* [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 130 additional inputs, on iter 1 have 126 / 256 * * * * [misc]points: Computing exacts on every 8 of 130 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 130 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 130 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 64 * * * * [misc]points: Setting MPFR precision to 320 * * * * [misc]points: Computing exacts for 130 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 67 additional inputs, on iter 2 have 189 / 256 * * * * [misc]points: Computing exacts on every 4 of 67 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 67 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 64 * * * * [misc]points: Setting MPFR precision to 320 * * * * [misc]points: Computing exacts for 67 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 26 additional inputs, on iter 3 have 230 / 256 * * * * [misc]points: Computing exacts for 26 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 12 additional inputs, on iter 4 have 244 / 256 * * * * [misc]points: Computing exacts for 12 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 5 have 254 / 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 * * * * [misc]points: Sampling 4 additional inputs, on iter 6 have 255 / 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 257 points with exact outputs * * * [misc]progress: [2/2] Setting up program. * [misc]progress: [Phase 2 of 3] Improving. * [enter]simplify: Simplifying (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (186 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))) * * [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 1) * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 2 1 2) * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 1) * * * * [misc]progress: [ 4 / 4 ] rewriting at (2) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 4 ] generating series at (2 1 1) * * * * [misc]progress: [ 2 / 4 ] generating series at (2 2 1 2) * [misc]approximate: Taking taylor expansion of (* (* v v) -6) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (* v v) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]taylor: Taking taylor expansion of (* (* v v) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 0 -6) 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 -6)) 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 (+ (* 0 0) (+ (* 0 0) (* 1 -6))) into -6 * [misc]backup-simplify: Simplify -6 into -6 * [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 -6)))) 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 0) (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 -6))))) 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 (+ (* 0 0) (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6)))))) 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 0) (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6))))))) 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 (+ (* 0 0) (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6)))))))) 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 (+ (* 0 0) (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6))))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* -6 (pow v 2)) into (* -6 (pow v 2)) * [misc]approximate: Taking taylor expansion of (* (* (/ 1 v) (/ 1 v)) -6) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (* (/ 1 v) (/ 1 v)) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]taylor: Taking taylor expansion of (* (* (/ 1 v) (/ 1 v)) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 -6) into -6 * [misc]backup-simplify: Simplify -6 into -6 * [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 (+ (* 1 0) (* 0 -6)) 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 (+ (* 1 0) (+ (* 0 0) (* 0 -6))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6)))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6))))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6)))))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* -6 (pow (/ 1 (/ 1 v)) 2)) into (* -6 (pow v 2)) * [misc]approximate: Taking taylor expansion of (* (* (/ 1 (- v)) (/ 1 (- v))) -6) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- v)) (/ 1 (- v))) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- v)) (/ 1 (- v))) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 1 -6) into -6 * [misc]backup-simplify: Simplify -6 into -6 * [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 (+ (* 1 0) (* 0 -6)) 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 (+ (* 1 0) (+ (* 0 0) (* 0 -6))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6)))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6))))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6)))))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* -6 (pow (/ 1 (/ 1 (- v))) 2)) into (* -6 (pow v 2)) * * * * [misc]progress: [ 3 / 4 ] generating series at (2 1) * [misc]approximate: Taking taylor expansion of (/ (/ 4/3 PI) (- 1 (* v v))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (/ (/ 4/3 PI) (- 1 (* v v))) in v * [misc]taylor: Taking taylor expansion of (/ 4/3 PI) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of PI in v * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (/ 4/3 PI) into (/ 4/3 PI) * [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 (* 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ (/ 4/3 PI) 1) into (/ 4/3 PI) * [misc]taylor: Taking taylor expansion of (/ (/ 4/3 PI) (- 1 (* v v))) in v * [misc]taylor: Taking taylor expansion of (/ 4/3 PI) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of PI in v * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (/ 4/3 PI) into (/ 4/3 PI) * [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 (* 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ (/ 4/3 PI) 1) into (/ 4/3 PI) * [misc]backup-simplify: Simplify (/ 4/3 PI) into (/ 4/3 PI) * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)))) into 0 * [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 1) (+ (* (/ 4/3 PI) (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)))) 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 1) (+ (* (/ 4/3 PI) (/ -1 1)) (* 0 (/ 0 1)))) into (* 4/3 (/ 1 PI)) * [misc]backup-simplify: Simplify (* 4/3 (/ 1 PI)) into (/ 4/3 PI) * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) 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 (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (/ 4/3 PI) (/ 0 1)) (* 0 (/ -1 1)) (* (* 4/3 (/ 1 PI)) (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) 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 1) (+ (* (/ 4/3 PI) (/ 0 1)) (* 0 (/ 0 1)) (* (* 4/3 (/ 1 PI)) (/ -1 1)) (* 0 (/ 0 1)))) into (* 4/3 (/ 1 PI)) * [misc]backup-simplify: Simplify (* 4/3 (/ 1 PI)) into (/ 4/3 PI) * [misc]backup-simplify: Simplify (+ (* (/ 4/3 PI) (pow v 4)) (+ (* (/ 4/3 PI) (pow v 2)) (/ 4/3 PI))) into (+ (* 4/3 (/ (pow v 2) PI)) (+ (* 4/3 (/ 1 PI)) (* 4/3 (/ (pow v 4) PI)))) * [misc]approximate: Taking taylor expansion of (/ (/ 4/3 PI) (- 1 (* (/ 1 v) (/ 1 v)))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (/ (/ 4/3 PI) (- 1 (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of (/ 4/3 PI) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of PI in v * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (/ 4/3 PI) into (/ 4/3 PI) * [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 1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ (/ 4/3 PI) -1) into (/ -4/3 PI) * [misc]taylor: Taking taylor expansion of (/ (/ 4/3 PI) (- 1 (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of (/ 4/3 PI) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of PI in v * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (/ 4/3 PI) into (/ 4/3 PI) * [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 1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ (/ 4/3 PI) -1) into (/ -4/3 PI) * [misc]backup-simplify: Simplify (/ -4/3 PI) into (/ -4/3 PI) * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)))) 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 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 -1) (+ (* (/ -4/3 PI) (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)))) 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 (- (/ 0 -1) (+ (* (/ -4/3 PI) (/ 1 -1)) (* 0 (/ 0 -1)))) into (- (* 4/3 (/ 1 PI))) * [misc]backup-simplify: Simplify (- (* 4/3 (/ 1 PI))) into (- (* 4/3 (/ 1 PI))) * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) 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 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 -1) (+ (* (/ -4/3 PI) (/ 0 -1)) (* 0 (/ 1 -1)) (* (- (* 4/3 (/ 1 PI))) (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) 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 (- (/ 0 -1) (+ (* (/ -4/3 PI) (/ 0 -1)) (* 0 (/ 0 -1)) (* (- (* 4/3 (/ 1 PI))) (/ 1 -1)) (* 0 (/ 0 -1)))) into (- (* 4/3 (/ 1 PI))) * [misc]backup-simplify: Simplify (- (* 4/3 (/ 1 PI))) into (- (* 4/3 (/ 1 PI))) * [misc]backup-simplify: Simplify (+ (* (- (* 4/3 (/ 1 PI))) (pow (/ 1 v) 6)) (+ (* (- (* 4/3 (/ 1 PI))) (pow (/ 1 v) 4)) (* (/ -4/3 PI) (pow (/ 1 v) 2)))) into (- (+ (* 4/3 (/ 1 (* (pow v 2) PI))) (+ (* 4/3 (/ 1 (* (pow v 4) PI))) (* 4/3 (/ 1 (* (pow v 6) PI)))))) * [misc]approximate: Taking taylor expansion of (/ (/ 4/3 PI) (- 1 (* (/ 1 (- v)) (/ 1 (- v))))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (/ (/ 4/3 PI) (- 1 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of (/ 4/3 PI) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of PI in v * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (/ 4/3 PI) into (/ 4/3 PI) * [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 -1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ (/ 4/3 PI) -1) into (/ -4/3 PI) * [misc]taylor: Taking taylor expansion of (/ (/ 4/3 PI) (- 1 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of (/ 4/3 PI) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of PI in v * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (/ 4/3 PI) into (/ 4/3 PI) * [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 -1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ (/ 4/3 PI) -1) into (/ -4/3 PI) * [misc]backup-simplify: Simplify (/ -4/3 PI) into (/ -4/3 PI) * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)))) 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 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 -1) (+ (* (/ -4/3 PI) (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)))) 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 -1) (+ (* (/ -4/3 PI) (/ 1 -1)) (* 0 (/ 0 -1)))) into (- (* 4/3 (/ 1 PI))) * [misc]backup-simplify: Simplify (- (* 4/3 (/ 1 PI))) into (- (* 4/3 (/ 1 PI))) * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) 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 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 -1) (+ (* (/ -4/3 PI) (/ 0 -1)) (* 0 (/ 1 -1)) (* (- (* 4/3 (/ 1 PI))) (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) 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 -1) (+ (* (/ -4/3 PI) (/ 0 -1)) (* 0 (/ 0 -1)) (* (- (* 4/3 (/ 1 PI))) (/ 1 -1)) (* 0 (/ 0 -1)))) into (- (* 4/3 (/ 1 PI))) * [misc]backup-simplify: Simplify (- (* 4/3 (/ 1 PI))) into (- (* 4/3 (/ 1 PI))) * [misc]backup-simplify: Simplify (+ (* (- (* 4/3 (/ 1 PI))) (pow (/ 1 (- v)) 6)) (+ (* (- (* 4/3 (/ 1 PI))) (pow (/ 1 (- v)) 4)) (* (/ -4/3 PI) (pow (/ 1 (- v)) 2)))) into (- (+ (* 4/3 (/ 1 (* (pow v 2) PI))) (+ (* 4/3 (/ 1 (* (pow v 4) PI))) (* 4/3 (/ 1 (* (pow v 6) PI)))))) * * * * [misc]progress: [ 4 / 4 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))) in v * [misc]taylor: Taking taylor expansion of (/ (/ 4/3 PI) (- 1 (* v v))) in v * [misc]taylor: Taking taylor expansion of (/ 4/3 PI) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of PI in v * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (/ 4/3 PI) into (/ 4/3 PI) * [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 (* 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ (/ 4/3 PI) 1) into (/ 4/3 PI) * [misc]taylor: Taking taylor expansion of (sqrt (+ 2 (* (* v v) -6))) in v * [misc]taylor: Taking taylor expansion of (+ 2 (* (* v v) -6)) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* (* v v) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 0 -6) into 0 * [misc]backup-simplify: Simplify (+ 2 0) into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 0 -6)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (/ (/ 4/3 PI) (sqrt 2)) into (/ 4/3 (* (sqrt 2) PI)) * [misc]taylor: Taking taylor expansion of (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))) in v * [misc]taylor: Taking taylor expansion of (/ (/ 4/3 PI) (- 1 (* v v))) in v * [misc]taylor: Taking taylor expansion of (/ 4/3 PI) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of PI in v * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (/ 4/3 PI) into (/ 4/3 PI) * [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 (* 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ (/ 4/3 PI) 1) into (/ 4/3 PI) * [misc]taylor: Taking taylor expansion of (sqrt (+ 2 (* (* v v) -6))) in v * [misc]taylor: Taking taylor expansion of (+ 2 (* (* v v) -6)) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* (* v v) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 0 -6) into 0 * [misc]backup-simplify: Simplify (+ 2 0) into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 0 -6)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (/ (/ 4/3 PI) (sqrt 2)) into (/ 4/3 (* (sqrt 2) PI)) * [misc]backup-simplify: Simplify (/ 4/3 (* (sqrt 2) PI)) into (/ 4/3 (* (sqrt 2) PI)) * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)))) into 0 * [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 1) (+ (* (/ 4/3 PI) (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt 2)) (+ (* (/ 4/3 (* (sqrt 2) PI)) (/ 0 (sqrt 2))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)))) 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 1) (+ (* (/ 4/3 PI) (/ -1 1)) (* 0 (/ 0 1)))) into (* 4/3 (/ 1 PI)) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 1) (* 0 0))) into 1 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 0 0) (* 1 -6))) into -6 * [misc]backup-simplify: Simplify (+ 0 -6) into -6 * [misc]backup-simplify: Simplify (/ (- -6 (pow 0 2) (+)) (* 2 (sqrt 2))) into (/ -3 (sqrt 2)) * [misc]backup-simplify: Simplify (- (/ (* 4/3 (/ 1 PI)) (sqrt 2)) (+ (* (/ 4/3 (* (sqrt 2) PI)) (/ (/ -3 (sqrt 2)) (sqrt 2))) (* 0 (/ 0 (sqrt 2))))) into (+ (* 4 (/ 1 (* (pow (sqrt 2) 3) PI))) (* 4/3 (/ 1 (* (sqrt 2) PI)))) * [misc]backup-simplify: Simplify (+ (* 4 (/ 1 (* (pow (sqrt 2) 3) PI))) (* 4/3 (/ 1 (* (sqrt 2) PI)))) into (+ (* 4 (/ 1 (* (pow (sqrt 2) 3) PI))) (* 4/3 (/ 1 (* (sqrt 2) PI)))) * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) 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 (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (/ 4/3 PI) (/ 0 1)) (* 0 (/ -1 1)) (* (* 4/3 (/ 1 PI)) (/ 0 1)))) 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 -6)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (/ -3 (sqrt 2)))))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt 2)) (+ (* (/ 4/3 (* (sqrt 2) PI)) (/ 0 (sqrt 2))) (* 0 (/ (/ -3 (sqrt 2)) (sqrt 2))) (* (+ (* 4 (/ 1 (* (pow (sqrt 2) 3) PI))) (* 4/3 (/ 1 (* (sqrt 2) PI)))) (/ 0 (sqrt 2))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) 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 1) (+ (* (/ 4/3 PI) (/ 0 1)) (* 0 (/ 0 1)) (* (* 4/3 (/ 1 PI)) (/ -1 1)) (* 0 (/ 0 1)))) into (* 4/3 (/ 1 PI)) * [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 -6))))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ -3 (sqrt 2)) 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into (/ -9/2 (pow (sqrt 2) 3)) * [misc]backup-simplify: Simplify (- (/ (* 4/3 (/ 1 PI)) (sqrt 2)) (+ (* (/ 4/3 (* (sqrt 2) PI)) (/ (/ -9/2 (pow (sqrt 2) 3)) (sqrt 2))) (* 0 (/ 0 (sqrt 2))) (* (+ (* 4 (/ 1 (* (pow (sqrt 2) 3) PI))) (* 4/3 (/ 1 (* (sqrt 2) PI)))) (/ (/ -3 (sqrt 2)) (sqrt 2))) (* 0 (/ 0 (sqrt 2))))) into (+ (* 4 (/ 1 (* (pow (sqrt 2) 3) PI))) (+ (* 4/3 (/ 1 (* (sqrt 2) PI))) (* 18 (/ 1 (* (pow (sqrt 2) 5) PI))))) * [misc]backup-simplify: Simplify (+ (* 4 (/ 1 (* (pow (sqrt 2) 3) PI))) (+ (* 4/3 (/ 1 (* (sqrt 2) PI))) (* 18 (/ 1 (* (pow (sqrt 2) 5) PI))))) into (+ (* 4 (/ 1 (* (pow (sqrt 2) 3) PI))) (+ (* 4/3 (/ 1 (* (sqrt 2) PI))) (* 18 (/ 1 (* (pow (sqrt 2) 5) PI))))) * [misc]backup-simplify: Simplify (+ (* (+ (* 4 (/ 1 (* (pow (sqrt 2) 3) PI))) (+ (* 4/3 (/ 1 (* (sqrt 2) PI))) (* 18 (/ 1 (* (pow (sqrt 2) 5) PI))))) (pow v 4)) (+ (* (+ (* 4 (/ 1 (* (pow (sqrt 2) 3) PI))) (* 4/3 (/ 1 (* (sqrt 2) PI)))) (pow v 2)) (/ 4/3 (* (sqrt 2) PI)))) into (+ (* 4/3 (/ (pow v 4) (* (sqrt 2) PI))) (+ (* 4/3 (/ 1 (* (sqrt 2) PI))) (+ (* 4 (/ (pow v 4) (* (pow (sqrt 2) 3) PI))) (+ (* 18 (/ (pow v 4) (* (pow (sqrt 2) 5) PI))) (+ (* 4 (/ (pow v 2) (* (pow (sqrt 2) 3) PI))) (* 4/3 (/ (pow v 2) (* (sqrt 2) PI)))))))) * [misc]approximate: Taking taylor expansion of (/ (/ (/ 4/3 PI) (- 1 (* (/ 1 v) (/ 1 v)))) (sqrt (+ 2 (* (* (/ 1 v) (/ 1 v)) -6)))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (/ (/ (/ 4/3 PI) (- 1 (* (/ 1 v) (/ 1 v)))) (sqrt (+ 2 (* (* (/ 1 v) (/ 1 v)) -6)))) in v * [misc]taylor: Taking taylor expansion of (/ (/ 4/3 PI) (- 1 (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of (/ 4/3 PI) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of PI in v * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (/ 4/3 PI) into (/ 4/3 PI) * [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 1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ (/ 4/3 PI) -1) into (/ -4/3 PI) * [misc]taylor: Taking taylor expansion of (sqrt (+ 2 (* (* (/ 1 v) (/ 1 v)) -6))) in v * [misc]taylor: Taking taylor expansion of (+ 2 (* (* (/ 1 v) (/ 1 v)) -6)) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* (* (/ 1 v) (/ 1 v)) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 -6) into -6 * [misc]backup-simplify: Simplify (+ 0 -6) into -6 * [misc]backup-simplify: Simplify (sqrt -6) into (sqrt -6) * [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 (+ (* 1 0) (* 0 -6)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -6))) into 0 * [misc]backup-simplify: Simplify (/ (/ -4/3 PI) (sqrt -6)) into (/ -4/3 (* (sqrt -6) PI)) * [misc]taylor: Taking taylor expansion of (/ (/ (/ 4/3 PI) (- 1 (* (/ 1 v) (/ 1 v)))) (sqrt (+ 2 (* (* (/ 1 v) (/ 1 v)) -6)))) in v * [misc]taylor: Taking taylor expansion of (/ (/ 4/3 PI) (- 1 (* (/ 1 v) (/ 1 v)))) in v * [misc]taylor: Taking taylor expansion of (/ 4/3 PI) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of PI in v * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (/ 4/3 PI) into (/ 4/3 PI) * [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 1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ (/ 4/3 PI) -1) into (/ -4/3 PI) * [misc]taylor: Taking taylor expansion of (sqrt (+ 2 (* (* (/ 1 v) (/ 1 v)) -6))) in v * [misc]taylor: Taking taylor expansion of (+ 2 (* (* (/ 1 v) (/ 1 v)) -6)) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* (* (/ 1 v) (/ 1 v)) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 -6) into -6 * [misc]backup-simplify: Simplify (+ 0 -6) into -6 * [misc]backup-simplify: Simplify (sqrt -6) into (sqrt -6) * [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 (+ (* 1 0) (* 0 -6)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -6))) into 0 * [misc]backup-simplify: Simplify (/ (/ -4/3 PI) (sqrt -6)) into (/ -4/3 (* (sqrt -6) PI)) * [misc]backup-simplify: Simplify (/ -4/3 (* (sqrt -6) PI)) into (/ -4/3 (* (sqrt -6) PI)) * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)))) 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 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 -1) (+ (* (/ -4/3 PI) (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt -6)) (+ (* (/ -4/3 (* (sqrt -6) PI)) (/ 0 (sqrt -6))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)))) 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 (- (/ 0 -1) (+ (* (/ -4/3 PI) (/ 1 -1)) (* 0 (/ 0 -1)))) into (- (* 4/3 (/ 1 PI))) * [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 (+ (* 1 0) (+ (* 0 0) (* 0 -6))) into 0 * [misc]backup-simplify: Simplify (+ 2 0) into 2 * [misc]backup-simplify: Simplify (/ (- 2 (pow 0 2) (+)) (* 2 (sqrt -6))) into (/ 1 (sqrt -6)) * [misc]backup-simplify: Simplify (- (/ (- (* 4/3 (/ 1 PI))) (sqrt -6)) (+ (* (/ -4/3 (* (sqrt -6) PI)) (/ (/ 1 (sqrt -6)) (sqrt -6))) (* 0 (/ 0 (sqrt -6))))) into (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (* 4/3 (/ 1 (* (sqrt -6) PI)))) * [misc]backup-simplify: Simplify (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (* 4/3 (/ 1 (* (sqrt -6) PI)))) into (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (* 4/3 (/ 1 (* (sqrt -6) PI)))) * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) 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 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 -1) (+ (* (/ -4/3 PI) (/ 0 -1)) (* 0 (/ 1 -1)) (* (- (* 4/3 (/ 1 PI))) (/ 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (/ 1 (sqrt -6)))))) (* 2 (sqrt -6))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt -6)) (+ (* (/ -4/3 (* (sqrt -6) PI)) (/ 0 (sqrt -6))) (* 0 (/ (/ 1 (sqrt -6)) (sqrt -6))) (* (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (* 4/3 (/ 1 (* (sqrt -6) PI)))) (/ 0 (sqrt -6))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) 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 (- (/ 0 -1) (+ (* (/ -4/3 PI) (/ 0 -1)) (* 0 (/ 0 -1)) (* (- (* 4/3 (/ 1 PI))) (/ 1 -1)) (* 0 (/ 0 -1)))) into (- (* 4/3 (/ 1 PI))) * [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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6))))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ 1 (sqrt -6)) 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt -6))) into (/ -1/2 (pow (sqrt -6) 3)) * [misc]backup-simplify: Simplify (- (/ (- (* 4/3 (/ 1 PI))) (sqrt -6)) (+ (* (/ -4/3 (* (sqrt -6) PI)) (/ (/ -1/2 (pow (sqrt -6) 3)) (sqrt -6))) (* 0 (/ 0 (sqrt -6))) (* (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (* 4/3 (/ 1 (* (sqrt -6) PI)))) (/ (/ 1 (sqrt -6)) (sqrt -6))) (* 0 (/ 0 (sqrt -6))))) into (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (+ (* 4/3 (/ 1 (* (sqrt -6) PI))) (* 2 (/ 1 (* (pow (sqrt -6) 5) PI))))) * [misc]backup-simplify: Simplify (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (+ (* 4/3 (/ 1 (* (sqrt -6) PI))) (* 2 (/ 1 (* (pow (sqrt -6) 5) PI))))) into (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (+ (* 4/3 (/ 1 (* (sqrt -6) PI))) (* 2 (/ 1 (* (pow (sqrt -6) 5) PI))))) * [misc]backup-simplify: Simplify (+ (* (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (+ (* 4/3 (/ 1 (* (sqrt -6) PI))) (* 2 (/ 1 (* (pow (sqrt -6) 5) PI))))) (pow (/ 1 v) 7)) (+ (* (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (* 4/3 (/ 1 (* (sqrt -6) PI)))) (pow (/ 1 v) 5)) (* (/ -4/3 (* (sqrt -6) PI)) (pow (/ 1 v) 3)))) into (- (+ (* 4/3 (/ 1 (* (pow v 7) (* (pow (sqrt -6) 3) PI)))) (* 4/3 (/ 1 (* (pow v 5) (* (pow (sqrt -6) 3) PI))))) (+ (* 4/3 (/ 1 (* (pow v 7) (* (sqrt -6) PI)))) (+ (* 4/3 (/ 1 (* (pow v 3) (* (sqrt -6) PI)))) (+ (* 2 (/ 1 (* (pow v 7) (* (pow (sqrt -6) 5) PI)))) (* 4/3 (/ 1 (* (pow v 5) (* (sqrt -6) PI)))))))) * [misc]approximate: Taking taylor expansion of (/ (/ (/ 4/3 PI) (- 1 (* (/ 1 (- v)) (/ 1 (- v))))) (sqrt (+ 2 (* (* (/ 1 (- v)) (/ 1 (- v))) -6)))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (/ (/ (/ 4/3 PI) (- 1 (* (/ 1 (- v)) (/ 1 (- v))))) (sqrt (+ 2 (* (* (/ 1 (- v)) (/ 1 (- v))) -6)))) in v * [misc]taylor: Taking taylor expansion of (/ (/ 4/3 PI) (- 1 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of (/ 4/3 PI) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of PI in v * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (/ 4/3 PI) into (/ 4/3 PI) * [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 -1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ (/ 4/3 PI) -1) into (/ -4/3 PI) * [misc]taylor: Taking taylor expansion of (sqrt (+ 2 (* (* (/ 1 (- v)) (/ 1 (- v))) -6))) in v * [misc]taylor: Taking taylor expansion of (+ 2 (* (* (/ 1 (- v)) (/ 1 (- v))) -6)) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- v)) (/ 1 (- v))) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 1 -6) into -6 * [misc]backup-simplify: Simplify (+ 0 -6) into -6 * [misc]backup-simplify: Simplify (sqrt -6) into (sqrt -6) * [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 (+ (* 1 0) (* 0 -6)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -6))) into 0 * [misc]backup-simplify: Simplify (/ (/ -4/3 PI) (sqrt -6)) into (/ -4/3 (* (sqrt -6) PI)) * [misc]taylor: Taking taylor expansion of (/ (/ (/ 4/3 PI) (- 1 (* (/ 1 (- v)) (/ 1 (- v))))) (sqrt (+ 2 (* (* (/ 1 (- v)) (/ 1 (- v))) -6)))) in v * [misc]taylor: Taking taylor expansion of (/ (/ 4/3 PI) (- 1 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [misc]taylor: Taking taylor expansion of (/ 4/3 PI) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of PI in v * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (/ 4/3 PI) into (/ 4/3 