misc]progress: [ 869 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 870 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 871 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 872 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 873 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 874 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 875 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 876 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 877 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 878 / 890 ] simplifiying candidate # * * * * [misc]progress: [ 879 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 1/4 (sqrt 2)) (* 3/32 (* (sqrt 2) (pow v 4)))) (* 5/8 (* (sqrt 2) (pow v 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (133 enodes) * * [misc]simplify: iters left: 2 (232 enodes) * * [misc]simplify: iters left: 1 (314 enodes) * [exit]simplify: Simplified to (* (+ (+ 1/4 (* (pow v 4) 3/32)) (* (* -5/8 v) v)) (sqrt 2)) * [misc]simplify: Simplified (2) to (λ (v) (* (+ (+ 1/4 (* (pow v 4) 3/32)) (* (* -5/8 v) v)) (sqrt 2))) * * * * [misc]progress: [ 880 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (pow (sqrt 2) 2)) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2))) (- (+ (* +nan.0 (* (pow (sqrt 2) 3) (* v (pow (sqrt -3) 3)))) (- (+ (* +nan.0 (* (pow (sqrt 2) 4) (pow (sqrt -3) 4))) (- (* +nan.0 (* (pow (sqrt 2) 2) (* (pow v 2) (pow (sqrt -3) 2))))))))))))) * [misc]simplify: Simplified (2) to (λ (v) +nan.0) * * * * [misc]progress: [ 881 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (pow (sqrt 2) 2)) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (pow (sqrt -3) 2))) (- (+ (* +nan.0 (* (pow (sqrt 2) 3) (* v (pow (sqrt -3) 3)))) (- (+ (* +nan.0 (* (pow (sqrt 2) 4) (pow (sqrt -3) 4))) (- (* +nan.0 (* (pow (sqrt 2) 2) (* (pow v 2) (pow (sqrt -3) 2))))))))))))) * [misc]simplify: Simplified (2) to (λ (v) +nan.0) * * * * [misc]progress: [ 882 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 9/32 (* (sqrt 2) (pow v 6))) (* 3/8 (* (sqrt 2) (pow v 4)))) (* 1/4 (* (sqrt 2) (pow v 2)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (245 enodes) * * [misc]simplify: iters left: 1 (365 enodes) * [exit]simplify: Simplified to (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)) * [misc]simplify: Simplified (2 2 1 2) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)))))) * * * * [misc]progress: [ 883 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* 1/32 (/ (sqrt 2) (* v (pow (sqrt -3) 3)))) (+ (* 1/4 (* (sqrt 2) (* (pow v 3) (sqrt -3)))) (* 1/8 (/ (* (sqrt 2) v) (sqrt -3))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (129 enodes) * * [misc]simplify: iters left: 3 (360 enodes) * [exit]simplify: Simplified to (- (* (/ (sqrt 2) (sqrt -3)) (- (/ -1/96 v) (* v 1/8))) (* (* (* v v) (sqrt -3)) (* (sqrt 2) (* v 1/4)))) * [misc]simplify: Simplified (2 2 1 2) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (- (* (/ (sqrt 2) (sqrt -3)) (- (/ -1/96 v) (* v 1/8))) (* (* (* v v) (sqrt -3)) (* (sqrt 2) (* v 1/4)))))))) * * * * [misc]progress: [ 884 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 1/4 (* (sqrt 2) (* (pow v 3) (sqrt -3)))) (* 1/8 (/ (* (sqrt 2) v) (sqrt -3)))) (* 1/32 (/ (sqrt 2) (* v (pow (sqrt -3) 3))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (138 enodes) * * [misc]simplify: iters left: 3 (344 enodes) * [exit]simplify: Simplified to (+ (* (* (* v 1/4) (sqrt 2)) (* (* v v) (sqrt -3))) (* (/ (sqrt 2) (sqrt -3)) (- (* v 1/8) (/ -1/96 v)))) * [misc]simplify: Simplified (2 2 1 2) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (+ (* (* (* v 1/4) (sqrt 2)) (* (* v v) (sqrt -3))) (* (/ (sqrt 2) (sqrt -3)) (- (* v 1/8) (/ -1/96 v)))))))) * * * * [misc]progress: [ 885 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 9/32 (* (sqrt 2) (pow v 6))) (* 3/8 (* (sqrt 2) (pow v 4)))) (* 1/4 (* (sqrt 2) (pow v 2)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (245 enodes) * * [misc]simplify: iters left: 1 (365 enodes) * [exit]simplify: Simplified to (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)) * [misc]simplify: Simplified (2 1 1 2) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (+ (- (* (pow v 6) 9/32) (* (* v v) 1/4)) (* 3/8 (pow v 4))) (sqrt 2)))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * * * [misc]progress: [ 886 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* 1/32 (/ (sqrt 2) (* v (pow (sqrt -3) 3)))) (+ (* 1/4 (* (sqrt 2) (* (pow v 3) (sqrt -3)))) (* 1/8 (/ (* (sqrt 2) v) (sqrt -3))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (129 enodes) * * [misc]simplify: iters left: 3 (360 enodes) * [exit]simplify: Simplified to (- (* (/ (sqrt 2) (sqrt -3)) (- (/ -1/96 v) (* v 1/8))) (* (* (* v v) (sqrt -3)) (* (sqrt 2) (* v 1/4)))) * [misc]simplify: Simplified (2 1 1 2) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (- (* (/ (sqrt 2) (sqrt -3)) (- (/ -1/96 v) (* v 1/8))) (* (* (* v v) (sqrt -3)) (* (sqrt 2) (* v 1/4)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * * * [misc]progress: [ 887 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 1/4 (* (sqrt 2) (* (pow v 3) (sqrt -3)))) (* 1/8 (/ (* (sqrt 2) v) (sqrt -3)))) (* 1/32 (/ (sqrt 2) (* v (pow (sqrt -3) 3))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (138 enodes) * * [misc]simplify: iters left: 3 (344 enodes) * [exit]simplify: Simplified to (+ (* (* (* v 1/4) (sqrt 2)) (* (* v v) (sqrt -3))) (* (/ (sqrt 2) (sqrt -3)) (- (* v 1/8) (/ -1/96 v)))) * [misc]simplify: Simplified (2 1 1 2) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (+ (* (* (* v 1/4) (sqrt 2)) (* (* v v) (sqrt -3))) (* (/ (sqrt 2) (sqrt -3)) (- (* v 1/8) (/ -1/96 v)))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))))) * * * * [misc]progress: [ 888 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* 3 (pow v 2)) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * * [misc]simplify: iters left: 1 (11 enodes) * [exit]simplify: Simplified to (* (* v v) 3) * [misc]simplify: Simplified (2 2 1 2 1 2 1 2) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v v) 3)))) (- (* v v))))))) * * * * [misc]progress: [ 889 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* 3 (pow v 2)) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * * [misc]simplify: iters left: 1 (11 enodes) * [exit]simplify: Simplified to (* (* v v) 3) * [misc]simplify: Simplified (2 2 1 2 1 2 1 2) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v v) 3)))) (- (* v v))))))) * * * * [misc]progress: [ 890 / 890 ] simplifiying candidate # * [enter]simplify: Simplifying (* 3 (pow v 2)) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * * [misc]simplify: iters left: 1 (11 enodes) * [exit]simplify: Simplified to (* (* v v) 3) * [misc]simplify: Simplified (2 2 1 2 1 2 1 2) to (λ (v) (* (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- (* v v))))) (sqrt (+ (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) 1) (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* (* v v) 3)))) (- (* v v))))))) * * * [misc]progress: adding candidates to table