PI) * [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 -1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ (/ 4/3 PI) -1) into (/ -4/3 PI) * [misc]taylor: Taking taylor expansion of (sqrt (+ 2 (* (* (/ 1 (- v)) (/ 1 (- v))) -6))) in v * [misc]taylor: Taking taylor expansion of (+ 2 (* (* (/ 1 (- v)) (/ 1 (- v))) -6)) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- v)) (/ 1 (- v))) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 1 -6) into -6 * [misc]backup-simplify: Simplify (+ 0 -6) into -6 * [misc]backup-simplify: Simplify (sqrt -6) into (sqrt -6) * [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 (+ (* 1 0) (* 0 -6)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -6))) into 0 * [misc]backup-simplify: Simplify (/ (/ -4/3 PI) (sqrt -6)) into (/ -4/3 (* (sqrt -6) PI)) * [misc]backup-simplify: Simplify (/ -4/3 (* (sqrt -6) PI)) into (/ -4/3 (* (sqrt -6) PI)) * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)))) 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 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 -1) (+ (* (/ -4/3 PI) (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt -6)) (+ (* (/ -4/3 (* (sqrt -6) PI)) (/ 0 (sqrt -6))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)))) 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 -1) (+ (* (/ -4/3 PI) (/ 1 -1)) (* 0 (/ 0 -1)))) into (- (* 4/3 (/ 1 PI))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-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 (+ (* 1 0) (+ (* 0 0) (* 0 -6))) into 0 * [misc]backup-simplify: Simplify (+ 2 0) into 2 * [misc]backup-simplify: Simplify (/ (- 2 (pow 0 2) (+)) (* 2 (sqrt -6))) into (/ 1 (sqrt -6)) * [misc]backup-simplify: Simplify (- (/ (- (* 4/3 (/ 1 PI))) (sqrt -6)) (+ (* (/ -4/3 (* (sqrt -6) PI)) (/ (/ 1 (sqrt -6)) (sqrt -6))) (* 0 (/ 0 (sqrt -6))))) into (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (* 4/3 (/ 1 (* (sqrt -6) PI)))) * [misc]backup-simplify: Simplify (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (* 4/3 (/ 1 (* (sqrt -6) PI)))) into (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (* 4/3 (/ 1 (* (sqrt -6) PI)))) * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) 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 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 -1) (+ (* (/ -4/3 PI) (/ 0 -1)) (* 0 (/ 1 -1)) (* (- (* 4/3 (/ 1 PI))) (/ 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (/ 1 (sqrt -6)))))) (* 2 (sqrt -6))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt -6)) (+ (* (/ -4/3 (* (sqrt -6) PI)) (/ 0 (sqrt -6))) (* 0 (/ (/ 1 (sqrt -6)) (sqrt -6))) (* (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (* 4/3 (/ 1 (* (sqrt -6) PI)))) (/ 0 (sqrt -6))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) 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 -1) (+ (* (/ -4/3 PI) (/ 0 -1)) (* 0 (/ 0 -1)) (* (- (* 4/3 (/ 1 PI))) (/ 1 -1)) (* 0 (/ 0 -1)))) into (- (* 4/3 (/ 1 PI))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6))))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ 1 (sqrt -6)) 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt -6))) into (/ -1/2 (pow (sqrt -6) 3)) * [misc]backup-simplify: Simplify (- (/ (- (* 4/3 (/ 1 PI))) (sqrt -6)) (+ (* (/ -4/3 (* (sqrt -6) PI)) (/ (/ -1/2 (pow (sqrt -6) 3)) (sqrt -6))) (* 0 (/ 0 (sqrt -6))) (* (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (* 4/3 (/ 1 (* (sqrt -6) PI)))) (/ (/ 1 (sqrt -6)) (sqrt -6))) (* 0 (/ 0 (sqrt -6))))) into (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (+ (* 4/3 (/ 1 (* (sqrt -6) PI))) (* 2 (/ 1 (* (pow (sqrt -6) 5) PI))))) * [misc]backup-simplify: Simplify (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (+ (* 4/3 (/ 1 (* (sqrt -6) PI))) (* 2 (/ 1 (* (pow (sqrt -6) 5) PI))))) into (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (+ (* 4/3 (/ 1 (* (sqrt -6) PI))) (* 2 (/ 1 (* (pow (sqrt -6) 5) PI))))) * [misc]backup-simplify: Simplify (+ (* (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (+ (* 4/3 (/ 1 (* (sqrt -6) PI))) (* 2 (/ 1 (* (pow (sqrt -6) 5) PI))))) (pow (/ 1 (- v)) 7)) (+ (* (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (* 4/3 (/ 1 (* (sqrt -6) PI)))) (pow (/ 1 (- v)) 5)) (* (/ -4/3 (* (sqrt -6) PI)) (pow (/ 1 (- v)) 3)))) into (- (+ (* 4/3 (/ 1 (* (pow v 7) (* (sqrt -6) PI)))) (+ (* 4/3 (/ 1 (* (pow v 5) (* (sqrt -6) PI)))) (+ (* 4/3 (/ 1 (* (pow v 3) (* (sqrt -6) PI)))) (* 2 (/ 1 (* (pow v 7) (* (pow (sqrt -6) 5) PI))))))) (+ (* 4/3 (/ 1 (* (pow v 7) (* (pow (sqrt -6) 3) PI)))) (* 4/3 (/ 1 (* (pow v 5) (* (pow (sqrt -6) 3) PI)))))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 2 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 3 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 4 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 5 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 6 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 7 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 8 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 9 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 10 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 11 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 12 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 13 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 14 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 15 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 16 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 17 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 18 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 19 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 20 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 21 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (/ 4/3 PI)) (log (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (64 enodes) * * [misc]simplify: iters left: 1 (81 enodes) * [exit]simplify: Simplified to (- (log (/ 4/3 PI)) (log (- 1 (* v v)))) * [misc]simplify: Simplified (2 1 1) to (λ (v) (/ (exp (- (log (/ 4/3 PI)) (log (- 1 (* v v))))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 22 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 23 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 24 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (/ 4/3 PI) (/ 4/3 PI)) (/ 4/3 PI)) (* (* (- 1 (* v v)) (- 1 (* v v))) (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (101 enodes) * * [misc]simplify: iters left: 3 (325 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 64/27 PI) (* PI PI)) (- 1 (* v v))) (* (- 1 (* v v)) (- 1 (* v v)))) * [misc]simplify: Simplified (2 1 1) to (λ (v) (/ (cbrt (/ (/ (/ (/ 64/27 PI) (* PI PI)) (- 1 (* v v))) (* (- 1 (* v v)) (- 1 (* v v))))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 25 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 26 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 27 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 28 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 29 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * * [misc]simplify: iters left: 2 (41 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1 1) to (λ (v) (/ (* (* (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v))))) (sqrt (+ 2 (* (* v v) -6))))) * [enter]simplify: Simplifying (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1 2) to (λ (v) (/ (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v))))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 30 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1 1) to (λ (v) (/ (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* v v)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (sqrt (+ 2 (* (* v v) -6))))) * [enter]simplify: Simplifying (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1 2) to (λ (v) (/ (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* v v)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 31 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * * [misc]simplify: iters left: 2 (57 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 1 1) to (λ (v) (/ (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (/ (cbrt (/ 4/3 PI)) (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6))))) * [enter]simplify: Simplifying (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) * [misc]simplify: Simplified (2 1 2) to (λ (v) (/ (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (/ (cbrt (/ 4/3 PI)) (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 32 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 4/3 PI)) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1 1) to (λ (v) (/ (* (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v))))) (sqrt (+ 2 (* (* v v) -6))))) * [enter]simplify: Simplifying (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1 2) to (λ (v) (/ (* (/ (sqrt (/ 4/3 PI)) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v))))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 33 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1 1) to (λ (v) (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (sqrt (+ 2 (* (* v v) -6))))) * [enter]simplify: Simplifying (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1 2) to (λ (v) (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 34 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 4/3 PI)) 1) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * * [misc]simplify: iters left: 3 (10 enodes) * [exit]simplify: Simplified to (sqrt (/ 4/3 PI)) * [misc]simplify: Simplified (2 1 1) to (λ (v) (/ (* (sqrt (/ 4/3 PI)) (/ (sqrt (/ 4/3 PI)) (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6))))) * [enter]simplify: Simplifying (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) * [misc]simplify: Simplified (2 1 2) to (λ (v) (/ (* (sqrt (/ 4/3 PI)) (/ (sqrt (/ 4/3 PI)) (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 35 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1 1) to (λ (v) (/ (* (/ (/ 1 (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) (/ (/ 4/3 PI) (cbrt (- 1 (* v v))))) (sqrt (+ 2 (* (* v v) -6))))) * [enter]simplify: Simplifying (/ (/ 4/3 PI) (cbrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (cbrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1 2) to (λ (v) (/ (* (/ 1 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (/ (/ 4/3 PI) (cbrt (- 1 (* v v))))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 36 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1 1) to (λ (v) (/ (* (/ 1 (sqrt (- 1 (* v v)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (+ 2 (* (* v v) -6))))) * [enter]simplify: Simplifying (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1 2) to (λ (v) (/ (* (/ 1 (sqrt (- 1 (* v v)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 37 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 1) * * [misc]simplify: iters left: 2 (2 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 1 1) to (λ (v) (/ (* 1 (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6))))) * [enter]simplify: Simplifying (/ (/ 4/3 PI) (- 1 (* v v))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * * [misc]simplify: iters left: 2 (41 enodes) * * [misc]simplify: iters left: 1 (52 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (- 1 (* v v))) * [misc]simplify: Simplified (2 1 2) to (λ (v) (/ (* 1 (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 38 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 4/3 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * [exit]simplify: Simplified to (/ 4/3 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1 1) to (λ (v) (/ (* (/ 4/3 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (/ (/ 1 PI) (cbrt (- 1 (* v v))))) (sqrt (+ 2 (* (* v v) -6))))) * [enter]simplify: Simplifying (/ (/ 1 PI) (cbrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * [exit]simplify: Simplified to (/ (/ 1 PI) (cbrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1 2) to (λ (v) (/ (* (/ 4/3 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (/ (/ 1 PI) (cbrt (- 1 (* v v))))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 39 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 4/3 (sqrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1 1) to (λ (v) (/ (* (/ 4/3 (sqrt (- 1 (* v v)))) (/ (/ 1 PI) (sqrt (- 1 (* v v))))) (sqrt (+ 2 (* (* v v) -6))))) * [enter]simplify: Simplifying (/ (/ 1 PI) (sqrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * [exit]simplify: Simplified to (/ (/ 1 PI) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1 2) to (λ (v) (/ (* (/ 4/3 (sqrt (- 1 (* v v)))) (/ (/ 1 PI) (sqrt (- 1 (* v v))))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 40 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 4/3 1) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (5 enodes) * [exit]simplify: Simplified to 4/3 * [misc]simplify: Simplified (2 1 1) to (λ (v) (/ (* 4/3 (/ (/ 1 PI) (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6))))) * [enter]simplify: Simplifying (/ (/ 1 PI) (- 1 (* v v))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * * [misc]simplify: iters left: 2 (40 enodes) * * [misc]simplify: iters left: 1 (51 enodes) * [exit]simplify: Simplified to (/ (/ 1 PI) (- 1 (* v v))) * [misc]simplify: Simplified (2 1 2) to (λ (v) (/ (* 4/3 (/ (/ 1 PI) (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 41 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 42 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 43 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 44 / 212 ] 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 1 2) to (λ (v) (/ (/ (/ (/ 4/3 PI) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (cbrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 45 / 212 ] 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 1 2) to (λ (v) (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 46 / 212 ] 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 1 2) to (λ (v) (/ (/ (/ (/ 4/3 PI) 1) (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 47 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) * * [misc]simplify: iters left: 5 (5 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 1 1) to (λ (v) (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (/ (- 1 (* v v)) (cbrt (/ 4/3 PI)))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 48 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ 4/3 PI)) * * [misc]simplify: iters left: 3 (4 enodes) * [exit]simplify: Simplified to (sqrt (/ 4/3 PI)) * [misc]simplify: Simplified (2 1 1) to (λ (v) (/ (/ (sqrt (/ 4/3 PI)) (/ (- 1 (* v v)) (sqrt (/ 4/3 PI)))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 49 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 50 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 51 / 212 ] 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 1 2) to (λ (v) (/ (* (/ (/ 4/3 PI) (- (pow 1 3) (pow (* v v) 3))) (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 52 / 212 ] 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 1 2) to (λ (v) (/ (* (/ (/ 4/3 PI) (- (* 1 1) (* (* v v) (* v v)))) (+ 1 (* v v))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 53 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 54 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 55 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (log (/ 4/3 PI)) (log (- 1 (* v v)))) (log (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (117 enodes) * * [misc]simplify: iters left: 2 (271 enodes) * [exit]simplify: Simplified to (- (- (log (/ 4/3 PI)) (log (- 1 (* v v)))) (log (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (exp (- (- (log (/ 4/3 PI)) (log (- 1 (* v v)))) (log (sqrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 56 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (/ (/ 4/3 PI) (- 1 (* v v)))) (log (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (161 enodes) * * [misc]simplify: iters left: 1 (338 enodes) * [exit]simplify: Simplified to (- (log (/ (/ 4/3 PI) (- 1 (* v v)))) (log (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (exp (- (log (/ (/ 4/3 PI) (- 1 (* v v)))) (log (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 57 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 58 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 59 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (* (/ 4/3 PI) (/ 4/3 PI)) (/ 4/3 PI)) (* (* (- 1 (* v v)) (- 1 (* v v))) (- 1 (* v v)))) (* (* (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (173 enodes) * [exit]simplify: Simplified to (* (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* (* -6 v) v) 2))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (/ (+ (* (* -6 v) v) 2) (/ (/ 4/3 PI) (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (cbrt (* (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* (* -6 v) v) 2))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (/ (+ (* (* -6 v) v) 2) (/ (/ 4/3 PI) (- 1 (* v v)))))))) * * * * [misc]progress: [ 60 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (/ (/ 4/3 PI) (- 1 (* v v))) (/ (/ 4/3 PI) (- 1 (* v v)))) (/ (/ 4/3 PI) (- 1 (* v v)))) (* (* (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (131 enodes) * [exit]simplify: Simplified to (/ (* (* (/ (/ 4/3 PI) (- 1 (* v v))) (/ (/ 4/3 PI) (- 1 (* v v)))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (+ (* (* -6 v) v) 2))) (sqrt (+ (* (* -6 v) v) 2))) * [misc]simplify: Simplified (2 1) to (λ (v) (cbrt (/ (* (* (/ (/ 4/3 PI) (- 1 (* v v))) (/ (/ 4/3 PI) (- 1 (* v v)))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (+ (* (* -6 v) v) 2))) (sqrt (+ (* (* -6 v) v) 2))))) * * * * [misc]progress: [ 61 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 62 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 63 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 64 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 65 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (/ (/ 4/3 PI) (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (79 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) (/ (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (67 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (/ (/ 4/3 PI) (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (/ (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 66 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (/ (/ 4/3 PI) (- 1 (* v v))))) (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (64 enodes) * * [misc]simplify: iters left: 1 (75 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (/ (/ 4/3 PI) (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (/ (/ 4/3 PI) (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (cbrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (cbrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (67 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (/ (/ 4/3 PI) (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (cbrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 67 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (/ (/ 4/3 PI) (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (62 enodes) * * [misc]simplify: iters left: 1 (73 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (/ (/ 4/3 PI) (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (/ (/ 4/3 PI) (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (67 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (/ (/ 4/3 PI) (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 68 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (/ (/ 4/3 PI) (- 1 (* v v))))) (sqrt 1)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * * [misc]simplify: iters left: 2 (68 enodes) * * [misc]simplify: iters left: 1 (80 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (/ (/ 4/3 PI) (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (/ (/ 4/3 PI) (- 1 (* v v))))) (/ (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (66 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (/ (/ 4/3 PI) (- 1 (* v v))))) (/ (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 69 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (/ (/ 4/3 PI) (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (62 enodes) * * [misc]simplify: iters left: 1 (73 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (/ (/ 4/3 PI) (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (/ (/ 4/3 PI) (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (67 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (/ (/ 4/3 PI) (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 70 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (/ (/ 4/3 PI) (- 1 (* v v))))) 1) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (92 enodes) * * [misc]simplify: iters left: 1 (103 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (/ (/ 4/3 PI) (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (/ (/ 4/3 PI) (- 1 (* v v))))) (/ (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (66 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (/ (/ 4/3 PI) (- 1 (* v v))))) (/ (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 71 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (67 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 72 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * * [misc]simplify: iters left: 2 (58 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (fabs (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (fabs (cbrt (+ (* v (* v -6)) 2)))) (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (cbrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (cbrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (67 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (fabs (cbrt (+ (* v (* v -6)) 2)))) (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (cbrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 73 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (67 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (67 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 74 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt 1)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * * [misc]simplify: iters left: 2 (46 enodes) * * [misc]simplify: iters left: 1 (57 enodes) * [exit]simplify: Simplified to (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (66 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 75 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (67 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (67 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 76 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) 1) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * * [misc]simplify: iters left: 2 (45 enodes) * * [misc]simplify: iters left: 1 (56 enodes) * [exit]simplify: Simplified to (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (66 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 77 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (250 enodes) * * [misc]simplify: iters left: 1 (310 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) (/ (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (cbrt (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (/ (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (cbrt (sqrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 78 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (95 enodes) * * [misc]simplify: iters left: 2 (129 enodes) * * [misc]simplify: iters left: 1 (146 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (cbrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (cbrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (cbrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (cbrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 79 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (93 enodes) * * [misc]simplify: iters left: 2 (128 enodes) * * [misc]simplify: iters left: 1 (147 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 80 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (sqrt 1)) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (80 enodes) * * [misc]simplify: iters left: 2 (258 enodes) * * [misc]simplify: iters left: 1 (392 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v))))) (/ (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (+ (* -6 (* v v)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v))))) (/ (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (+ (* -6 (* v v)) 2))))) * * * * [misc]progress: [ 81 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (93 enodes) * * [misc]simplify: iters left: 2 (128 enodes) * * [misc]simplify: iters left: 1 (147 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 82 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) 1) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (277 enodes) * * [misc]simplify: iters left: 1 (371 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v))))) (/ (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (+ (* -6 (* v v)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v))))) (/ (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (+ (* -6 (* v v)) 2))))) * * * * [misc]progress: [ 83 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* v v)))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (129 enodes) * * [misc]simplify: iters left: 1 (150 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* v v)))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 84 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* v v)))) (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (69 enodes) * * [misc]simplify: iters left: 1 (72 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* v v)))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* v v)))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* v v)))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 85 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 86 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* v v)))) (sqrt 1)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (142 enodes) * * [misc]simplify: iters left: 1 (146 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* v v)))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* -6 (* v v)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* v v)))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* -6 (* v v)) 2))))) * * * * [misc]progress: [ 87 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 88 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* v v)))) 1) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (147 enodes) * * [misc]simplify: iters left: 1 (162 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* v v)))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* -6 (* v v)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* v v)))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* -6 (* v v)) 2))))) * * * * [misc]progress: [ 89 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (119 enodes) * * [misc]simplify: iters left: 2 (339 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ (* v (* v -6)) 2)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ (* v (* v -6)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ (* v (* v -6)) 2)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ (* v (* v -6)) 2))))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (cbrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (78 enodes) * * [misc]simplify: iters left: 2 (127 enodes) * * [misc]simplify: iters left: 1 (161 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ (* v (* v -6)) 2)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ (* v (* v -6)) 2))))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 90 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1) (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (127 enodes) * * [misc]simplify: iters left: 1 (173 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (+ (* (* v -6) v) 2)))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (cbrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (cbrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (78 enodes) * * [misc]simplify: iters left: 2 (127 enodes) * * [misc]simplify: iters left: 1 (161 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (+ (* (* v -6) v) 2)))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 91 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (84 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (195 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (78 enodes) * * [misc]simplify: iters left: 2 (127 enodes) * * [misc]simplify: iters left: 1 (161 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 92 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1) (sqrt 1)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (77 enodes) * * [misc]simplify: iters left: 2 (126 enodes) * * [misc]simplify: iters left: 1 (163 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 93 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (84 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (195 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (78 enodes) * * [misc]simplify: iters left: 2 (127 enodes) * * [misc]simplify: iters left: 1 (161 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 94 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1) 1) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (77 enodes) * * [misc]simplify: iters left: 2 (126 enodes) * * [misc]simplify: iters left: 1 (163 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 95 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (78 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (cbrt (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (cbrt (sqrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 96 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * * [misc]simplify: iters left: 2 (53 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) (fabs (cbrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) (fabs (cbrt (+ (* (* -6 v) v) 2)))) (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (cbrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (cbrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (cbrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) (fabs (cbrt (+ (* (* -6 v) v) 2)))) (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (cbrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 97 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (51 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 98 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (sqrt 1)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * * [misc]simplify: iters left: 2 (38 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (+ (* -6 (* v v)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (+ (* -6 (* v v)) 2))))) * * * * [misc]progress: [ 99 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (51 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 100 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) 1) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * * [misc]simplify: iters left: 2 (39 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (+ (* -6 (* v v)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (sqrt (+ (* -6 (* v v)) 2))))) * * * * [misc]progress: [ 101 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * * [misc]simplify: iters left: 2 (49 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* -6 (* v v)) 2)))) (cbrt (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* -6 (* v v)) 2)))) (cbrt (sqrt (+ (* -6 (* v v)) 2)))) (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 102 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (fabs (cbrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (fabs (cbrt (+ (* -6 (* v v)) 2)))) (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (fabs (cbrt (+ (* -6 (* v v)) 2)))) (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 103 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 104 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt 1)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * * [misc]simplify: iters left: 2 (30 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* -6 (* v v)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* -6 (* v v)) 2))))) * * * * [misc]progress: [ 105 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 106 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) 1) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * * [misc]simplify: iters left: 2 (29 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* -6 (* v v)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* -6 (* v v)) 2))))) * * * * [misc]progress: [ 107 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) 1) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (cbrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (78 enodes) * * [misc]simplify: iters left: 2 (127 enodes) * * [misc]simplify: iters left: 1 (161 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 108 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) 1) (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (+ (* (* -6 v) v) 2)))) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (cbrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (cbrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (78 enodes) * * [misc]simplify: iters left: 2 (127 enodes) * * [misc]simplify: iters left: 1 (161 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (+ (* (* -6 v) v) 2)))) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 109 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) 1) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (78 enodes) * * [misc]simplify: iters left: 2 (127 enodes) * * [misc]simplify: iters left: 1 (161 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 110 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) 1) (sqrt 1)) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * [exit]simplify: Simplified to (sqrt (/ 4/3 PI)) * [misc]simplify: Simplified (2 1) to (λ (v) (* (sqrt (/ 4/3 PI)) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (77 enodes) * * [misc]simplify: iters left: 2 (126 enodes) * * [misc]simplify: iters left: 1 (163 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (sqrt (/ 4/3 PI)) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 111 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) 1) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (78 enodes) * * [misc]simplify: iters left: 2 (127 enodes) * * [misc]simplify: iters left: 1 (161 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 112 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) 1) 1) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (9 enodes) * [exit]simplify: Simplified to (sqrt (/ 4/3 PI)) * [misc]simplify: Simplified (2 1) to (λ (v) (* (sqrt (/ 4/3 PI)) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (77 enodes) * * [misc]simplify: iters left: 2 (126 enodes) * * [misc]simplify: iters left: 1 (163 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (sqrt (/ 4/3 PI)) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 113 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (71 enodes) * * [misc]simplify: iters left: 1 (74 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (/ (/ 4/3 PI) (cbrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (cbrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * * [misc]simplify: iters left: 2 (60 enodes) * * [misc]simplify: iters left: 1 (61 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (cbrt (- 1 (* v v)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (/ (/ (/ 4/3 PI) (cbrt (- 1 (* v v)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 114 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (49 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ (/ (/ 4/3 PI) (cbrt (- 1 (* v v)))) (sqrt (cbrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (cbrt (- 1 (* v v)))) (sqrt (cbrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * * [misc]simplify: iters left: 2 (60 enodes) * * [misc]simplify: iters left: 1 (61 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (cbrt (- 1 (* v v)))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ (/ (/ 4/3 PI) (cbrt (- 1 (* v v)))) (sqrt (cbrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 115 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (/ (/ 4/3 PI) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * * [misc]simplify: iters left: 2 (60 enodes) * * [misc]simplify: iters left: 1 (61 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 4/3 PI) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 116 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (sqrt 1)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * * [misc]simplify: iters left: 2 (30 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) (/ (/ (/ 4/3 PI) (cbrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (cbrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (60 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (cbrt (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) (/ (/ (/ 4/3 PI) (cbrt (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 117 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (/ (/ 4/3 PI) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * * [misc]simplify: iters left: 2 (60 enodes) * * [misc]simplify: iters left: 1 (61 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 4/3 PI) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 118 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) 1) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * * [misc]simplify: iters left: 2 (30 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) (/ (/ (/ 4/3 PI) (cbrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (cbrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (60 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (cbrt (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) (/ (/ (/ 4/3 PI) (cbrt (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 119 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * * [misc]simplify: iters left: 2 (45 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (* v v)))) (* (cbrt (sqrt (+ (* (* v -6) v) 2))) (cbrt (sqrt (+ (* (* v -6) v) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (* v v)))) (* (cbrt (sqrt (+ (* (* v -6) v) 2))) (cbrt (sqrt (+ (* (* v -6) v) 2))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * * [misc]simplify: iters left: 2 (60 enodes) * * [misc]simplify: iters left: 1 (61 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (* v v)))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 120 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (* v v)))) (fabs (cbrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (* v v)))) (fabs (cbrt (+ (* (* v -6) v) 2)))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * * [misc]simplify: iters left: 2 (60 enodes) * * [misc]simplify: iters left: 1 (61 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (* v v)))) (fabs (cbrt (+ (* (* v -6) v) 2)))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 121 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * * [misc]simplify: iters left: 2 (60 enodes) * * [misc]simplify: iters left: 1 (61 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 122 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (sqrt 1)) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (- 1 (* v v)))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (60 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (- 1 (* v v)))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 123 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * * [misc]simplify: iters left: 2 (60 enodes) * * [misc]simplify: iters left: 1 (61 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 124 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) 1) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (- 1 (* v v)))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (60 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (- 1 (* v v)))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 125 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (12 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 (/ 1 (* (cbrt (sqrt (+ 2 (* (* v -6) v)))) (cbrt (sqrt (+ 2 (* (* v -6) v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (* (cbrt (sqrt (+ 2 (* (* v -6) v)))) (cbrt (sqrt (+ 2 (* (* v -6) v)))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (cbrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (- 1 (* v v))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (184 enodes) * * [misc]simplify: iters left: 1 (310 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (* (cbrt (sqrt (+ 2 (* (* v -6) v)))) (cbrt (sqrt (+ 2 (* (* v -6) v)))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 126 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (/ 1 (fabs (cbrt (+ 2 (* (* v -6) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (fabs (cbrt (+ 2 (* (* v -6) v))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (cbrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (cbrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (184 enodes) * * [misc]simplify: iters left: 1 (310 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (fabs (cbrt (+ 2 (* (* v -6) v))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 127 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (184 enodes) * * [misc]simplify: iters left: 1 (310 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 128 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (sqrt 1)) * * [misc]simplify: iters left: 4 (4 enodes) * * [misc]simplify: iters left: 3 (6 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 1) to (λ (v) (* 1 (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (173 enodes) * * [misc]simplify: iters left: 1 (299 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* -6 (* v v)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* 1 (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* -6 (* v v)) 2))))) * * * * [misc]progress: [ 129 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (184 enodes) * * [misc]simplify: iters left: 1 (310 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 130 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) 1) * * [misc]simplify: iters left: 4 (3 enodes) * * [misc]simplify: iters left: 3 (5 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 1) to (λ (v) (* 1 (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (173 enodes) * * [misc]simplify: iters left: 1 (299 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* -6 (* v v)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* 1 (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* -6 (* v v)) 2))))) * * * * [misc]progress: [ 131 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (72 enodes) * * [misc]simplify: iters left: 1 (75 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (/ (/ 1 PI) (cbrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (/ 1 PI) (cbrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (60 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (cbrt (- 1 (* v v)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (/ (/ (/ 1 PI) (cbrt (- 1 (* v v)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 132 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * * [misc]simplify: iters left: 2 (50 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (/ (/ 1 PI) (cbrt (- 1 (* v v)))) (sqrt (cbrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (/ 1 PI) (cbrt (- 1 (* v v)))) (sqrt (cbrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (60 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (cbrt (- 1 (* v v)))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (/ (/ 1 PI) (cbrt (- 1 (* v v)))) (sqrt (cbrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 133 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (/ 1 PI) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (/ 1 PI) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (60 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 1 PI) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 134 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (sqrt 1)) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * * [misc]simplify: iters left: 2 (31 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) (/ (/ (/ 1 PI) (cbrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (/ (/ 1 PI) (cbrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * * [misc]simplify: iters left: 2 (58 enodes) * * [misc]simplify: iters left: 1 (59 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (cbrt (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) (/ (/ (/ 1 PI) (cbrt (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 135 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (/ 1 PI) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (/ 1 PI) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (60 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 1 PI) (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 136 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) 1) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * * [misc]simplify: iters left: 2 (31 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) (/ (/ (/ 1 PI) (cbrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (/ (/ 1 PI) (cbrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * * [misc]simplify: iters left: 2 (58 enodes) * * [misc]simplify: iters left: 1 (59 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (cbrt (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) (/ (/ (/ 1 PI) (cbrt (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 137 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 (sqrt (- 1 (* v v)))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (46 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (60 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (* v v)))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 138 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 (sqrt (- 1 (* v v)))) (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (- 1 (* v v)))) (fabs (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (* v v)))) (fabs (cbrt (+ (* v (* v -6)) 2)))) (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (60 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (* v v)))) (fabs (cbrt (+ (* v (* v -6)) 2)))) (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 139 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (60 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 140 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 (sqrt (- 1 (* v v)))) (sqrt 1)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (sqrt (- 1 (* v v)))) (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * * [misc]simplify: iters left: 2 (58 enodes) * * [misc]simplify: iters left: 1 (59 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (sqrt (- 1 (* v v)))) (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 141 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (60 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 142 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 (sqrt (- 1 (* v v)))) 1) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (sqrt (- 1 (* v v)))) (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * * [misc]simplify: iters left: 2 (58 enodes) * * [misc]simplify: iters left: 1 (59 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (sqrt (- 1 (* v v)))) (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 143 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 1) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ 4/3 (* (cbrt (sqrt (+ 2 (* v (* -6 v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (* (cbrt (sqrt (+ 2 (* v (* -6 v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ (/ 1 PI) (- 1 (* v v))) (cbrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (/ 1 PI) (- 1 (* v v))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (173 enodes) * * [misc]simplify: iters left: 1 (299 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (- 1 (* v v))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (* (cbrt (sqrt (+ 2 (* v (* -6 v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ (/ 1 PI) (- 1 (* v v))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 144 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 1) (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6)))))) * * [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 (/ 4/3 (fabs (cbrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (fabs (cbrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (cbrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (cbrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (173 enodes) * * [misc]simplify: iters left: 1 (299 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (cbrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (fabs (cbrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (cbrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 145 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 1) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (173 enodes) * * [misc]simplify: iters left: 1 (299 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 146 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 1) (sqrt 1)) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to 4/3 * [misc]simplify: Simplified (2 1) to (λ (v) (* 4/3 (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (96 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (314 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (+ (* (* -6 v) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* 4/3 (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (+ (* (* -6 v) v) 2))))) * * * * [misc]progress: [ 147 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 1) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (173 enodes) * * [misc]simplify: iters left: 1 (299 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 148 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 1) 1) * * [misc]simplify: iters left: 4 (4 enodes) * * [misc]simplify: iters left: 3 (6 enodes) * [exit]simplify: Simplified to 4/3 * [misc]simplify: Simplified (2 1) to (λ (v) (* 4/3 (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (96 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (314 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (+ (* (* -6 v) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* 4/3 (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (+ (* (* -6 v) v) 2))))) * * * * [misc]progress: [ 149 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (cbrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (- 1 (* v v))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (184 enodes) * * [misc]simplify: iters left: 1 (310 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 150 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (/ 1 (fabs (cbrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (fabs (cbrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (cbrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (cbrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (184 enodes) * * [misc]simplify: iters left: 1 (310 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (fabs (cbrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 151 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (184 enodes) * * [misc]simplify: iters left: 1 (310 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 152 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt 1)) * * [misc]simplify: iters left: 3 (3 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 1) to (λ (v) (* 1 (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (173 enodes) * * [misc]simplify: iters left: 1 (299 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* -6 (* v v)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* 1 (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* -6 (* v v)) 2))))) * * * * [misc]progress: [ 153 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (184 enodes) * * [misc]simplify: iters left: 1 (310 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 154 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 1) * * [misc]simplify: iters left: 2 (2 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 1) to (λ (v) (* 1 (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (173 enodes) * * [misc]simplify: iters left: 1 (299 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* -6 (* v v)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* 1 (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* -6 (* v v)) 2))))) * * * * [misc]progress: [ 155 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 PI) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (36 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (* (cbrt (sqrt (+ 2 (* v (* -6 v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (* (cbrt (sqrt (+ 2 (* v (* -6 v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ 1 (- 1 (* v v))) (cbrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ 1 (- 1 (* v v))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (123 enodes) * * [misc]simplify: iters left: 1 (177 enodes) * [exit]simplify: Simplified to (/ (/ 1 (- 1 (* v v))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (/ (/ 1 (- 1 (* v v))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 156 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 PI) (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (fabs (cbrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (fabs (cbrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (- 1 (* v v))) (sqrt (cbrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ 1 (- 1 (* v v))) (sqrt (cbrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (123 enodes) * * [misc]simplify: iters left: 1 (177 enodes) * [exit]simplify: Simplified to (/ (/ 1 (- 1 (* v v))) (sqrt (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (fabs (cbrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (- 1 (* v v))) (sqrt (cbrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 157 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 PI) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (12 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 (/ (/ 4/3 PI) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (- 1 (* v v))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ 1 (- 1 (* v v))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (123 enodes) * * [misc]simplify: iters left: 1 (177 enodes) * [exit]simplify: Simplified to (/ (/ 1 (- 1 (* v v))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (- 1 (* v v))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 158 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 PI) (sqrt 1)) * * [misc]simplify: iters left: 4 (6 enodes) * * [misc]simplify: iters left: 3 (10 enodes) * [exit]simplify: Simplified to (/ 4/3 PI) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 PI) (/ (/ 1 (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (/ 1 (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (73 enodes) * * [misc]simplify: iters left: 2 (122 enodes) * * [misc]simplify: iters left: 1 (154 enodes) * [exit]simplify: Simplified to (/ (/ 1 (- 1 (* v v))) (sqrt (+ 2 (* -6 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 PI) (/ (/ 1 (- 1 (* v v))) (sqrt (+ 2 (* -6 (* v v))))))) * * * * [misc]progress: [ 159 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 PI) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (12 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 (/ (/ 4/3 PI) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (- 1 (* v v))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ 1 (- 1 (* v v))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (123 enodes) * * [misc]simplify: iters left: 1 (177 enodes) * [exit]simplify: Simplified to (/ (/ 1 (- 1 (* v v))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (- 1 (* v v))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 160 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 PI) 1) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (9 enodes) * [exit]simplify: Simplified to (/ 4/3 PI) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 PI) (/ (/ 1 (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (/ 1 (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (73 enodes) * * [misc]simplify: iters left: 2 (122 enodes) * * [misc]simplify: iters left: 1 (154 enodes) * [exit]simplify: Simplified to (/ (/ 1 (- 1 (* v v))) (sqrt (+ 2 (* -6 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 PI) (/ (/ 1 (- 1 (* v v))) (sqrt (+ 2 (* -6 (* v v))))))) * * * * [misc]progress: [ 161 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (- (pow 1 3) (pow (* v v) 3))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (77 enodes) * * [misc]simplify: iters left: 3 (203 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* (pow v 3) (pow v 3)))) (* (cbrt (sqrt (+ (* -6 (* v v)) 2))) (cbrt (sqrt (+ (* -6 (* v v)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (- 1 (* (pow v 3) (pow v 3)))) (* (cbrt (sqrt (+ (* -6 (* v v)) 2))) (cbrt (sqrt (+ (* -6 (* v v)) 2))))) (/ (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (166 enodes) * * [misc]simplify: iters left: 1 (197 enodes) * [exit]simplify: Simplified to (/ (+ 1 (+ (* v v) (pow v 4))) (cbrt (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (- (pow 1 3) (pow (* v v) 3))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (/ (+ 1 (+ (* v v) (pow v 4))) (cbrt (sqrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 162 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (- (pow 1 3) (pow (* v v) 3))) (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * * [misc]simplify: iters left: 2 (378 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (pow v 6))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (- 1 (pow v 6))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))) (sqrt (cbrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))) (sqrt (cbrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (166 enodes) * * [misc]simplify: iters left: 1 (197 enodes) * [exit]simplify: Simplified to (/ (+ 1 (+ (* v v) (pow v 4))) (sqrt (cbrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (- 1 (pow v 6))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ (+ 1 (+ (* v v) (pow v 4))) (sqrt (cbrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 163 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (- (pow 1 3) (pow (* v v) 3))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (171 enodes) * * [misc]simplify: iters left: 2 (414 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (pow v 6))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (- 1 (pow v 6))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (166 enodes) * * [misc]simplify: iters left: 1 (197 enodes) * [exit]simplify: Simplified to (/ (+ 1 (+ (* v v) (pow v 4))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (- 1 (pow v 6))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (+ 1 (+ (* v v) (pow v 4))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 164 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (- (pow 1 3) (pow (* v v) 3))) (sqrt 1)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (134 enodes) * * [misc]simplify: iters left: 2 (306 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (- 1 (pow v 6))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (- 1 (pow v 6))) (/ (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (149 enodes) * * [misc]simplify: iters left: 1 (170 enodes) * [exit]simplify: Simplified to (/ (+ 1 (+ (* v v) (pow v 4))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (- 1 (pow v 6))) (/ (+ 1 (+ (* v v) (pow v 4))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 165 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (- (pow 1 3) (pow (* v v) 3))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (171 enodes) * * [misc]simplify: iters left: 2 (414 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (pow v 6))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (- 1 (pow v 6))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (166 enodes) * * [misc]simplify: iters left: 1 (197 enodes) * [exit]simplify: Simplified to (/ (+ 1 (+ (* v v) (pow v 4))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (- 1 (pow v 6))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (+ 1 (+ (* v v) (pow v 4))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 166 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (- (pow 1 3) (pow (* v v) 3))) 1) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (134 enodes) * * [misc]simplify: iters left: 2 (308 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (- 1 (pow v 6))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (- 1 (pow v 6))) (/ (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (149 enodes) * * [misc]simplify: iters left: 1 (170 enodes) * [exit]simplify: Simplified to (/ (+ 1 (+ (* v v) (pow v 4))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (- 1 (pow v 6))) (/ (+ 1 (+ (* v v) (pow v 4))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 167 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (- (* 1 1) (* (* v v) (* v v)))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (416 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (cbrt (sqrt (+ (* -6 (* v v)) 2)))) (* (- PI (* PI (pow v 4))) (cbrt (sqrt (+ (* -6 (* v v)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (cbrt (sqrt (+ (* -6 (* v v)) 2)))) (* (- PI (* PI (pow v 4))) (cbrt (sqrt (+ (* -6 (* v v)) 2))))) (/ (+ 1 (* v v)) (cbrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (+ 1 (* v v)) (cbrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (/ (+ 1 (* v v)) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (cbrt (sqrt (+ (* -6 (* v v)) 2)))) (* (- PI (* PI (pow v 4))) (cbrt (sqrt (+ (* -6 (* v v)) 2))))) (/ (+ 1 (* v v)) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 168 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (- (* 1 1) (* (* v v) (* v v)))) (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (115 enodes) * * [misc]simplify: iters left: 2 (270 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (pow v 4))) (fabs (cbrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (- 1 (pow v 4))) (fabs (cbrt (+ (* -6 (* v v)) 2)))) (/ (+ 1 (* v v)) (sqrt (cbrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (+ 1 (* v v)) (sqrt (cbrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (/ (+ 1 (* v v)) (sqrt (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (- 1 (pow v 4))) (fabs (cbrt (+ (* -6 (* v v)) 2)))) (/ (+ 1 (* v v)) (sqrt (cbrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 169 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (- (* 1 1) (* (* v v) (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (134 enodes) * * [misc]simplify: iters left: 2 (289 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (pow v 4))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (- 1 (pow v 4))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) (/ (+ 1 (* v v)) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (+ 1 (* v v)) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (/ (+ 1 (* v v)) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (- 1 (pow v 4))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) (/ (+ 1 (* v v)) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 170 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (- (* 1 1) (* (* v v) (* v v)))) (sqrt 1)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (99 enodes) * * [misc]simplify: iters left: 2 (215 enodes) * * [misc]simplify: iters left: 1 (361 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (- 1 (pow v 4))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (- 1 (pow v 4))) (/ (+ 1 (* v v)) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (+ 1 (* v v)) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * [exit]simplify: Simplified to (/ (+ 1 (* v v)) (sqrt (+ (* (* v v) -6) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (- 1 (pow v 4))) (/ (+ 1 (* v v)) (sqrt (+ (* (* v v) -6) 2))))) * * * * [misc]progress: [ 171 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (- (* 1 1) (* (* v v) (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (134 enodes) * * [misc]simplify: iters left: 2 (289 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (pow v 4))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (- 1 (pow v 4))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) (/ (+ 1 (* v v)) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (+ 1 (* v v)) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (/ (+ 1 (* v v)) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (- 1 (pow v 4))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) (/ (+ 1 (* v v)) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 172 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (- (* 1 1) (* (* v v) (* v v)))) 1) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (99 enodes) * * [misc]simplify: iters left: 2 (186 enodes) * * [misc]simplify: iters left: 1 (324 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (- 1 (pow v 4))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (- 1 (pow v 4))) (/ (+ 1 (* v v)) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (+ 1 (* v v)) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * [exit]simplify: Simplified to (/ (+ 1 (* v v)) (sqrt (+ (* (* v v) -6) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (- 1 (pow v 4))) (/ (+ 1 (* v v)) (sqrt (+ (* (* v v) -6) 2))))) * * * * [misc]progress: [ 173 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 174 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 175 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 176 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (cbrt (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (15 enodes) * [exit]simplify: Simplified to (cbrt (sqrt (+ 2 (* (* v v) -6)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ (/ 4/3 PI) (- 1 (* v v))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * * * * [misc]progress: [ 177 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (cbrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (15 enodes) * [exit]simplify: Simplified to (sqrt (cbrt (+ 2 (* (* v v) -6)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6)))))) (sqrt (cbrt (+ 2 (* (* v v) -6)))))) * * * * [misc]progress: [ 178 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (15 enodes) * [exit]simplify: Simplified to (sqrt (sqrt (+ 2 (* (* v v) -6)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (sqrt (sqrt (+ 2 (* (* v v) -6)))))) * * * * [misc]progress: [ 179 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (+ 2 (* (* v v) -6))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (14 enodes) * [exit]simplify: Simplified to (sqrt (+ 2 (* (* v v) -6))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt 1)) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 180 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (15 enodes) * [exit]simplify: Simplified to (sqrt (sqrt (+ 2 (* (* v v) -6)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (sqrt (sqrt (+ 2 (* (* v v) -6)))))) * * * * [misc]progress: [ 181 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (+ 2 (* (* v v) -6))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (14 enodes) * [exit]simplify: Simplified to (sqrt (+ 2 (* (* v v) -6))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ (/ 4/3 PI) (- 1 (* v v))) 1) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 182 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (/ (/ 4/3 PI) (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * * [misc]simplify: iters left: 2 (43 enodes) * * [misc]simplify: iters left: 1 (54 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (/ (/ 4/3 PI) (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (cbrt (/ (/ 4/3 PI) (- 1 (* v v)))) (cbrt (/ (/ 4/3 PI) (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (cbrt (/ (/ 4/3 PI) (- 1 (* v v))))))) * * * * [misc]progress: [ 183 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * * [misc]simplify: iters left: 2 (42 enodes) * * [misc]simplify: iters left: 1 (53 enodes) * [exit]simplify: Simplified to (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (sqrt (/ (/ 4/3 PI) (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (/ (/ 4/3 PI) (- 1 (* v v))))))) * * * * [misc]progress: [ 184 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * * [misc]simplify: iters left: 2 (41 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (cbrt (- 1 (* v v))))))) * * * * [misc]progress: [ 185 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 186 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * * [misc]simplify: iters left: 2 (57 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (- 1 (* v v)))))) * * * * [misc]progress: [ 187 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 4/3 PI)) (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (/ (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (cbrt (- 1 (* v v))))))) * * * * [misc]progress: [ 188 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 189 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 4/3 PI)) 1) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * * [misc]simplify: iters left: 3 (10 enodes) * [exit]simplify: Simplified to (sqrt (/ 4/3 PI)) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (sqrt (/ 4/3 PI)) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (- 1 (* v v)))))) * * * * [misc]progress: [ 190 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (/ (/ 1 (cbrt (- 1 (* v v)))) (cbrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (cbrt (- 1 (* v v))))))) * * * * [misc]progress: [ 191 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 192 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 1) * * [misc]simplify: iters left: 2 (2 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 1) to (λ (v) (/ 1 (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (- 1 (* v v)))))) * * * * [misc]progress: [ 193 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 4/3 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * [exit]simplify: Simplified to (/ 4/3 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (/ 4/3 (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (cbrt (- 1 (* v v))))))) * * * * [misc]progress: [ 194 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 4/3 (sqrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (/ 4/3 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 195 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 4/3 1) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (5 enodes) * [exit]simplify: Simplified to 4/3 * [misc]simplify: Simplified (2 1) to (λ (v) (/ 4/3 (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (- 1 (* v v)))))) * * * * [misc]progress: [ 196 / 212 ] simplifiying candidate # * * * * [misc]progress: [ 197 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 4/3 PI) * * [misc]simplify: iters left: 2 (3 enodes) * [exit]simplify: Simplified to (/ 4/3 PI) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (/ 4/3 PI) (/ (sqrt (+ 2 (* (* v v) -6))) (/ 1 (- 1 (* v v)))))) * * * * [misc]progress: [ 198 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 PI) (- (pow 1 3) (pow (* v v) 3))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (86 enodes) * * [misc]simplify: iters left: 2 (128 enodes) * * [misc]simplify: iters left: 1 (269 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (- 1 (pow v 6))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (/ (/ 4/3 PI) (- 1 (pow v 6))) (/ (sqrt (+ 2 (* (* v v) -6))) (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * * * [misc]progress: [ 199 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 PI) (- (* 1 1) (* (* v v) (* v v)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (89 enodes) * * [misc]simplify: iters left: 1 (155 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (- 1 (pow v 4))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (/ (/ 4/3 PI) (- 1 (pow v 4))) (/ (sqrt (+ 2 (* (* v v) -6))) (+ 1 (* v v))))) * * * * [misc]progress: [ 200 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (+ (* 2 2) (- (* (* (* v v) -6) (* (* v v) -6)) (* 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (219 enodes) * * [misc]simplify: iters left: 2 (389 enodes) * * [misc]simplify: iters left: 1 (497 enodes) * [exit]simplify: Simplified to (sqrt (+ (* (pow v 4) 36) (+ (* (* 12 v) v) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (pow 2 3) (pow (* (* v v) -6) 3)))) (sqrt (+ (* (pow v 4) 36) (+ (* (* 12 v) v) 4))))) * * * * [misc]progress: [ 201 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (- 2 (* (* v v) -6))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (sqrt (- 2 (* (* v v) -6))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (- (* 2 2) (* (* (* v v) -6) (* (* v v) -6))))) (sqrt (- 2 (* (* v v) -6))))) * * * * [misc]progress: [ 202 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 4/3 PI) * * [misc]simplify: iters left: 2 (3 enodes) * [exit]simplify: Simplified to (/ 4/3 PI) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (/ 4/3 PI) (* (sqrt (+ 2 (* (* v v) -6))) (- 1 (* v v))))) * * * * [misc]progress: [ 203 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (173 enodes) * * [misc]simplify: iters left: 1 (299 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* -6 (* v v)) 2))) * [misc]simplify: Simplified (2) to (λ (v) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* -6 (* v v)) 2)))) * * * * [misc]progress: [ 204 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (* -6 (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) -6) * [misc]simplify: Simplified (2 2 1 2) to (λ (v) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 205 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (* -6 (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) -6) * [misc]simplify: Simplified (2 2 1 2) to (λ (v) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 206 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (* -6 (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) -6) * [misc]simplify: Simplified (2 2 1 2) to (λ (v) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 207 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* 4/3 (/ (pow v 2) PI)) (+ (* 4/3 (/ 1 PI)) (* 4/3 (/ (pow v 4) PI)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (126 enodes) * * [misc]simplify: iters left: 1 (203 enodes) * [exit]simplify: Simplified to (+ (/ 4/3 PI) (* (+ (pow v 4) (* v v)) (/ 4/3 PI))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (+ (/ 4/3 PI) (* (+ (pow v 4) (* v v)) (/ 4/3 PI))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 208 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 4/3 (/ 1 (* (pow v 2) PI))) (+ (* 4/3 (/ 1 (* (pow v 4) PI))) (* 4/3 (/ 1 (* (pow v 6) PI)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (105 enodes) * * [misc]simplify: iters left: 3 (237 enodes) * * [misc]simplify: iters left: 2 (443 enodes) * [exit]simplify: Simplified to (- (/ -4/3 (* (* v PI) v)) (+ (/ (/ 4/3 PI) (pow v 6)) (/ (/ 4/3 PI) (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (/ -4/3 (* (* v PI) v)) (+ (/ (/ 4/3 PI) (pow v 6)) (/ (/ 4/3 PI) (pow v 4)))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 209 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 4/3 (/ 1 (* (pow v 2) PI))) (+ (* 4/3 (/ 1 (* (pow v 4) PI))) (* 4/3 (/ 1 (* (pow v 6) PI)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (105 enodes) * * [misc]simplify: iters left: 3 (237 enodes) * * [misc]simplify: iters left: 2 (443 enodes) * [exit]simplify: Simplified to (- (/ -4/3 (* (* v PI) v)) (+ (/ (/ 4/3 PI) (pow v 6)) (/ (/ 4/3 PI) (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (/ -4/3 (* (* v PI) v)) (+ (/ (/ 4/3 PI) (pow v 6)) (/ (/ 4/3 PI) (pow v 4)))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 210 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* 4/3 (/ (pow v 4) (* (sqrt 2) PI))) (+ (* 4/3 (/ 1 (* (sqrt 2) PI))) (+ (* 4 (/ (pow v 4) (* (pow (sqrt 2) 3) PI))) (+ (* 18 (/ (pow v 4) (* (pow (sqrt 2) 5) PI))) (+ (* 4 (/ (pow v 2) (* (pow (sqrt 2) 3) PI))) (* 4/3 (/ (pow v 2) (* (sqrt 2) PI)))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (86 enodes) * * [misc]simplify: iters left: 4 (261 enodes) * [exit]simplify: Simplified to (+ (+ (* (/ (pow v 4) PI) (/ 2 (sqrt 2))) (+ (/ (/ 4/3 (sqrt 2)) PI) (/ (* (/ 4/3 PI) (pow v 4)) (sqrt 2)))) (+ (* (/ v (/ PI v)) (+ (/ 4/3 (sqrt 2)) (/ 2 (sqrt 2)))) (/ (* (/ 18 PI) (pow v 4)) (pow (sqrt 2) 5)))) * [misc]simplify: Simplified (2) to (λ (v) (+ (+ (* (/ (pow v 4) PI) (/ 2 (sqrt 2))) (+ (/ (/ 4/3 (sqrt 2)) PI) (/ (* (/ 4/3 PI) (pow v 4)) (sqrt 2)))) (+ (* (/ v (/ PI v)) (+ (/ 4/3 (sqrt 2)) (/ 2 (sqrt 2)))) (/ (* (/ 18 PI) (pow v 4)) (pow (sqrt 2) 5))))) * * * * [misc]progress: [ 211 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 4/3 (/ 1 (* (pow v 7) (* (pow (sqrt -6) 3) PI)))) (* 4/3 (/ 1 (* (pow v 5) (* (pow (sqrt -6) 3) PI))))) (+ (* 4/3 (/ 1 (* (pow v 7) (* (sqrt -6) PI)))) (+ (* 4/3 (/ 1 (* (pow v 3) (* (sqrt -6) PI)))) (+ (* 2 (/ 1 (* (pow v 7) (* (pow (sqrt -6) 5) PI)))) (* 4/3 (/ 1 (* (pow v 5) (* (sqrt -6) PI)))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (109 enodes) * * [misc]simplify: iters left: 4 (259 enodes) * [exit]simplify: Simplified to (- (- (+ (/ (/ 4/3 (pow v 5)) (* (sqrt -6) (* PI -6))) (/ (/ 4/3 (pow v 7)) (* (sqrt -6) (* PI -6)))) (/ (/ 4/3 (pow v 7)) (* PI (sqrt -6)))) (+ (/ (/ 2 (pow v 7)) (* (pow (sqrt -6) 5) PI)) (+ (/ (/ 4/3 (pow v 5)) (* PI (sqrt -6))) (/ (/ 4/3 (pow v 3)) (* PI (sqrt -6)))))) * [misc]simplify: Simplified (2) to (λ (v) (- (- (+ (/ (/ 4/3 (pow v 5)) (* (sqrt -6) (* PI -6))) (/ (/ 4/3 (pow v 7)) (* (sqrt -6) (* PI -6)))) (/ (/ 4/3 (pow v 7)) (* PI (sqrt -6)))) (+ (/ (/ 2 (pow v 7)) (* (pow (sqrt -6) 5) PI)) (+ (/ (/ 4/3 (pow v 5)) (* PI (sqrt -6))) (/ (/ 4/3 (pow v 3)) (* PI (sqrt -6))))))) * * * * [misc]progress: [ 212 / 212 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 4/3 (/ 1 (* (pow v 7) (* (sqrt -6) PI)))) (+ (* 4/3 (/ 1 (* (pow v 5) (* (sqrt -6) PI)))) (+ (* 4/3 (/ 1 (* (pow v 3) (* (sqrt -6) PI)))) (* 2 (/ 1 (* (pow v 7) (* (pow (sqrt -6) 5) PI))))))) (+ (* 4/3 (/ 1 (* (pow v 7) (* (pow (sqrt -6) 3) PI)))) (* 4/3 (/ 1 (* (pow v 5) (* (pow (sqrt -6) 3) PI)))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (109 enodes) * * [misc]simplify: iters left: 4 (262 enodes) * [exit]simplify: Simplified to (+ (+ (+ (/ (/ 4/3 (pow v 7)) (* PI (sqrt -6))) (/ (/ 4/3 (pow v 3)) (* PI (sqrt -6)))) (/ (/ 2 (pow v 7)) (* (pow (sqrt -6) 5) PI))) (- (- (/ (/ 4/3 (pow v 5)) (* PI (sqrt -6))) (/ (/ 4/3 (pow v 7)) (* (sqrt -6) (* PI -6)))) (/ (/ 4/3 (pow v 5)) (* (sqrt -6) (* PI -6))))) * [misc]simplify: Simplified (2) to (λ (v) (+ (+ (+ (/ (/ 4/3 (pow v 7)) (* PI (sqrt -6))) (/ (/ 4/3 (pow v 3)) (* PI (sqrt -6)))) (/ (/ 2 (pow v 7)) (* (pow (sqrt -6) 5) PI))) (- (- (/ (/ 4/3 (pow v 5)) (* PI (sqrt -6))) (/ (/ 4/3 (pow v 7)) (* (sqrt -6) (* PI -6)))) (/ (/ 4/3 (pow v 5)) (* (sqrt -6) (* PI -6)))))) * * * [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 1) * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 2 1 2) * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 1 2) * * * * [misc]progress: [ 4 / 4 ] rewriting at (2) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 4 ] generating series at (2 1) * [misc]approximate: Taking taylor expansion of (/ 4/3 (* (- 1 (* v v)) PI)) in (v) around 0 * [misc]taylor: Taking taylor expansion of (/ 4/3 (* (- 1 (* v v)) PI)) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of (* (- 1 (* v v)) PI) in v * [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 PI in v * [misc]backup-simplify: Simplify PI into PI * [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 PI) into PI * [misc]backup-simplify: Simplify (/ 4/3 PI) into (/ 4/3 PI) * [misc]taylor: Taking taylor expansion of (/ 4/3 (* (- 1 (* v v)) PI)) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of (* (- 1 (* v v)) PI) in v * [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 PI in v * [misc]backup-simplify: Simplify PI into PI * [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 PI) into PI * [misc]backup-simplify: Simplify (/ 4/3 PI) into (/ 4/3 PI) * [misc]backup-simplify: Simplify (/ 4/3 PI) into (/ 4/3 PI) * [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 (+ (* 1 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)))) 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 (+ (* 1 0) (+ (* 0 0) (* -1 PI))) into (- PI) * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ (- PI) PI)) (* 0 (/ 0 PI)))) into (* 4/3 (/ 1 PI)) * [misc]backup-simplify: Simplify (* 4/3 (/ 1 PI)) into (/ 4/3 PI) * [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 (+ (* 1 0) (+ (* 0 0) (+ (* -1 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ (- PI) PI)) (* (* 4/3 (/ 1 PI)) (/ 0 PI)))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* -1 0) (+ (* 0 0) (* 0 PI))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* (* 4/3 (/ 1 PI)) (/ (- PI) PI)) (* 0 (/ 0 PI)))) into (* 4/3 (/ 1 PI)) * [misc]backup-simplify: Simplify (* 4/3 (/ 1 PI)) into (/ 4/3 PI) * [misc]backup-simplify: Simplify (+ (* (/ 4/3 PI) (pow v 4)) (+ (* (/ 4/3 PI) (pow v 2)) (/ 4/3 PI))) into (+ (* 4/3 (/ (pow v 2) PI)) (+ (* 4/3 (/ 1 PI)) (* 4/3 (/ (pow v 4) PI)))) * [misc]approximate: Taking taylor expansion of (/ 4/3 (* (- 1 (* (/ 1 v) (/ 1 v))) PI)) in (v) around 0 * [misc]taylor: Taking taylor expansion of (/ 4/3 (* (- 1 (* (/ 1 v) (/ 1 v))) PI)) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of (* (- 1 (* (/ 1 v) (/ 1 v))) PI) in v * [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 PI in v * [misc]backup-simplify: Simplify PI into PI * [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 PI) into (* -1 PI) * [misc]backup-simplify: Simplify (/ 4/3 (* -1 PI)) into (/ -4/3 PI) * [misc]taylor: Taking taylor expansion of (/ 4/3 (* (- 1 (* (/ 1 v) (/ 1 v))) PI)) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of (* (- 1 (* (/ 1 v) (/ 1 v))) PI) in v * [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 PI in v * [misc]backup-simplify: Simplify PI into PI * [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 PI) into (* -1 PI) * [misc]backup-simplify: Simplify (/ 4/3 (* -1 PI)) into (/ -4/3 PI) * [misc]backup-simplify: Simplify (/ -4/3 PI) into (/ -4/3 PI) * [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 (+ (* -1 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* -1 PI)) (+ (* (/ -4/3 PI) (/ 0 (* -1 PI))))) 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) (+ (* 0 0) (* 1 PI))) into PI * [misc]backup-simplify: Simplify (- (/ 0 (* -1 PI)) (+ (* (/ -4/3 PI) (/ PI (* -1 PI))) (* 0 (/ 0 (* -1 PI))))) into (- (* 4/3 (/ 1 PI))) * [misc]backup-simplify: Simplify (- (* 4/3 (/ 1 PI))) into (- (* 4/3 (/ 1 PI))) * [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) (+ (* 0 0) (+ (* 1 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* -1 PI)) (+ (* (/ -4/3 PI) (/ 0 (* -1 PI))) (* 0 (/ PI (* -1 PI))) (* (- (* 4/3 (/ 1 PI))) (/ 0 (* -1 PI))))) 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) (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* -1 PI)) (+ (* (/ -4/3 PI) (/ 0 (* -1 PI))) (* 0 (/ 0 (* -1 PI))) (* (- (* 4/3 (/ 1 PI))) (/ PI (* -1 PI))) (* 0 (/ 0 (* -1 PI))))) into (- (* 4/3 (/ 1 PI))) * [misc]backup-simplify: Simplify (- (* 4/3 (/ 1 PI))) into (- (* 4/3 (/ 1 PI))) * [misc]backup-simplify: Simplify (+ (* (- (* 4/3 (/ 1 PI))) (pow (/ 1 v) 6)) (+ (* (- (* 4/3 (/ 1 PI))) (pow (/ 1 v) 4)) (* (/ -4/3 PI) (pow (/ 1 v) 2)))) into (- (+ (* 4/3 (/ 1 (* (pow v 2) PI))) (+ (* 4/3 (/ 1 (* (pow v 4) PI))) (* 4/3 (/ 1 (* (pow v 6) PI)))))) * [misc]approximate: Taking taylor expansion of (/ 4/3 (* (- 1 (* (/ 1 (- v)) (/ 1 (- v)))) PI)) in (v) around 0 * [misc]taylor: Taking taylor expansion of (/ 4/3 (* (- 1 (* (/ 1 (- v)) (/ 1 (- v)))) PI)) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of (* (- 1 (* (/ 1 (- v)) (/ 1 (- v)))) PI) in v * [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 PI in v * [misc]backup-simplify: Simplify PI into PI * [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 PI) into (* -1 PI) * [misc]backup-simplify: Simplify (/ 4/3 (* -1 PI)) into (/ -4/3 PI) * [misc]taylor: Taking taylor expansion of (/ 4/3 (* (- 1 (* (/ 1 (- v)) (/ 1 (- v)))) PI)) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of (* (- 1 (* (/ 1 (- v)) (/ 1 (- v)))) PI) in v * [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 PI in v * [misc]backup-simplify: Simplify PI into PI * [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 PI) into (* -1 PI) * [misc]backup-simplify: Simplify (/ 4/3 (* -1 PI)) into (/ -4/3 PI) * [misc]backup-simplify: Simplify (/ -4/3 PI) into (/ -4/3 PI) * [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 (+ (* -1 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* -1 PI)) (+ (* (/ -4/3 PI) (/ 0 (* -1 PI))))) 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 (+ (* -1 0) (+ (* 0 0) (* 1 PI))) into PI * [misc]backup-simplify: Simplify (- (/ 0 (* -1 PI)) (+ (* (/ -4/3 PI) (/ PI (* -1 PI))) (* 0 (/ 0 (* -1 PI))))) into (- (* 4/3 (/ 1 PI))) * [misc]backup-simplify: Simplify (- (* 4/3 (/ 1 PI))) into (- (* 4/3 (/ 1 PI))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]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 (+ (* -1 0) (+ (* 0 0) (+ (* 1 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* -1 PI)) (+ (* (/ -4/3 PI) (/ 0 (* -1 PI))) (* 0 (/ PI (* -1 PI))) (* (- (* 4/3 (/ 1 PI))) (/ 0 (* -1 PI))))) 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 (+ (* -1 0) (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* -1 PI)) (+ (* (/ -4/3 PI) (/ 0 (* -1 PI))) (* 0 (/ 0 (* -1 PI))) (* (- (* 4/3 (/ 1 PI))) (/ PI (* -1 PI))) (* 0 (/ 0 (* -1 PI))))) into (- (* 4/3 (/ 1 PI))) * [misc]backup-simplify: Simplify (- (* 4/3 (/ 1 PI))) into (- (* 4/3 (/ 1 PI))) * [misc]backup-simplify: Simplify (+ (* (- (* 4/3 (/ 1 PI))) (pow (/ 1 (- v)) 6)) (+ (* (- (* 4/3 (/ 1 PI))) (pow (/ 1 (- v)) 4)) (* (/ -4/3 PI) (pow (/ 1 (- v)) 2)))) into (- (+ (* 4/3 (/ 1 (* (pow v 2) PI))) (+ (* 4/3 (/ 1 (* (pow v 4) PI))) (* 4/3 (/ 1 (* (pow v 6) PI)))))) * * * * [misc]progress: [ 2 / 4 ] generating series at (2 2 1 2) * [misc]approximate: Taking taylor expansion of (* (* v v) -6) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (* v v) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]taylor: Taking taylor expansion of (* (* v v) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 0 -6) 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 -6)) 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 (+ (* 0 0) (+ (* 0 0) (* 1 -6))) into -6 * [misc]backup-simplify: Simplify -6 into -6 * [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 -6)))) 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 0) (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 -6))))) 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 (+ (* 0 0) (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6)))))) 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 0) (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6))))))) 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 (+ (* 0 0) (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6)))))))) 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 (+ (* 0 0) (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6))))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* -6 (pow v 2)) into (* -6 (pow v 2)) * [misc]approximate: Taking taylor expansion of (* (* (/ 1 v) (/ 1 v)) -6) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (* (/ 1 v) (/ 1 v)) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]taylor: Taking taylor expansion of (* (* (/ 1 v) (/ 1 v)) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 -6) into -6 * [misc]backup-simplify: Simplify -6 into -6 * [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 (+ (* 1 0) (* 0 -6)) 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 (+ (* 1 0) (+ (* 0 0) (* 0 -6))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6)))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6))))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6)))))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* -6 (pow (/ 1 (/ 1 v)) 2)) into (* -6 (pow v 2)) * [misc]approximate: Taking taylor expansion of (* (* (/ 1 (- v)) (/ 1 (- v))) -6) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- v)) (/ 1 (- v))) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- v)) (/ 1 (- v))) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 1 -6) into -6 * [misc]backup-simplify: Simplify -6 into -6 * [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 (+ (* 1 0) (* 0 -6)) 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 (+ (* 1 0) (+ (* 0 0) (* 0 -6))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6)))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6))))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6)))))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* -6 (pow (/ 1 (/ 1 (- v))) 2)) into (* -6 (pow v 2)) * * * * [misc]progress: [ 3 / 4 ] generating series at (2 1 2) * [misc]approximate: Taking taylor expansion of (* (- 1 (* v v)) PI) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (- 1 (* v v)) PI) in v * [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 PI in v * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* (- 1 (* v v)) PI) in v * [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 PI in v * [misc]backup-simplify: Simplify PI into PI * [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 PI) into PI * [misc]backup-simplify: Simplify PI into PI * [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 (+ (* 1 0) (* 0 PI)) 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 (+ (* 1 0) (+ (* 0 0) (* -1 PI))) into (- PI) * [misc]backup-simplify: Simplify (- PI) into (- PI) * [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 (+ (* 1 0) (+ (* 0 0) (+ (* -1 0) (* 0 PI)))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* -1 0) (+ (* 0 0) (* 0 PI))))) 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 (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) 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 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) 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 (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) 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 (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* (- PI) (pow v 2)) PI) into (- PI (* (pow v 2) PI)) * [misc]approximate: Taking taylor expansion of (* (- 1 (* (/ 1 v) (/ 1 v))) PI) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (- 1 (* (/ 1 v) (/ 1 v))) PI) in v * [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 PI in v * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* (- 1 (* (/ 1 v) (/ 1 v))) PI) in v * [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 PI in v * [misc]backup-simplify: Simplify PI into PI * [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 PI) into (* -1 PI) * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) * [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 (+ (* -1 0) (* 0 PI)) 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) (+ (* 0 0) (* 1 PI))) into PI * [misc]backup-simplify: Simplify PI into PI * [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) (+ (* 0 0) (+ (* 1 0) (* 0 PI)))) 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) (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI))))) 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 (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) 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 (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) 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)) (* 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)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 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 (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) 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)) (* 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)) (* 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 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) (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ PI (* (* -1 PI) (pow (/ 1 (/ 1 v)) 2))) into (- PI (* (pow v 2) PI)) * [misc]approximate: Taking taylor expansion of (* (- 1 (* (/ 1 (- v)) (/ 1 (- v)))) PI) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (- 1 (* (/ 1 (- v)) (/ 1 (- v)))) PI) in v * [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 PI in v * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* (- 1 (* (/ 1 (- v)) (/ 1 (- v)))) PI) in v * [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 PI in v * [misc]backup-simplify: Simplify PI into PI * [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 PI) into (* -1 PI) * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) * [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 (+ (* -1 0) (* 0 PI)) 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 (+ (* -1 0) (+ (* 0 0) (* 1 PI))) into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]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 (+ (* -1 0) (+ (* 0 0) (+ (* 1 0) (* 0 PI)))) 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 (+ (* -1 0) (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI))))) 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 (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) 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 (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) 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 (- 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)) (* 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 (- 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)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 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 (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) 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 (- 0) into 0 * [misc]backup-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)) (* 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 (- 0) into 0 * [misc]backup-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)) (* 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 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) (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ PI (* (* -1 PI) (pow (/ 1 (/ 1 (- v))) 2))) into (- PI (* (pow v 2) PI)) * * * * [misc]progress: [ 4 / 4 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (/ (/ 4/3 (* (- 1 (* v v)) PI)) (sqrt (+ 2 (* (* v v) -6)))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (/ (/ 4/3 (* (- 1 (* v v)) PI)) (sqrt (+ 2 (* (* v v) -6)))) in v * [misc]taylor: Taking taylor expansion of (/ 4/3 (* (- 1 (* v v)) PI)) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of (* (- 1 (* v v)) PI) in v * [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 PI in v * [misc]backup-simplify: Simplify PI into PI * [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 PI) into PI * [misc]backup-simplify: Simplify (/ 4/3 PI) into (/ 4/3 PI) * [misc]taylor: Taking taylor expansion of (sqrt (+ 2 (* (* v v) -6))) in v * [misc]taylor: Taking taylor expansion of (+ 2 (* (* v v) -6)) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* (* v v) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 0 -6) into 0 * [misc]backup-simplify: Simplify (+ 2 0) into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 0 -6)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (/ (/ 4/3 PI) (sqrt 2)) into (/ 4/3 (* (sqrt 2) PI)) * [misc]taylor: Taking taylor expansion of (/ (/ 4/3 (* (- 1 (* v v)) PI)) (sqrt (+ 2 (* (* v v) -6)))) in v * [misc]taylor: Taking taylor expansion of (/ 4/3 (* (- 1 (* v v)) PI)) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of (* (- 1 (* v v)) PI) in v * [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 PI in v * [misc]backup-simplify: Simplify PI into PI * [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 PI) into PI * [misc]backup-simplify: Simplify (/ 4/3 PI) into (/ 4/3 PI) * [misc]taylor: Taking taylor expansion of (sqrt (+ 2 (* (* v v) -6))) in v * [misc]taylor: Taking taylor expansion of (+ 2 (* (* v v) -6)) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* (* v v) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 0 -6) into 0 * [misc]backup-simplify: Simplify (+ 2 0) into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 0 -6)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (/ (/ 4/3 PI) (sqrt 2)) into (/ 4/3 (* (sqrt 2) PI)) * [misc]backup-simplify: Simplify (/ 4/3 (* (sqrt 2) PI)) into (/ 4/3 (* (sqrt 2) PI)) * [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 (+ (* 1 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt 2)) (+ (* (/ 4/3 (* (sqrt 2) PI)) (/ 0 (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 (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* -1 PI))) into (- PI) * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ (- PI) PI)) (* 0 (/ 0 PI)))) into (* 4/3 (/ 1 PI)) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 1) (* 0 0))) into 1 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 0 0) (* 1 -6))) into -6 * [misc]backup-simplify: Simplify (+ 0 -6) into -6 * [misc]backup-simplify: Simplify (/ (- -6 (pow 0 2) (+)) (* 2 (sqrt 2))) into (/ -3 (sqrt 2)) * [misc]backup-simplify: Simplify (- (/ (* 4/3 (/ 1 PI)) (sqrt 2)) (+ (* (/ 4/3 (* (sqrt 2) PI)) (/ (/ -3 (sqrt 2)) (sqrt 2))) (* 0 (/ 0 (sqrt 2))))) into (+ (* 4 (/ 1 (* (pow (sqrt 2) 3) PI))) (* 4/3 (/ 1 (* (sqrt 2) PI)))) * [misc]backup-simplify: Simplify (+ (* 4 (/ 1 (* (pow (sqrt 2) 3) PI))) (* 4/3 (/ 1 (* (sqrt 2) PI)))) into (+ (* 4 (/ 1 (* (pow (sqrt 2) 3) PI))) (* 4/3 (/ 1 (* (sqrt 2) PI)))) * [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 (+ (* 1 0) (+ (* 0 0) (+ (* -1 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ (- PI) PI)) (* (* 4/3 (/ 1 PI)) (/ 0 PI)))) 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 -6)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (/ -3 (sqrt 2)))))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt 2)) (+ (* (/ 4/3 (* (sqrt 2) PI)) (/ 0 (sqrt 2))) (* 0 (/ (/ -3 (sqrt 2)) (sqrt 2))) (* (+ (* 4 (/ 1 (* (pow (sqrt 2) 3) PI))) (* 4/3 (/ 1 (* (sqrt 2) PI)))) (/ 0 (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 (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* -1 0) (+ (* 0 0) (* 0 PI))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* (* 4/3 (/ 1 PI)) (/ (- PI) PI)) (* 0 (/ 0 PI)))) into (* 4/3 (/ 1 PI)) * [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 -6))))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ -3 (sqrt 2)) 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into (/ -9/2 (pow (sqrt 2) 3)) * [misc]backup-simplify: Simplify (- (/ (* 4/3 (/ 1 PI)) (sqrt 2)) (+ (* (/ 4/3 (* (sqrt 2) PI)) (/ (/ -9/2 (pow (sqrt 2) 3)) (sqrt 2))) (* 0 (/ 0 (sqrt 2))) (* (+ (* 4 (/ 1 (* (pow (sqrt 2) 3) PI))) (* 4/3 (/ 1 (* (sqrt 2) PI)))) (/ (/ -3 (sqrt 2)) (sqrt 2))) (* 0 (/ 0 (sqrt 2))))) into (+ (* 4 (/ 1 (* (pow (sqrt 2) 3) PI))) (+ (* 4/3 (/ 1 (* (sqrt 2) PI))) (* 18 (/ 1 (* (pow (sqrt 2) 5) PI))))) * [misc]backup-simplify: Simplify (+ (* 4 (/ 1 (* (pow (sqrt 2) 3) PI))) (+ (* 4/3 (/ 1 (* (sqrt 2) PI))) (* 18 (/ 1 (* (pow (sqrt 2) 5) PI))))) into (+ (* 4 (/ 1 (* (pow (sqrt 2) 3) PI))) (+ (* 4/3 (/ 1 (* (sqrt 2) PI))) (* 18 (/ 1 (* (pow (sqrt 2) 5) PI))))) * [misc]backup-simplify: Simplify (+ (* (+ (* 4 (/ 1 (* (pow (sqrt 2) 3) PI))) (+ (* 4/3 (/ 1 (* (sqrt 2) PI))) (* 18 (/ 1 (* (pow (sqrt 2) 5) PI))))) (pow v 4)) (+ (* (+ (* 4 (/ 1 (* (pow (sqrt 2) 3) PI))) (* 4/3 (/ 1 (* (sqrt 2) PI)))) (pow v 2)) (/ 4/3 (* (sqrt 2) PI)))) into (+ (* 4/3 (/ (pow v 4) (* (sqrt 2) PI))) (+ (* 4/3 (/ 1 (* (sqrt 2) PI))) (+ (* 4 (/ (pow v 4) (* (pow (sqrt 2) 3) PI))) (+ (* 18 (/ (pow v 4) (* (pow (sqrt 2) 5) PI))) (+ (* 4 (/ (pow v 2) (* (pow (sqrt 2) 3) PI))) (* 4/3 (/ (pow v 2) (* (sqrt 2) PI)))))))) * [misc]approximate: Taking taylor expansion of (/ (/ 4/3 (* (- 1 (* (/ 1 v) (/ 1 v))) PI)) (sqrt (+ 2 (* (* (/ 1 v) (/ 1 v)) -6)))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (/ (/ 4/3 (* (- 1 (* (/ 1 v) (/ 1 v))) PI)) (sqrt (+ 2 (* (* (/ 1 v) (/ 1 v)) -6)))) in v * [misc]taylor: Taking taylor expansion of (/ 4/3 (* (- 1 (* (/ 1 v) (/ 1 v))) PI)) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of (* (- 1 (* (/ 1 v) (/ 1 v))) PI) in v * [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 PI in v * [misc]backup-simplify: Simplify PI into PI * [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 PI) into (* -1 PI) * [misc]backup-simplify: Simplify (/ 4/3 (* -1 PI)) into (/ -4/3 PI) * [misc]taylor: Taking taylor expansion of (sqrt (+ 2 (* (* (/ 1 v) (/ 1 v)) -6))) in v * [misc]taylor: Taking taylor expansion of (+ 2 (* (* (/ 1 v) (/ 1 v)) -6)) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* (* (/ 1 v) (/ 1 v)) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 -6) into -6 * [misc]backup-simplify: Simplify (+ 0 -6) into -6 * [misc]backup-simplify: Simplify (sqrt -6) into (sqrt -6) * [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 (+ (* 1 0) (* 0 -6)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -6))) into 0 * [misc]backup-simplify: Simplify (/ (/ -4/3 PI) (sqrt -6)) into (/ -4/3 (* (sqrt -6) PI)) * [misc]taylor: Taking taylor expansion of (/ (/ 4/3 (* (- 1 (* (/ 1 v) (/ 1 v))) PI)) (sqrt (+ 2 (* (* (/ 1 v) (/ 1 v)) -6)))) in v * [misc]taylor: Taking taylor expansion of (/ 4/3 (* (- 1 (* (/ 1 v) (/ 1 v))) PI)) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of (* (- 1 (* (/ 1 v) (/ 1 v))) PI) in v * [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 PI in v * [misc]backup-simplify: Simplify PI into PI * [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 PI) into (* -1 PI) * [misc]backup-simplify: Simplify (/ 4/3 (* -1 PI)) into (/ -4/3 PI) * [misc]taylor: Taking taylor expansion of (sqrt (+ 2 (* (* (/ 1 v) (/ 1 v)) -6))) in v * [misc]taylor: Taking taylor expansion of (+ 2 (* (* (/ 1 v) (/ 1 v)) -6)) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* (* (/ 1 v) (/ 1 v)) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 -6) into -6 * [misc]backup-simplify: Simplify (+ 0 -6) into -6 * [misc]backup-simplify: Simplify (sqrt -6) into (sqrt -6) * [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 (+ (* 1 0) (* 0 -6)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -6))) into 0 * [misc]backup-simplify: Simplify (/ (/ -4/3 PI) (sqrt -6)) into (/ -4/3 (* (sqrt -6) PI)) * [misc]backup-simplify: Simplify (/ -4/3 (* (sqrt -6) PI)) into (/ -4/3 (* (sqrt -6) PI)) * [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 (+ (* -1 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* -1 PI)) (+ (* (/ -4/3 PI) (/ 0 (* -1 PI))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt -6)) (+ (* (/ -4/3 (* (sqrt -6) PI)) (/ 0 (sqrt -6))))) 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) (+ (* 0 0) (* 1 PI))) into PI * [misc]backup-simplify: Simplify (- (/ 0 (* -1 PI)) (+ (* (/ -4/3 PI) (/ PI (* -1 PI))) (* 0 (/ 0 (* -1 PI))))) into (- (* 4/3 (/ 1 PI))) * [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 (+ (* 1 0) (+ (* 0 0) (* 0 -6))) into 0 * [misc]backup-simplify: Simplify (+ 2 0) into 2 * [misc]backup-simplify: Simplify (/ (- 2 (pow 0 2) (+)) (* 2 (sqrt -6))) into (/ 1 (sqrt -6)) * [misc]backup-simplify: Simplify (- (/ (- (* 4/3 (/ 1 PI))) (sqrt -6)) (+ (* (/ -4/3 (* (sqrt -6) PI)) (/ (/ 1 (sqrt -6)) (sqrt -6))) (* 0 (/ 0 (sqrt -6))))) into (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (* 4/3 (/ 1 (* (sqrt -6) PI)))) * [misc]backup-simplify: Simplify (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (* 4/3 (/ 1 (* (sqrt -6) PI)))) into (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (* 4/3 (/ 1 (* (sqrt -6) PI)))) * [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) (+ (* 0 0) (+ (* 1 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* -1 PI)) (+ (* (/ -4/3 PI) (/ 0 (* -1 PI))) (* 0 (/ PI (* -1 PI))) (* (- (* 4/3 (/ 1 PI))) (/ 0 (* -1 PI))))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (/ 1 (sqrt -6)))))) (* 2 (sqrt -6))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt -6)) (+ (* (/ -4/3 (* (sqrt -6) PI)) (/ 0 (sqrt -6))) (* 0 (/ (/ 1 (sqrt -6)) (sqrt -6))) (* (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (* 4/3 (/ 1 (* (sqrt -6) PI)))) (/ 0 (sqrt -6))))) 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) (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* -1 PI)) (+ (* (/ -4/3 PI) (/ 0 (* -1 PI))) (* 0 (/ 0 (* -1 PI))) (* (- (* 4/3 (/ 1 PI))) (/ PI (* -1 PI))) (* 0 (/ 0 (* -1 PI))))) into (- (* 4/3 (/ 1 PI))) * [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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6))))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ 1 (sqrt -6)) 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt -6))) into (/ -1/2 (pow (sqrt -6) 3)) * [misc]backup-simplify: Simplify (- (/ (- (* 4/3 (/ 1 PI))) (sqrt -6)) (+ (* (/ -4/3 (* (sqrt -6) PI)) (/ (/ -1/2 (pow (sqrt -6) 3)) (sqrt -6))) (* 0 (/ 0 (sqrt -6))) (* (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (* 4/3 (/ 1 (* (sqrt -6) PI)))) (/ (/ 1 (sqrt -6)) (sqrt -6))) (* 0 (/ 0 (sqrt -6))))) into (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (+ (* 4/3 (/ 1 (* (sqrt -6) PI))) (* 2 (/ 1 (* (pow (sqrt -6) 5) PI))))) * [misc]backup-simplify: Simplify (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (+ (* 4/3 (/ 1 (* (sqrt -6) PI))) (* 2 (/ 1 (* (pow (sqrt -6) 5) PI))))) into (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (+ (* 4/3 (/ 1 (* (sqrt -6) PI))) (* 2 (/ 1 (* (pow (sqrt -6) 5) PI))))) * [misc]backup-simplify: Simplify (+ (* (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (+ (* 4/3 (/ 1 (* (sqrt -6) PI))) (* 2 (/ 1 (* (pow (sqrt -6) 5) PI))))) (pow (/ 1 v) 7)) (+ (* (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (* 4/3 (/ 1 (* (sqrt -6) PI)))) (pow (/ 1 v) 5)) (* (/ -4/3 (* (sqrt -6) PI)) (pow (/ 1 v) 3)))) into (- (+ (* 4/3 (/ 1 (* (pow v 7) (* (pow (sqrt -6) 3) PI)))) (* 4/3 (/ 1 (* (pow v 5) (* (pow (sqrt -6) 3) PI))))) (+ (* 4/3 (/ 1 (* (pow v 7) (* (sqrt -6) PI)))) (+ (* 4/3 (/ 1 (* (pow v 3) (* (sqrt -6) PI)))) (+ (* 2 (/ 1 (* (pow v 7) (* (pow (sqrt -6) 5) PI)))) (* 4/3 (/ 1 (* (pow v 5) (* (sqrt -6) PI)))))))) * [misc]approximate: Taking taylor expansion of (/ (/ 4/3 (* (- 1 (* (/ 1 (- v)) (/ 1 (- v)))) PI)) (sqrt (+ 2 (* (* (/ 1 (- v)) (/ 1 (- v))) -6)))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (/ (/ 4/3 (* (- 1 (* (/ 1 (- v)) (/ 1 (- v)))) PI)) (sqrt (+ 2 (* (* (/ 1 (- v)) (/ 1 (- v))) -6)))) in v * [misc]taylor: Taking taylor expansion of (/ 4/3 (* (- 1 (* (/ 1 (- v)) (/ 1 (- v)))) PI)) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of (* (- 1 (* (/ 1 (- v)) (/ 1 (- v)))) PI) in v * [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 PI in v * [misc]backup-simplify: Simplify PI into PI * [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 PI) into (* -1 PI) * [misc]backup-simplify: Simplify (/ 4/3 (* -1 PI)) into (/ -4/3 PI) * [misc]taylor: Taking taylor expansion of (sqrt (+ 2 (* (* (/ 1 (- v)) (/ 1 (- v))) -6))) in v * [misc]taylor: Taking taylor expansion of (+ 2 (* (* (/ 1 (- v)) (/ 1 (- v))) -6)) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- v)) (/ 1 (- v))) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 1 -6) into -6 * [misc]backup-simplify: Simplify (+ 0 -6) into -6 * [misc]backup-simplify: Simplify (sqrt -6) into (sqrt -6) * [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 (+ (* 1 0) (* 0 -6)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -6))) into 0 * [misc]backup-simplify: Simplify (/ (/ -4/3 PI) (sqrt -6)) into (/ -4/3 (* (sqrt -6) PI)) * [misc]taylor: Taking taylor expansion of (/ (/ 4/3 (* (- 1 (* (/ 1 (- v)) (/ 1 (- v)))) PI)) (sqrt (+ 2 (* (* (/ 1 (- v)) (/ 1 (- v))) -6)))) in v * [misc]taylor: Taking taylor expansion of (/ 4/3 (* (- 1 (* (/ 1 (- v)) (/ 1 (- v)))) PI)) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of (* (- 1 (* (/ 1 (- v)) (/ 1 (- v)))) PI) in v * [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 PI in v * [misc]backup-simplify: Simplify PI into PI * [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 PI) into (* -1 PI) * [misc]backup-simplify: Simplify (/ 4/3 (* -1 PI)) into (/ -4/3 PI) * [misc]taylor: Taking taylor expansion of (sqrt (+ 2 (* (* (/ 1 (- v)) (/ 1 (- v))) -6))) in v * [misc]taylor: Taking taylor expansion of (+ 2 (* (* (/ 1 (- v)) (/ 1 (- v))) -6)) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- v)) (/ 1 (- v))) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 1 -6) into -6 * [misc]backup-simplify: Simplify (+ 0 -6) into -6 * [misc]backup-simplify: Simplify (sqrt -6) into (sqrt -6) * [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 (+ (* 1 0) (* 0 -6)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -6))) into 0 * [misc]backup-simplify: Simplify (/ (/ -4/3 PI) (sqrt -6)) into (/ -4/3 (* (sqrt -6) PI)) * [misc]backup-simplify: Simplify (/ -4/3 (* (sqrt -6) PI)) into (/ -4/3 (* (sqrt -6) PI)) * [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 (+ (* -1 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* -1 PI)) (+ (* (/ -4/3 PI) (/ 0 (* -1 PI))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt -6)) (+ (* (/ -4/3 (* (sqrt -6) PI)) (/ 0 (sqrt -6))))) 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 (+ (* -1 0) (+ (* 0 0) (* 1 PI))) into PI * [misc]backup-simplify: Simplify (- (/ 0 (* -1 PI)) (+ (* (/ -4/3 PI) (/ PI (* -1 PI))) (* 0 (/ 0 (* -1 PI))))) into (- (* 4/3 (/ 1 PI))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-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 (+ (* 1 0) (+ (* 0 0) (* 0 -6))) into 0 * [misc]backup-simplify: Simplify (+ 2 0) into 2 * [misc]backup-simplify: Simplify (/ (- 2 (pow 0 2) (+)) (* 2 (sqrt -6))) into (/ 1 (sqrt -6)) * [misc]backup-simplify: Simplify (- (/ (- (* 4/3 (/ 1 PI))) (sqrt -6)) (+ (* (/ -4/3 (* (sqrt -6) PI)) (/ (/ 1 (sqrt -6)) (sqrt -6))) (* 0 (/ 0 (sqrt -6))))) into (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (* 4/3 (/ 1 (* (sqrt -6) PI)))) * [misc]backup-simplify: Simplify (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (* 4/3 (/ 1 (* (sqrt -6) PI)))) into (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (* 4/3 (/ 1 (* (sqrt -6) PI)))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]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 (+ (* -1 0) (+ (* 0 0) (+ (* 1 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* -1 PI)) (+ (* (/ -4/3 PI) (/ 0 (* -1 PI))) (* 0 (/ PI (* -1 PI))) (* (- (* 4/3 (/ 1 PI))) (/ 0 (* -1 PI))))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (/ 1 (sqrt -6)))))) (* 2 (sqrt -6))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt -6)) (+ (* (/ -4/3 (* (sqrt -6) PI)) (/ 0 (sqrt -6))) (* 0 (/ (/ 1 (sqrt -6)) (sqrt -6))) (* (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (* 4/3 (/ 1 (* (sqrt -6) PI)))) (/ 0 (sqrt -6))))) 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 (+ (* -1 0) (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* -1 PI)) (+ (* (/ -4/3 PI) (/ 0 (* -1 PI))) (* 0 (/ 0 (* -1 PI))) (* (- (* 4/3 (/ 1 PI))) (/ PI (* -1 PI))) (* 0 (/ 0 (* -1 PI))))) into (- (* 4/3 (/ 1 PI))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6))))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ 1 (sqrt -6)) 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt -6))) into (/ -1/2 (pow (sqrt -6) 3)) * [misc]backup-simplify: Simplify (- (/ (- (* 4/3 (/ 1 PI))) (sqrt -6)) (+ (* (/ -4/3 (* (sqrt -6) PI)) (/ (/ -1/2 (pow (sqrt -6) 3)) (sqrt -6))) (* 0 (/ 0 (sqrt -6))) (* (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (* 4/3 (/ 1 (* (sqrt -6) PI)))) (/ (/ 1 (sqrt -6)) (sqrt -6))) (* 0 (/ 0 (sqrt -6))))) into (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (+ (* 4/3 (/ 1 (* (sqrt -6) PI))) (* 2 (/ 1 (* (pow (sqrt -6) 5) PI))))) * [misc]backup-simplify: Simplify (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (+ (* 4/3 (/ 1 (* (sqrt -6) PI))) (* 2 (/ 1 (* (pow (sqrt -6) 5) PI))))) into (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (+ (* 4/3 (/ 1 (* (sqrt -6) PI))) (* 2 (/ 1 (* (pow (sqrt -6) 5) PI))))) * [misc]backup-simplify: Simplify (+ (* (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (+ (* 4/3 (/ 1 (* (sqrt -6) PI))) (* 2 (/ 1 (* (pow (sqrt -6) 5) PI))))) (pow (/ 1 (- v)) 7)) (+ (* (- (* 4/3 (/ 1 (* (pow (sqrt -6) 3) PI))) (* 4/3 (/ 1 (* (sqrt -6) PI)))) (pow (/ 1 (- v)) 5)) (* (/ -4/3 (* (sqrt -6) PI)) (pow (/ 1 (- v)) 3)))) into (- (+ (* 4/3 (/ 1 (* (pow v 7) (* (sqrt -6) PI)))) (+ (* 4/3 (/ 1 (* (pow v 5) (* (sqrt -6) PI)))) (+ (* 4/3 (/ 1 (* (pow v 3) (* (sqrt -6) PI)))) (* 2 (/ 1 (* (pow v 7) (* (pow (sqrt -6) 5) PI))))))) (+ (* 4/3 (/ 1 (* (pow v 7) (* (pow (sqrt -6) 3) PI)))) (* 4/3 (/ 1 (* (pow v 5) (* (pow (sqrt -6) 3) PI)))))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 2 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 3 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 4 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 5 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 6 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 7 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 8 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 9 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 10 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 11 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 12 / 110 ] 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 1 2) to (λ (v) (/ (* (/ 4/3 (* (- (pow 1 3) (pow (* v v) 3)) PI)) (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 13 / 110 ] 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 1 2) to (λ (v) (/ (* (/ 4/3 (* (- (* 1 1) (* (* v v) (* v v))) PI)) (+ 1 (* v v))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 14 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 15 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 16 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 17 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 18 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 19 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 20 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 21 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 22 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 23 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 24 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 25 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 26 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 27 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 28 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 29 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 30 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * [exit]simplify: Simplified to (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1 2 1) to (λ (v) (/ (/ 4/3 (* (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))) (* (cbrt (- 1 (* v v))) PI))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 31 / 110 ] 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 1 2 1) to (λ (v) (/ (/ 4/3 (* (sqrt (- 1 (* v v))) (* (sqrt (- 1 (* v v))) PI))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 32 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 33 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (* (- (pow 1 3) (pow (* v v) 3)) PI) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (234 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (- PI (* (pow v 6) PI)) * [misc]simplify: Simplified (2 1 2 1) to (λ (v) (/ (/ 4/3 (/ (- PI (* (pow v 6) PI)) (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 34 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (* (- (* 1 1) (* (* v v) (* v v))) PI) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (72 enodes) * * [misc]simplify: iters left: 2 (133 enodes) * * [misc]simplify: iters left: 1 (157 enodes) * [exit]simplify: Simplified to (- PI (* PI (pow v 4))) * [misc]simplify: Simplified (2 1 2 1) to (λ (v) (/ (/ 4/3 (/ (- PI (* PI (pow v 4))) (+ 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 35 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 36 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 37 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (/ 4/3 (* (- 1 (* v v)) PI))) (log (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (102 enodes) * * [misc]simplify: iters left: 2 (185 enodes) * * [misc]simplify: iters left: 1 (331 enodes) * [exit]simplify: Simplified to (- (+ (- (log PI)) (log (/ 4/3 (- 1 (* v v))))) (log (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (exp (- (+ (- (log PI)) (log (/ 4/3 (- 1 (* v v))))) (log (sqrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 38 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 39 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 40 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (/ 4/3 (* (- 1 (* v v)) PI)) (/ 4/3 (* (- 1 (* v v)) PI))) (/ 4/3 (* (- 1 (* v v)) PI))) (* (* (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (150 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (* (- 1 (* v v)) PI)) (* (/ (- 1 (* v v)) (/ 4/3 PI)) (/ (- 1 (* v v)) (/ 4/3 PI)))) (* (+ (* (* v v) -6) 2) (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (cbrt (/ (/ (/ 4/3 (* (- 1 (* v v)) PI)) (* (/ (- 1 (* v v)) (/ 4/3 PI)) (/ (- 1 (* v v)) (/ 4/3 PI)))) (* (+ (* (* v v) -6) 2) (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 41 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 42 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 43 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 44 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 45 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 4/3 (* (- 1 (* v v)) PI))) (cbrt (/ 4/3 (* (- 1 (* v v)) PI)))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (73 enodes) * * [misc]simplify: iters left: 2 (87 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 4/3 (- PI (* (* v v) PI)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (cbrt (/ 4/3 (- PI (* (* v v) PI)))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 4/3 (- PI (* (* v v) PI)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (cbrt (/ 4/3 (- PI (* (* v v) PI)))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (cbrt (/ 4/3 (* (- 1 (* v v)) PI))) (cbrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 4/3 (* (- 1 (* v v)) PI))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (64 enodes) * * [misc]simplify: iters left: 1 (66 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 4/3 (- PI (* (* v v) PI)))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 (* (- 1 (* v v)) PI))) (cbrt (/ 4/3 (* (- 1 (* v v)) PI)))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (/ (cbrt (/ 4/3 (- PI (* (* v v) PI)))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 46 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 4/3 (* (- 1 (* v v)) PI))) (cbrt (/ 4/3 (* (- 1 (* v v)) PI)))) (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (72 enodes) * * [misc]simplify: iters left: 1 (74 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 4/3 (- PI (* (* v v) PI)))) (/ (fabs (cbrt (+ (* (* v v) -6) 2))) (cbrt (/ 4/3 (- PI (* (* v v) PI)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (cbrt (/ 4/3 (- PI (* (* v v) PI)))) (/ (fabs (cbrt (+ (* (* v v) -6) 2))) (cbrt (/ 4/3 (- PI (* (* v v) PI)))))) (/ (cbrt (/ 4/3 (* (- 1 (* v v)) PI))) (sqrt (cbrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 4/3 (* (- 1 (* v v)) PI))) (sqrt (cbrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (64 enodes) * * [misc]simplify: iters left: 1 (66 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 4/3 (- PI (* (* v v) PI)))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (cbrt (/ 4/3 (- PI (* (* v v) PI)))) (/ (fabs (cbrt (+ (* (* v v) -6) 2))) (cbrt (/ 4/3 (- PI (* (* v v) PI)))))) (/ (cbrt (/ 4/3 (- PI (* (* v v) PI)))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 47 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 4/3 (* (- 1 (* v v)) PI))) (cbrt (/ 4/3 (* (- 1 (* v v)) PI)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (70 enodes) * * [misc]simplify: iters left: 1 (72 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 4/3 (- PI (* (* v v) PI)))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (/ 4/3 (- PI (* (* v v) PI)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (cbrt (/ 4/3 (- PI (* (* v v) PI)))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (/ 4/3 (- PI (* (* v v) PI)))))) (/ (cbrt (/ 4/3 (* (- 1 (* v v)) PI))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 4/3 (* (- 1 (* v v)) PI))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (64 enodes) * * [misc]simplify: iters left: 1 (66 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 4/3 (- PI (* (* v v) PI)))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 (* (- 1 (* v v)) PI))) (cbrt (/ 4/3 (* (- 1 (* v v)) PI)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (cbrt (/ 4/3 (- PI (* (* v v) PI)))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 48 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 4/3 (* (- 1 (* v v)) PI))) (cbrt (/ 4/3 (* (- 1 (* v v)) PI)))) (sqrt 1)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (79 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 4/3 (- PI (* (* v v) PI)))) (cbrt (/ 4/3 (- PI (* (* v v) PI))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (/ 4/3 (- PI (* (* v v) PI)))) (cbrt (/ 4/3 (- PI (* (* v v) PI))))) (/ (cbrt (/ 4/3 (* (- 1 (* v v)) PI))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (cbrt (/ 4/3 (* (- 1 (* v v)) PI))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (63 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 4/3 (- PI (* (* v v) PI)))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (cbrt (/ 4/3 (- PI (* (* v v) PI)))) (cbrt (/ 4/3 (- PI (* (* v v) PI))))) (/ (cbrt (/ 4/3 (- PI (* (* v v) PI)))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 49 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 4/3 (* (- 1 (* v v)) PI))) (cbrt (/ 4/3 (* (- 1 (* v v)) PI)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (70 enodes) * * [misc]simplify: iters left: 1 (72 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 4/3 (- PI (* (* v v) PI)))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (/ 4/3 (- PI (* (* v v) PI)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (cbrt (/ 4/3 (- PI (* (* v v) PI)))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (/ 4/3 (- PI (* (* v v) PI)))))) (/ (cbrt (/ 4/3 (* (- 1 (* v v)) PI))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 4/3 (* (- 1 (* v v)) PI))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (64 enodes) * * [misc]simplify: iters left: 1 (66 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 4/3 (- PI (* (* v v) PI)))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 (* (- 1 (* v v)) PI))) (cbrt (/ 4/3 (* (- 1 (* v v)) PI)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (cbrt (/ 4/3 (- PI (* (* v v) PI)))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 50 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 4/3 (* (- 1 (* v v)) PI))) (cbrt (/ 4/3 (* (- 1 (* v v)) PI)))) 1) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (100 enodes) * * [misc]simplify: iters left: 1 (105 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 4/3 (- PI (* (* v v) PI)))) (cbrt (/ 4/3 (- PI (* (* v v) PI))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (/ 4/3 (- PI (* (* v v) PI)))) (cbrt (/ 4/3 (- PI (* (* v v) PI))))) (/ (cbrt (/ 4/3 (* (- 1 (* v v)) PI))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (cbrt (/ 4/3 (* (- 1 (* v v)) PI))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (63 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 4/3 (- PI (* (* v v) PI)))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (cbrt (/ 4/3 (- PI (* (* v v) PI)))) (cbrt (/ 4/3 (- PI (* (* v v) PI))))) (/ (cbrt (/ 4/3 (- PI (* (* v v) PI)))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 51 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 4/3 (* (- 1 (* v v)) PI))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (56 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 (- PI (* (* v v) PI)))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 (- PI (* (* v v) PI)))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (/ (sqrt (/ 4/3 (* (- 1 (* v v)) PI))) (cbrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 4/3 (* (- 1 (* v v)) PI))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (64 enodes) * * [misc]simplify: iters left: 1 (66 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 (- PI (* (* v v) PI)))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 (* (- 1 (* v v)) PI))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (/ (sqrt (/ 4/3 (- PI (* (* v v) PI)))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 52 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 4/3 (* (- 1 (* v v)) PI))) (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 (- PI (* (* v v) PI)))) (fabs (cbrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 (- PI (* (* v v) PI)))) (fabs (cbrt (+ (* -6 (* v v)) 2)))) (/ (sqrt (/ 4/3 (* (- 1 (* v v)) PI))) (sqrt (cbrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 4/3 (* (- 1 (* v v)) PI))) (sqrt (cbrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (64 enodes) * * [misc]simplify: iters left: 1 (66 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 (- PI (* (* v v) PI)))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 (- PI (* (* v v) PI)))) (fabs (cbrt (+ (* -6 (* v v)) 2)))) (/ (sqrt (/ 4/3 (- PI (* (* v v) PI)))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 53 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 4/3 (* (- 1 (* v v)) PI))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (64 enodes) * * [misc]simplify: iters left: 1 (66 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 (- PI (* (* v v) PI)))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 (- PI (* (* v v) PI)))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) (/ (sqrt (/ 4/3 (* (- 1 (* v v)) PI))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 4/3 (* (- 1 (* v v)) PI))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (64 enodes) * * [misc]simplify: iters left: 1 (66 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 (- PI (* (* v v) PI)))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 (* (- 1 (* v v)) PI))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 (- PI (* (* v v) PI)))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 54 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 4/3 (* (- 1 (* v v)) PI))) (sqrt 1)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (54 enodes) * * [misc]simplify: iters left: 1 (56 enodes) * [exit]simplify: Simplified to (sqrt (/ 4/3 (- PI (* (* v v) PI)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (sqrt (/ 4/3 (- PI (* (* v v) PI)))) (/ (sqrt (/ 4/3 (* (- 1 (* v v)) PI))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (sqrt (/ 4/3 (* (- 1 (* v v)) PI))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (63 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 (- PI (* (* v v) PI)))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (sqrt (/ 4/3 (- PI (* (* v v) PI)))) (/ (sqrt (/ 4/3 (- PI (* (* v v) PI)))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 55 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 4/3 (* (- 1 (* v v)) PI))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (64 enodes) * * [misc]simplify: iters left: 1 (66 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 (- PI (* (* v v) PI)))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 (- PI (* (* v v) PI)))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) (/ (sqrt (/ 4/3 (* (- 1 (* v v)) PI))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 4/3 (* (- 1 (* v v)) PI))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (64 enodes) * * [misc]simplify: iters left: 1 (66 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 (- PI (* (* v v) PI)))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 (* (- 1 (* v v)) PI))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 (- PI (* (* v v) PI)))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 56 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 4/3 (* (- 1 (* v v)) PI))) 1) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * * [misc]simplify: iters left: 2 (53 enodes) * * [misc]simplify: iters left: 1 (55 enodes) * [exit]simplify: Simplified to (sqrt (/ 4/3 (- PI (* (* v v) PI)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (sqrt (/ 4/3 (- PI (* (* v v) PI)))) (/ (sqrt (/ 4/3 (* (- 1 (* v v)) PI))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (sqrt (/ 4/3 (* (- 1 (* v v)) PI))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (63 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 (- PI (* (* v v) PI)))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (sqrt (/ 4/3 (- PI (* (* v v) PI)))) (/ (sqrt (/ 4/3 (- PI (* (* v v) PI)))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 57 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 4/3 (* (- 1 (* v v)) PI)) (cbrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ 4/3 (* (- 1 (* v v)) PI)) (cbrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (82 enodes) * * [misc]simplify: iters left: 2 (190 enodes) * * [misc]simplify: iters left: 1 (335 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (- PI (* (* v v) PI))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (/ (/ 4/3 (- PI (* (* v v) PI))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 58 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (/ 1 (fabs (cbrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (fabs (cbrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 (* (- 1 (* v v)) PI)) (sqrt (cbrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ 4/3 (* (- 1 (* v v)) PI)) (sqrt (cbrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (82 enodes) * * [misc]simplify: iters left: 2 (190 enodes) * * [misc]simplify: iters left: 1 (335 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (- PI (* (* v v) PI))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (fabs (cbrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 (- PI (* (* v v) PI))) (sqrt (cbrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 59 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 (* (- 1 (* v v)) PI)) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ 4/3 (* (- 1 (* v v)) PI)) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (82 enodes) * * [misc]simplify: iters left: 2 (190 enodes) * * [misc]simplify: iters left: 1 (335 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (- PI (* (* v v) PI))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 (- PI (* (* v v) PI))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 60 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt 1)) * * [misc]simplify: iters left: 3 (3 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 1) to (λ (v) (* 1 (/ (/ 4/3 (* (- 1 (* v v)) PI)) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (/ 4/3 (* (- 1 (* v v)) PI)) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (81 enodes) * * [misc]simplify: iters left: 2 (189 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (- PI (* (* v v) PI))) (sqrt (+ (* (* v v) -6) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* 1 (/ (/ 4/3 (- PI (* (* v v) PI))) (sqrt (+ (* (* v v) -6) 2))))) * * * * [misc]progress: [ 61 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 (* (- 1 (* v v)) PI)) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ 4/3 (* (- 1 (* v v)) PI)) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (82 enodes) * * [misc]simplify: iters left: 2 (190 enodes) * * [misc]simplify: iters left: 1 (335 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (- PI (* (* v v) PI))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 (- PI (* (* v v) PI))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 62 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 1) * * [misc]simplify: iters left: 2 (2 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 1) to (λ (v) (* 1 (/ (/ 4/3 (* (- 1 (* v v)) PI)) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (/ 4/3 (* (- 1 (* v v)) PI)) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (81 enodes) * * [misc]simplify: iters left: 2 (189 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (- PI (* (* v v) PI))) (sqrt (+ (* (* v v) -6) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* 1 (/ (/ 4/3 (- PI (* (* v v) PI))) (sqrt (+ (* (* v v) -6) 2))))) * * * * [misc]progress: [ 63 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 4/3 (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * [exit]simplify: Simplified to (/ 4/3 (* (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (* (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) (/ (/ 1 (* (- 1 (* v v)) PI)) (cbrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ 1 (* (- 1 (* v v)) PI)) (cbrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (228 enodes) * * [misc]simplify: iters left: 1 (389 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (- 1 (* v v))) PI) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (/ (/ (/ 1 (- 1 (* v v))) PI) (cbrt (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 64 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 4/3 (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * [exit]simplify: Simplified to (/ 4/3 (fabs (cbrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (fabs (cbrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (* (- 1 (* v v)) PI)) (sqrt (cbrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ 1 (* (- 1 (* v v)) PI)) (sqrt (cbrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (228 enodes) * * [misc]simplify: iters left: 1 (389 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (- 1 (* v v))) PI) (sqrt (cbrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (fabs (cbrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 1 (- 1 (* v v))) PI) (sqrt (cbrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 65 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 4/3 (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * * [misc]simplify: iters left: 3 (17 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (* (- 1 (* v v)) PI)) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ 1 (* (- 1 (* v v)) PI)) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (228 enodes) * * [misc]simplify: iters left: 1 (389 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (- 1 (* v v))) PI) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 1 (- 1 (* v v))) PI) (sqrt (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 66 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 4/3 (sqrt 1)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (6 enodes) * [exit]simplify: Simplified to 4/3 * [misc]simplify: Simplified (2 1) to (λ (v) (* 4/3 (/ (/ 1 (* (- 1 (* v v)) PI)) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (/ 1 (* (- 1 (* v v)) PI)) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (87 enodes) * * [misc]simplify: iters left: 2 (227 enodes) * * [misc]simplify: iters left: 1 (394 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (- 1 (* v v))) PI) (sqrt (+ (* (* v v) -6) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* 4/3 (/ (/ (/ 1 (- 1 (* v v))) PI) (sqrt (+ (* (* v v) -6) 2))))) * * * * [misc]progress: [ 67 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 4/3 (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * * [misc]simplify: iters left: 3 (17 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (* (- 1 (* v v)) PI)) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (/ 1 (* (- 1 (* v v)) PI)) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (228 enodes) * * [misc]simplify: iters left: 1 (389 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (- 1 (* v v))) PI) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 1 (- 1 (* v v))) PI) (sqrt (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 68 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 4/3 1) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (5 enodes) * [exit]simplify: Simplified to 4/3 * [misc]simplify: Simplified (2 1) to (λ (v) (* 4/3 (/ (/ 1 (* (- 1 (* v v)) PI)) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (/ 1 (* (- 1 (* v v)) PI)) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (87 enodes) * * [misc]simplify: iters left: 2 (227 enodes) * * [misc]simplify: iters left: 1 (394 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (- 1 (* v v))) PI) (sqrt (+ (* (* v v) -6) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* 4/3 (/ (/ (/ 1 (- 1 (* v v))) PI) (sqrt (+ (* (* v v) -6) 2))))) * * * * [misc]progress: [ 69 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 (* (- (pow 1 3) (pow (* v v) 3)) PI)) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (79 enodes) * * [misc]simplify: iters left: 3 (193 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (cbrt (sqrt (+ (* (* v -6) v) 2)))) (* (cbrt (sqrt (+ (* (* v -6) v) 2))) (+ PI (* (* (* v v) (- v)) (* (* v v) (* v PI)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (cbrt (sqrt (+ (* (* v -6) v) 2)))) (* (cbrt (sqrt (+ (* (* v -6) v) 2))) (+ PI (* (* (* v v) (- v)) (* (* v v) (* v PI)))))) (/ (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (166 enodes) * * [misc]simplify: iters left: 1 (197 enodes) * [exit]simplify: Simplified to (/ (+ 1 (+ (* v v) (pow v 4))) (cbrt (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (* (- (pow 1 3) (pow (* v v) 3)) PI)) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (/ (+ 1 (+ (* v v) (pow v 4))) (cbrt (sqrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 70 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 (* (- (pow 1 3) (pow (* v v) 3)) PI)) (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (166 enodes) * * [misc]simplify: iters left: 2 (411 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (- PI (* (pow v 6) PI))) (fabs (cbrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (- PI (* (pow v 6) PI))) (fabs (cbrt (+ (* (* v -6) v) 2)))) (/ (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))) (sqrt (cbrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))) (sqrt (cbrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (166 enodes) * * [misc]simplify: iters left: 1 (197 enodes) * [exit]simplify: Simplified to (/ (+ 1 (+ (* v v) (pow v 4))) (sqrt (cbrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (- PI (* (pow v 6) PI))) (fabs (cbrt (+ (* (* v -6) v) 2)))) (/ (+ 1 (+ (* v v) (pow v 4))) (sqrt (cbrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 71 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 (* (- (pow 1 3) (pow (* v v) 3)) PI)) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (162 enodes) * * [misc]simplify: iters left: 2 (480 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (- PI (* (pow v 6) PI))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (- PI (* (pow v 6) PI))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (/ (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (166 enodes) * * [misc]simplify: iters left: 1 (197 enodes) * [exit]simplify: Simplified to (/ (+ 1 (+ (* v v) (pow v 4))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (- PI (* (pow v 6) PI))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (/ (+ 1 (+ (* v v) (pow v 4))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 72 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 (* (- (pow 1 3) (pow (* v v) 3)) PI)) (sqrt 1)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (131 enodes) * * [misc]simplify: iters left: 2 (311 enodes) * [exit]simplify: Simplified to (/ 4/3 (- PI (* PI (pow v 6)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (- PI (* PI (pow v 6)))) (/ (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (149 enodes) * * [misc]simplify: iters left: 1 (170 enodes) * [exit]simplify: Simplified to (/ (+ 1 (+ (* v v) (pow v 4))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (- PI (* PI (pow v 6)))) (/ (+ 1 (+ (* v v) (pow v 4))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 73 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 (* (- (pow 1 3) (pow (* v v) 3)) PI)) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (162 enodes) * * [misc]simplify: iters left: 2 (480 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (- PI (* (pow v 6) PI))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (- PI (* (pow v 6) PI))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (/ (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (166 enodes) * * [misc]simplify: iters left: 1 (197 enodes) * [exit]simplify: Simplified to (/ (+ 1 (+ (* v v) (pow v 4))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (- PI (* (pow v 6) PI))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (/ (+ 1 (+ (* v v) (pow v 4))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 74 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 (* (- (pow 1 3) (pow (* v v) 3)) PI)) 1) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (133 enodes) * * [misc]simplify: iters left: 2 (306 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (- 1 (pow v 6))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (- 1 (pow v 6))) (/ (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (149 enodes) * * [misc]simplify: iters left: 1 (170 enodes) * [exit]simplify: Simplified to (/ (+ 1 (+ (* v v) (pow v 4))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (- 1 (pow v 6))) (/ (+ 1 (+ (* v v) (pow v 4))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 75 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 (* (- (* 1 1) (* (* v v) (* v v))) PI)) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (156 enodes) * * [misc]simplify: iters left: 2 (443 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (- PI (* PI (pow v 4)))) (* (cbrt (sqrt (+ (* -6 (* v v)) 2))) (cbrt (sqrt (+ (* -6 (* v v)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (- PI (* PI (pow v 4)))) (* (cbrt (sqrt (+ (* -6 (* v v)) 2))) (cbrt (sqrt (+ (* -6 (* v v)) 2))))) (/ (+ 1 (* v v)) (cbrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (+ 1 (* v v)) (cbrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (/ (+ 1 (* v v)) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (- PI (* PI (pow v 4)))) (* (cbrt (sqrt (+ (* -6 (* v v)) 2))) (cbrt (sqrt (+ (* -6 (* v v)) 2))))) (/ (+ 1 (* v v)) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 76 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 (* (- (* 1 1) (* (* v v) (* v v))) PI)) (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (127 enodes) * * [misc]simplify: iters left: 2 (304 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (- PI (* PI (pow v 4)))) (fabs (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (- PI (* PI (pow v 4)))) (fabs (cbrt (+ (* v (* v -6)) 2)))) (/ (+ 1 (* v v)) (sqrt (cbrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (+ 1 (* v v)) (sqrt (cbrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (/ (+ 1 (* v v)) (sqrt (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (- PI (* PI (pow v 4)))) (fabs (cbrt (+ (* v (* v -6)) 2)))) (/ (+ 1 (* v v)) (sqrt (cbrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 77 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 (* (- (* 1 1) (* (* v v) (* v v))) PI)) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (125 enodes) * * [misc]simplify: iters left: 2 (349 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (- PI (* PI (pow v 4)))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (- PI (* PI (pow v 4)))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) (/ (+ 1 (* v v)) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (+ 1 (* v v)) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (/ (+ 1 (* v v)) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (- PI (* PI (pow v 4)))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) (/ (+ 1 (* v v)) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 78 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 (* (- (* 1 1) (* (* v v) (* v v))) PI)) (sqrt 1)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (94 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (338 enodes) * [exit]simplify: Simplified to (/ 4/3 (- PI (* (pow v 4) PI))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (- PI (* (pow v 4) PI))) (/ (+ 1 (* v v)) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (+ 1 (* v v)) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * [exit]simplify: Simplified to (/ (+ 1 (* v v)) (sqrt (+ (* (* v v) -6) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (- PI (* (pow v 4) PI))) (/ (+ 1 (* v v)) (sqrt (+ (* (* v v) -6) 2))))) * * * * [misc]progress: [ 79 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 (* (- (* 1 1) (* (* v v) (* v v))) PI)) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (125 enodes) * * [misc]simplify: iters left: 2 (349 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (- PI (* PI (pow v 4)))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (- PI (* PI (pow v 4)))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) (/ (+ 1 (* v v)) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * [enter]simplify: Simplifying (/ (+ 1 (* v v)) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (/ (+ 1 (* v v)) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (- PI (* PI (pow v 4)))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) (/ (+ 1 (* v v)) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 80 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 (* (- (* 1 1) (* (* v v) (* v v))) PI)) 1) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (94 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (337 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (- 1 (pow v 4))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (- 1 (pow v 4))) (/ (+ 1 (* v v)) (sqrt (+ 2 (* (* v v) -6)))))) * [enter]simplify: Simplifying (/ (+ 1 (* v v)) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * [exit]simplify: Simplified to (/ (+ 1 (* v v)) (sqrt (+ (* (* v v) -6) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (- 1 (pow v 4))) (/ (+ 1 (* v v)) (sqrt (+ (* (* v v) -6) 2))))) * * * * [misc]progress: [ 81 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 82 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 83 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 84 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (cbrt (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (15 enodes) * [exit]simplify: Simplified to (cbrt (sqrt (+ 2 (* (* v v) -6)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 4/3 (* (- 1 (* v v)) PI)) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * * * * [misc]progress: [ 85 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (cbrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (15 enodes) * [exit]simplify: Simplified to (sqrt (cbrt (+ 2 (* (* v v) -6)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 4/3 (* (- 1 (* v v)) PI)) (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6)))))) (sqrt (cbrt (+ 2 (* (* v v) -6)))))) * * * * [misc]progress: [ 86 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (15 enodes) * [exit]simplify: Simplified to (sqrt (sqrt (+ 2 (* (* v v) -6)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 4/3 (* (- 1 (* v v)) PI)) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (sqrt (sqrt (+ 2 (* (* v v) -6)))))) * * * * [misc]progress: [ 87 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (+ 2 (* (* v v) -6))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (14 enodes) * [exit]simplify: Simplified to (sqrt (+ 2 (* (* v v) -6))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 4/3 (* (- 1 (* v v)) PI)) (sqrt 1)) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 88 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (15 enodes) * [exit]simplify: Simplified to (sqrt (sqrt (+ 2 (* (* v v) -6)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 4/3 (* (- 1 (* v v)) PI)) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (sqrt (sqrt (+ 2 (* (* v v) -6)))))) * * * * [misc]progress: [ 89 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (+ 2 (* (* v v) -6))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (14 enodes) * [exit]simplify: Simplified to (sqrt (+ 2 (* (* v v) -6))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 4/3 (* (- 1 (* v v)) PI)) 1) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 90 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ 4/3 (* (- 1 (* v v)) PI))) (cbrt (/ 4/3 (* (- 1 (* v v)) PI)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * * [misc]simplify: iters left: 2 (51 enodes) * * [misc]simplify: iters left: 1 (53 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 4/3 (- PI (* (* v v) PI)))) (cbrt (/ 4/3 (- PI (* (* v v) PI))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (cbrt (/ 4/3 (- PI (* (* v v) PI)))) (cbrt (/ 4/3 (- PI (* (* v v) PI))))) (/ (sqrt (+ 2 (* (* v v) -6))) (cbrt (/ 4/3 (* (- 1 (* v v)) PI)))))) * * * * [misc]progress: [ 91 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ 4/3 (* (- 1 (* v v)) PI))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (50 enodes) * * [misc]simplify: iters left: 1 (52 enodes) * [exit]simplify: Simplified to (sqrt (/ 4/3 (- PI (* (* v v) PI)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (sqrt (/ 4/3 (- PI (* (* v v) PI)))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (/ 4/3 (* (- 1 (* v v)) PI)))))) * * * * [misc]progress: [ 92 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 93 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 94 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 4/3 (* (- (pow 1 3) (pow (* v v) 3)) PI)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (113 enodes) * * [misc]simplify: iters left: 2 (245 enodes) * * [misc]simplify: iters left: 1 (403 enodes) * [exit]simplify: Simplified to (/ 4/3 (- PI (* (pow v 6) PI))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (/ 4/3 (- PI (* (pow v 6) PI))) (/ (sqrt (+ 2 (* (* v v) -6))) (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * * * [misc]progress: [ 95 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 4/3 (* (- (* 1 1) (* (* v v) (* v v))) PI)) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (129 enodes) * * [misc]simplify: iters left: 1 (155 enodes) * [exit]simplify: Simplified to (/ 4/3 (- PI (* PI (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (/ 4/3 (- PI (* PI (pow v 4)))) (/ (sqrt (+ 2 (* (* v v) -6))) (+ 1 (* v v))))) * * * * [misc]progress: [ 96 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (+ (* 2 2) (- (* (* (* v v) -6) (* (* v v) -6)) (* 2 (* (* v v) -6))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (219 enodes) * * [misc]simplify: iters left: 2 (389 enodes) * * [misc]simplify: iters left: 1 (497 enodes) * [exit]simplify: Simplified to (sqrt (+ (* (pow v 4) 36) (+ (* (* 12 v) v) 4))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (* (- 1 (* v v)) PI)) (sqrt (+ (pow 2 3) (pow (* (* v v) -6) 3)))) (sqrt (+ (* (pow v 4) 36) (+ (* (* 12 v) v) 4))))) * * * * [misc]progress: [ 97 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (- 2 (* (* v v) -6))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (sqrt (- 2 (* (* v v) -6))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (* (- 1 (* v v)) PI)) (sqrt (- (* 2 2) (* (* (* v v) -6) (* (* v v) -6))))) (sqrt (- 2 (* (* v v) -6))))) * * * * [misc]progress: [ 98 / 110 ] simplifiying candidate # * * * * [misc]progress: [ 99 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* 4/3 (/ (pow v 2) PI)) (+ (* 4/3 (/ 1 PI)) (* 4/3 (/ (pow v 4) PI)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (126 enodes) * * [misc]simplify: iters left: 1 (203 enodes) * [exit]simplify: Simplified to (+ (/ 4/3 PI) (* (+ (pow v 4) (* v v)) (/ 4/3 PI))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (+ (/ 4/3 PI) (* (+ (pow v 4) (* v v)) (/ 4/3 PI))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 100 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 4/3 (/ 1 (* (pow v 2) PI))) (+ (* 4/3 (/ 1 (* (pow v 4) PI))) (* 4/3 (/ 1 (* (pow v 6) PI)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (105 enodes) * * [misc]simplify: iters left: 3 (237 enodes) * * [misc]simplify: iters left: 2 (443 enodes) * [exit]simplify: Simplified to (- (/ -4/3 (* (* v PI) v)) (+ (/ (/ 4/3 PI) (pow v 6)) (/ (/ 4/3 PI) (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (/ -4/3 (* (* v PI) v)) (+ (/ (/ 4/3 PI) (pow v 6)) (/ (/ 4/3 PI) (pow v 4)))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 101 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 4/3 (/ 1 (* (pow v 2) PI))) (+ (* 4/3 (/ 1 (* (pow v 4) PI))) (* 4/3 (/ 1 (* (pow v 6) PI)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (105 enodes) * * [misc]simplify: iters left: 3 (237 enodes) * * [misc]simplify: iters left: 2 (443 enodes) * [exit]simplify: Simplified to (- (/ -4/3 (* (* v PI) v)) (+ (/ (/ 4/3 PI) (pow v 6)) (/ (/ 4/3 PI) (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (- (/ -4/3 (* (* v PI) v)) (+ (/ (/ 4/3 PI) (pow v 6)) (/ (/ 4/3 PI) (pow v 4)))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 102 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (* -6 (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) -6) * [misc]simplify: Simplified (2 2 1 2) to (λ (v) (/ (/ 4/3 (* (- 1 (* v v)) PI)) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 103 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (* -6 (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) -6) * [misc]simplify: Simplified (2 2 1 2) to (λ (v) (/ (/ 4/3 (* (- 1 (* v v)) PI)) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 104 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (* -6 (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) -6) * [misc]simplify: Simplified (2 2 1 2) to (λ (v) (/ (/ 4/3 (* (- 1 (* v v)) PI)) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 105 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (- PI (* (pow v 2) PI)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (36 enodes) * * [misc]simplify: iters left: 1 (43 enodes) * [exit]simplify: Simplified to (- PI (* (* PI v) v)) * [misc]simplify: Simplified (2 1 2) to (λ (v) (/ (/ 4/3 (- PI (* (* PI v) v))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 106 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (- PI (* (pow v 2) PI)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (36 enodes) * * [misc]simplify: iters left: 1 (43 enodes) * [exit]simplify: Simplified to (- PI (* (* PI v) v)) * [misc]simplify: Simplified (2 1 2) to (λ (v) (/ (/ 4/3 (- PI (* (* PI v) v))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 107 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (- PI (* (pow v 2) PI)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (36 enodes) * * [misc]simplify: iters left: 1 (43 enodes) * [exit]simplify: Simplified to (- PI (* (* PI v) v)) * [misc]simplify: Simplified (2 1 2) to (λ (v) (/ (/ 4/3 (- PI (* (* PI v) v))) (sqrt (+ 2 (* (* v v) -6))))) * * * * [misc]progress: [ 108 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* 4/3 (/ (pow v 4) (* (sqrt 2) PI))) (+ (* 4/3 (/ 1 (* (sqrt 2) PI))) (+ (* 4 (/ (pow v 4) (* (pow (sqrt 2) 3) PI))) (+ (* 18 (/ (pow v 4) (* (pow (sqrt 2) 5) PI))) (+ (* 4 (/ (pow v 2) (* (pow (sqrt 2) 3) PI))) (* 4/3 (/ (pow v 2) (* (sqrt 2) PI)))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (86 enodes) * * [misc]simplify: iters left: 4 (261 enodes) * [exit]simplify: Simplified to (+ (+ (* (/ (pow v 4) PI) (/ 2 (sqrt 2))) (+ (/ (/ 4/3 (sqrt 2)) PI) (/ (* (/ 4/3 PI) (pow v 4)) (sqrt 2)))) (+ (* (/ v (/ PI v)) (+ (/ 4/3 (sqrt 2)) (/ 2 (sqrt 2)))) (/ (* (/ 18 PI) (pow v 4)) (pow (sqrt 2) 5)))) * [misc]simplify: Simplified (2) to (λ (v) (+ (+ (* (/ (pow v 4) PI) (/ 2 (sqrt 2))) (+ (/ (/ 4/3 (sqrt 2)) PI) (/ (* (/ 4/3 PI) (pow v 4)) (sqrt 2)))) (+ (* (/ v (/ PI v)) (+ (/ 4/3 (sqrt 2)) (/ 2 (sqrt 2)))) (/ (* (/ 18 PI) (pow v 4)) (pow (sqrt 2) 5))))) * * * * [misc]progress: [ 109 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 4/3 (/ 1 (* (pow v 7) (* (pow (sqrt -6) 3) PI)))) (* 4/3 (/ 1 (* (pow v 5) (* (pow (sqrt -6) 3) PI))))) (+ (* 4/3 (/ 1 (* (pow v 7) (* (sqrt -6) PI)))) (+ (* 4/3 (/ 1 (* (pow v 3) (* (sqrt -6) PI)))) (+ (* 2 (/ 1 (* (pow v 7) (* (pow (sqrt -6) 5) PI)))) (* 4/3 (/ 1 (* (pow v 5) (* (sqrt -6) PI)))))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (109 enodes) * * [misc]simplify: iters left: 4 (259 enodes) * [exit]simplify: Simplified to (- (- (+ (/ (/ 4/3 (pow v 5)) (* (sqrt -6) (* PI -6))) (/ (/ 4/3 (pow v 7)) (* (sqrt -6) (* PI -6)))) (/ (/ 4/3 (pow v 7)) (* PI (sqrt -6)))) (+ (/ (/ 2 (pow v 7)) (* (pow (sqrt -6) 5) PI)) (+ (/ (/ 4/3 (pow v 5)) (* PI (sqrt -6))) (/ (/ 4/3 (pow v 3)) (* PI (sqrt -6)))))) * [misc]simplify: Simplified (2) to (λ (v) (- (- (+ (/ (/ 4/3 (pow v 5)) (* (sqrt -6) (* PI -6))) (/ (/ 4/3 (pow v 7)) (* (sqrt -6) (* PI -6)))) (/ (/ 4/3 (pow v 7)) (* PI (sqrt -6)))) (+ (/ (/ 2 (pow v 7)) (* (pow (sqrt -6) 5) PI)) (+ (/ (/ 4/3 (pow v 5)) (* PI (sqrt -6))) (/ (/ 4/3 (pow v 3)) (* PI (sqrt -6))))))) * * * * [misc]progress: [ 110 / 110 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 4/3 (/ 1 (* (pow v 7) (* (sqrt -6) PI)))) (+ (* 4/3 (/ 1 (* (pow v 5) (* (sqrt -6) PI)))) (+ (* 4/3 (/ 1 (* (pow v 3) (* (sqrt -6) PI)))) (* 2 (/ 1 (* (pow v 7) (* (pow (sqrt -6) 5) PI))))))) (+ (* 4/3 (/ 1 (* (pow v 7) (* (pow (sqrt -6) 3) PI)))) (* 4/3 (/ 1 (* (pow v 5) (* (pow (sqrt -6) 3) PI)))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (109 enodes) * * [misc]simplify: iters left: 4 (262 enodes) * [exit]simplify: Simplified to (+ (+ (+ (/ (/ 4/3 (pow v 7)) (* PI (sqrt -6))) (/ (/ 4/3 (pow v 3)) (* PI (sqrt -6)))) (/ (/ 2 (pow v 7)) (* (pow (sqrt -6) 5) PI))) (- (- (/ (/ 4/3 (pow v 5)) (* PI (sqrt -6))) (/ (/ 4/3 (pow v 7)) (* (sqrt -6) (* PI -6)))) (/ (/ 4/3 (pow v 5)) (* (sqrt -6) (* PI -6))))) * [misc]simplify: Simplified (2) to (λ (v) (+ (+ (+ (/ (/ 4/3 (pow v 7)) (* PI (sqrt -6))) (/ (/ 4/3 (pow v 3)) (* PI (sqrt -6)))) (/ (/ 2 (pow v 7)) (* (pow (sqrt -6) 5) PI))) (- (- (/ (/ 4/3 (pow v 5)) (* PI (sqrt -6))) (/ (/ 4/3 (pow v 7)) (* (sqrt -6) (* PI -6)))) (/ (/ 4/3 (pow v 5)) (* (sqrt -6) (* PI -6)))))) * * * [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 2 1) * * * * [misc]progress: [ 2 / 4 ] rewriting at (2) * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 2 1 1 2) * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 2 2) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2 2 1) * * * * [misc]progress: [ 2 / 4 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (- 1 (* v v)))) in v * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* v v))) in v * [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 (* 0 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 (- 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 1) into 1 * [misc]taylor: Taking taylor expansion of (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) in v * [misc]taylor: Taking taylor expansion of (sqrt (+ 2 (* (* v v) -6))) in v * [misc]taylor: Taking taylor expansion of (+ 2 (* (* v v) -6)) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* (* v v) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 0 -6) into 0 * [misc]backup-simplify: Simplify (+ 2 0) into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 0 -6)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) in v * [misc]taylor: Taking taylor expansion of (/ 4/3 PI) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of PI in v * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (/ 4/3 PI) into (/ 4/3 PI) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* v v))) in v * [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 (* 0 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 (- 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 (/ (/ 4/3 PI) 1) into (/ 4/3 PI) * [misc]backup-simplify: Simplify (/ (sqrt 2) (/ 4/3 PI)) into (* 3/4 (* (sqrt 2) PI)) * [misc]backup-simplify: Simplify (/ 1 (* 3/4 (* (sqrt 2) PI))) into (/ 4/3 (* (sqrt 2) PI)) * [misc]taylor: Taking taylor expansion of (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (- 1 (* v v)))) in v * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* v v))) in v * [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 (* 0 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 (- 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 1) into 1 * [misc]taylor: Taking taylor expansion of (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) in v * [misc]taylor: Taking taylor expansion of (sqrt (+ 2 (* (* v v) -6))) in v * [misc]taylor: Taking taylor expansion of (+ 2 (* (* v v) -6)) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* (* v v) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 0 -6) into 0 * [misc]backup-simplify: Simplify (+ 2 0) into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (+ (* 0 1) (* 1 0)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 0 -6)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) in v * [misc]taylor: Taking taylor expansion of (/ 4/3 PI) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of PI in v * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (/ 4/3 PI) into (/ 4/3 PI) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* v v))) in v * [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 (* 0 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 (- 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 (/ (/ 4/3 PI) 1) into (/ 4/3 PI) * [misc]backup-simplify: Simplify (/ (sqrt 2) (/ 4/3 PI)) into (* 3/4 (* (sqrt 2) PI)) * [misc]backup-simplify: Simplify (/ 1 (* 3/4 (* (sqrt 2) PI))) into (/ 4/3 (* (sqrt 2) PI)) * [misc]backup-simplify: Simplify (/ 4/3 (* (sqrt 2) PI)) into (/ 4/3 (* (sqrt 2) PI)) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (/ 4/3 PI) (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (/ 4/3 PI)) (+ (* (* 3/4 (* (sqrt 2) PI)) (/ 0 (/ 4/3 PI))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* 3/4 (* (sqrt 2) PI))) (+ (* (/ 4/3 (* (sqrt 2) PI)) (/ 0 (* 3/4 (* (sqrt 2) PI)))))) 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 (/ (- -1 (pow 0 2) (+)) (* 2 1)) into -1/2 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ -1/2 1)) (* 0 (/ 0 1)))) into 1/2 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 1) (* 0 0))) into 1 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 0 0) (* 1 -6))) into -6 * [misc]backup-simplify: Simplify (+ 0 -6) into -6 * [misc]backup-simplify: Simplify (/ (- -6 (pow 0 2) (+)) (* 2 (sqrt 2))) into (/ -3 (sqrt 2)) * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)))) 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 (/ (- -1 (pow 0 2) (+)) (* 2 1)) into -1/2 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (/ 4/3 PI) (/ -1/2 1)) (* 0 (/ 0 1)))) into (* 2/3 (/ 1 PI)) * [misc]backup-simplify: Simplify (- (/ (/ -3 (sqrt 2)) (/ 4/3 PI)) (+ (* (* 3/4 (* (sqrt 2) PI)) (/ (* 2/3 (/ 1 PI)) (/ 4/3 PI))) (* 0 (/ 0 (/ 4/3 PI))))) into (- (+ (* 9/4 (/ PI (sqrt 2))) (* 3/8 (* (sqrt 2) PI)))) * [misc]backup-simplify: Simplify (- (/ 1/2 (* 3/4 (* (sqrt 2) PI))) (+ (* (/ 4/3 (* (sqrt 2) PI)) (/ (- (+ (* 9/4 (/ PI (sqrt 2))) (* 3/8 (* (sqrt 2) PI)))) (* 3/4 (* (sqrt 2) PI)))) (* 0 (/ 0 (* 3/4 (* (sqrt 2) PI)))))) into (+ (* 4 (/ 1 (* (pow (sqrt 2) 3) PI))) (* 4/3 (/ 1 (* (sqrt 2) PI)))) * [misc]backup-simplify: Simplify (+ (* 4 (/ 1 (* (pow (sqrt 2) 3) PI))) (* 4/3 (/ 1 (* (sqrt 2) PI)))) into (+ (* 4 (/ 1 (* (pow (sqrt 2) 3) PI))) (* 4/3 (/ 1 (* (sqrt 2) PI)))) * [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 (+ (* 2 (* 0 -1/2)))) (* 2 1)) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ -1/2 1)) (* 1/2 (/ 0 1)))) 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 -6)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (/ -3 (sqrt 2)))))) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) 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 (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 -1/2)))) (* 2 1)) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (/ 4/3 PI) (/ 0 1)) (* 0 (/ -1/2 1)) (* (* 2/3 (/ 1 PI)) (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (/ 4/3 PI)) (+ (* (* 3/4 (* (sqrt 2) PI)) (/ 0 (/ 4/3 PI))) (* 0 (/ (* 2/3 (/ 1 PI)) (/ 4/3 PI))) (* (- (+ (* 9/4 (/ PI (sqrt 2))) (* 3/8 (* (sqrt 2) PI)))) (/ 0 (/ 4/3 PI))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* 3/4 (* (sqrt 2) PI))) (+ (* (/ 4/3 (* (sqrt 2) PI)) (/ 0 (* 3/4 (* (sqrt 2) PI)))) (* 0 (/ (- (+ (* 9/4 (/ PI (sqrt 2))) (* 3/8 (* (sqrt 2) PI)))) (* 3/4 (* (sqrt 2) PI)))) (* (+ (* 4 (/ 1 (* (pow (sqrt 2) 3) PI))) (* 4/3 (/ 1 (* (sqrt 2) PI)))) (/ 0 (* 3/4 (* (sqrt 2) PI)))))) 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 (pow -1/2 2) (+ (* 2 (* 0 0)))) (* 2 1)) into -1/8 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ -1/8 1)) (* 0 (/ 0 1)) (* 1/2 (/ -1/2 1)) (* 0 (/ 0 1)))) into 3/8 * [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 -6))))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ -3 (sqrt 2)) 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into (/ -9/2 (pow (sqrt 2) 3)) * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) 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 (pow -1/2 2) (+ (* 2 (* 0 0)))) (* 2 1)) into -1/8 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (/ 4/3 PI) (/ -1/8 1)) (* 0 (/ 0 1)) (* (* 2/3 (/ 1 PI)) (/ -1/2 1)) (* 0 (/ 0 1)))) into (* 1/2 (/ 1 PI)) * [misc]backup-simplify: Simplify (- (/ (/ -9/2 (pow (sqrt 2) 3)) (/ 4/3 PI)) (+ (* (* 3/4 (* (sqrt 2) PI)) (/ (* 1/2 (/ 1 PI)) (/ 4/3 PI))) (* 0 (/ 0 (/ 4/3 PI))) (* (- (+ (* 9/4 (/ PI (sqrt 2))) (* 3/8 (* (sqrt 2) PI)))) (/ (* 2/3 (/ 1 PI)) (/ 4/3 PI))) (* 0 (/ 0 (/ 4/3 PI))))) into (- (* 9/8 (/ PI (sqrt 2))) (+ (* 27/8 (/ PI (pow (sqrt 2) 3))) (* 3/32 (* (sqrt 2) PI)))) * [misc]backup-simplify: Simplify (- (/ 3/8 (* 3/4 (* (sqrt 2) PI))) (+ (* (/ 4/3 (* (sqrt 2) PI)) (/ (- (* 9/8 (/ PI (sqrt 2))) (+ (* 27/8 (/ PI (pow (sqrt 2) 3))) (* 3/32 (* (sqrt 2) PI)))) (* 3/4 (* (sqrt 2) PI)))) (* 0 (/ 0 (* 3/4 (* (sqrt 2) PI)))) (* (+ (* 4 (/ 1 (* (pow (sqrt 2) 3) PI))) (* 4/3 (/ 1 (* (sqrt 2) PI)))) (/ (- (+ (* 9/4 (/ PI (sqrt 2))) (* 3/8 (* (sqrt 2) PI)))) (* 3/4 (* (sqrt 2) PI)))) (* 0 (/ 0 (* 3/4 (* (sqrt 2) PI)))))) into (+ (* 4 (/ 1 (* (pow (sqrt 2) 3) PI))) (+ (* 4/3 (/ 1 (* (sqrt 2) PI))) (* 18 (/ 1 (* (pow (sqrt 2) 5) PI))))) * [misc]backup-simplify: Simplify (+ (* 4 (/ 1 (* (pow (sqrt 2) 3) PI))) (+ (* 4/3 (/ 1 (* (sqrt 2) PI))) (* 18 (/ 1 (* (pow (sqrt 2) 5) PI))))) into (+ (* 4 (/ 1 (* (pow (sqrt 2) 3) PI))) (+ (* 4/3 (/ 1 (* (sqrt 2) PI))) (* 18 (/ 1 (* (pow (sqrt 2) 5) PI))))) * [misc]backup-simplify: Simplify (+ (* (+ (* 4 (/ 1 (* (pow (sqrt 2) 3) PI))) (+ (* 4/3 (/ 1 (* (sqrt 2) PI))) (* 18 (/ 1 (* (pow (sqrt 2) 5) PI))))) (pow v 4)) (+ (* (+ (* 4 (/ 1 (* (pow (sqrt 2) 3) PI))) (* 4/3 (/ 1 (* (sqrt 2) PI)))) (pow v 2)) (/ 4/3 (* (sqrt 2) PI)))) into (+ (* 4/3 (/ (pow v 4) (* (sqrt 2) PI))) (+ (* 4/3 (/ 1 (* (sqrt 2) PI))) (+ (* 4 (/ (pow v 4) (* (pow (sqrt 2) 3) PI))) (+ (* 18 (/ (pow v 4) (* (pow (sqrt 2) 5) PI))) (+ (* 4 (/ (pow v 2) (* (pow (sqrt 2) 3) PI))) (* 4/3 (/ (pow v 2) (* (sqrt 2) PI)))))))) * [misc]approximate: Taking taylor expansion of (/ (/ 1 (sqrt (- 1 (* (/ 1 v) (/ 1 v))))) (/ (sqrt (+ 2 (* (* (/ 1 v) (/ 1 v)) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* (/ 1 v) (/ 1 v))))))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (/ (/ 1 (sqrt (- 1 (* (/ 1 v) (/ 1 v))))) (/ (sqrt (+ 2 (* (* (/ 1 v) (/ 1 v)) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* (/ 1 v) (/ 1 v))))))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (- 1 (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* (/ 1 v) (/ 1 v)))) in v * [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 1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (sqrt -1) into (sqrt -1) * [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 (* 2 (sqrt -1))) into 0 * [misc]backup-simplify: Simplify (/ 1 (sqrt -1)) into (/ 1 (sqrt -1)) * [misc]taylor: Taking taylor expansion of (/ (sqrt (+ 2 (* (* (/ 1 v) (/ 1 v)) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* (/ 1 v) (/ 1 v)))))) in v * [misc]taylor: Taking taylor expansion of (sqrt (+ 2 (* (* (/ 1 v) (/ 1 v)) -6))) in v * [misc]taylor: Taking taylor expansion of (+ 2 (* (* (/ 1 v) (/ 1 v)) -6)) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* (* (/ 1 v) (/ 1 v)) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 -6) into -6 * [misc]backup-simplify: Simplify (+ 0 -6) into -6 * [misc]backup-simplify: Simplify (sqrt -6) into (sqrt -6) * [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 (+ (* 1 0) (* 0 -6)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -6))) into 0 * [misc]taylor: Taking taylor expansion of (/ (/ 4/3 PI) (sqrt (- 1 (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (/ 4/3 PI) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of PI in v * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (/ 4/3 PI) into (/ 4/3 PI) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* (/ 1 v) (/ 1 v)))) in v * [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 1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (sqrt -1) into (sqrt -1) * [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 (* 2 (sqrt -1))) into 0 * [misc]backup-simplify: Simplify (/ (/ 4/3 PI) (sqrt -1)) into (/ 4/3 (* (sqrt -1) PI)) * [misc]backup-simplify: Simplify (/ (sqrt -6) (/ 4/3 (* (sqrt -1) PI))) into (* 3/4 (* (sqrt -1) (* (sqrt -6) PI))) * [misc]backup-simplify: Simplify (/ (/ 1 (sqrt -1)) (* 3/4 (* (sqrt -1) (* (sqrt -6) PI)))) into (/ 4/3 (* (sqrt -6) (* (pow (sqrt -1) 2) PI))) * [misc]taylor: Taking taylor expansion of (/ (/ 1 (sqrt (- 1 (* (/ 1 v) (/ 1 v))))) (/ (sqrt (+ 2 (* (* (/ 1 v) (/ 1 v)) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* (/ 1 v) (/ 1 v))))))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (- 1 (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* (/ 1 v) (/ 1 v)))) in v * [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 1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (sqrt -1) into (sqrt -1) * [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 (* 2 (sqrt -1))) into 0 * [misc]backup-simplify: Simplify (/ 1 (sqrt -1)) into (/ 1 (sqrt -1)) * [misc]taylor: Taking taylor expansion of (/ (sqrt (+ 2 (* (* (/ 1 v) (/ 1 v)) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* (/ 1 v) (/ 1 v)))))) in v * [misc]taylor: Taking taylor expansion of (sqrt (+ 2 (* (* (/ 1 v) (/ 1 v)) -6))) in v * [misc]taylor: Taking taylor expansion of (+ 2 (* (* (/ 1 v) (/ 1 v)) -6)) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* (* (/ 1 v) (/ 1 v)) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 -6) into -6 * [misc]backup-simplify: Simplify (+ 0 -6) into -6 * [misc]backup-simplify: Simplify (sqrt -6) into (sqrt -6) * [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 (+ (* 1 0) (* 0 -6)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -6))) into 0 * [misc]taylor: Taking taylor expansion of (/ (/ 4/3 PI) (sqrt (- 1 (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (/ 4/3 PI) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of PI in v * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (/ 4/3 PI) into (/ 4/3 PI) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* (/ 1 v) (/ 1 v)))) in v * [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 1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (sqrt -1) into (sqrt -1) * [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 (* 2 (sqrt -1))) into 0 * [misc]backup-simplify: Simplify (/ (/ 4/3 PI) (sqrt -1)) into (/ 4/3 (* (sqrt -1) PI)) * [misc]backup-simplify: Simplify (/ (sqrt -6) (/ 4/3 (* (sqrt -1) PI))) into (* 3/4 (* (sqrt -1) (* (sqrt -6) PI))) * [misc]backup-simplify: Simplify (/ (/ 1 (sqrt -1)) (* 3/4 (* (sqrt -1) (* (sqrt -6) PI)))) into (/ 4/3 (* (sqrt -6) (* (pow (sqrt -1) 2) PI))) * [misc]backup-simplify: Simplify (/ 4/3 (* (sqrt -6) (* (pow (sqrt -1) 2) PI))) into (/ 4/3 (* (sqrt -6) (* (pow (sqrt -1) 2) PI))) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt -1)) (/ 0 (sqrt -1))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt -1)) (+ (* (/ 4/3 (* (sqrt -1) PI)) (/ 0 (sqrt -1))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (/ 4/3 (* (sqrt -1) PI))) (+ (* (* 3/4 (* (sqrt -1) (* (sqrt -6) PI))) (/ 0 (/ 4/3 (* (sqrt -1) PI)))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* 3/4 (* (sqrt -1) (* (sqrt -6) PI)))) (+ (* (/ 4/3 (* (sqrt -6) (* (pow (sqrt -1) 2) PI))) (/ 0 (* 3/4 (* (sqrt -1) (* (sqrt -6) PI))))))) 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 (pow 0 2) (+)) (* 2 (sqrt -1))) into (/ 1/2 (sqrt -1)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt -1)) (/ (/ 1/2 (sqrt -1)) (sqrt -1))) (* 0 (/ 0 (sqrt -1))))) into (* 1/2 (/ 1 (sqrt -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 (+ (* 1 0) (+ (* 0 0) (* 0 -6))) into 0 * [misc]backup-simplify: Simplify (+ 2 0) into 2 * [misc]backup-simplify: Simplify (/ (- 2 (pow 0 2) (+)) (* 2 (sqrt -6))) into (/ 1 (sqrt -6)) * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)))) 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 (pow 0 2) (+)) (* 2 (sqrt -1))) into (/ 1/2 (sqrt -1)) * [misc]backup-simplify: Simplify (- (/ 0 (sqrt -1)) (+ (* (/ 4/3 (* (sqrt -1) PI)) (/ (/ 1/2 (sqrt -1)) (sqrt -1))) (* 0 (/ 0 (sqrt -1))))) into (* 2/3 (/ 1 (* (sqrt -1) PI))) * [misc]backup-simplify: Simplify (- (/ (/ 1 (sqrt -6)) (/ 4/3 (* (sqrt -1) PI))) (+ (* (* 3/4 (* (sqrt -1) (* (sqrt -6) PI))) (/ (* 2/3 (/ 1 (* (sqrt -1) PI))) (/ 4/3 (* (sqrt -1) PI)))) (* 0 (/ 0 (/ 4/3 (* (sqrt -1) PI)))))) into (- (* 3/4 (/ (* (sqrt -1) PI) (sqrt -6))) (* 3/8 (* (sqrt -6) (* (sqrt -1) PI)))) * [misc]backup-simplify: Simplify (- (/ (* 1/2 (/ 1 (sqrt -1))) (* 3/4 (* (sqrt -1) (* (sqrt -6) PI)))) (+ (* (/ 4/3 (* (sqrt -6) (* (pow (sqrt -1) 2) PI))) (/ (- (* 3/4 (/ (* (sqrt -1) PI) (sqrt -6))) (* 3/8 (* (sqrt -6) (* (sqrt -1) PI)))) (* 3/4 (* (sqrt -1) (* (sqrt -6) PI))))) (* 0 (/ 0 (* 3/4 (* (sqrt -1) (* (sqrt -6) PI))))))) into (- (+ (* 2/3 (/ 1 (* (sqrt -6) (* (pow (sqrt -1) 2) PI)))) (* 2/3 (/ 1 (* (pow (sqrt -1) 2) (* (sqrt -6) PI))))) (* 4/3 (/ 1 (* (pow (sqrt -1) 2) (* (pow (sqrt -6) 3) PI))))) * [misc]backup-simplify: Simplify (- (+ (* 2/3 (/ 1 (* (sqrt -6) (* (pow (sqrt -1) 2) PI)))) (* 2/3 (/ 1 (* (pow (sqrt -1) 2) (* (sqrt -6) PI))))) (* 4/3 (/ 1 (* (pow (sqrt -1) 2) (* (pow (sqrt -6) 3) PI))))) into (- (+ (* 2/3 (/ 1 (* (sqrt -6) (* (pow (sqrt -1) 2) PI)))) (* 2/3 (/ 1 (* (pow (sqrt -1) 2) (* (sqrt -6) PI))))) (* 4/3 (/ 1 (* (pow (sqrt -1) 2) (* (pow (sqrt -6) 3) PI))))) * [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 (/ (- 0 (+ (* 2 (* 0 (/ 1/2 (sqrt -1)))))) (* 2 (sqrt -1))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt -1)) (/ 0 (sqrt -1))) (* 0 (/ (/ 1/2 (sqrt -1)) (sqrt -1))) (* (* 1/2 (/ 1 (sqrt -1))) (/ 0 (sqrt -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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (/ 1 (sqrt -6)))))) (* 2 (sqrt -6))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) 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 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (/ 1/2 (sqrt -1)))))) (* 2 (sqrt -1))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt -1)) (+ (* (/ 4/3 (* (sqrt -1) PI)) (/ 0 (sqrt -1))) (* 0 (/ (/ 1/2 (sqrt -1)) (sqrt -1))) (* (* 2/3 (/ 1 (* (sqrt -1) PI))) (/ 0 (sqrt -1))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (/ 4/3 (* (sqrt -1) PI))) (+ (* (* 3/4 (* (sqrt -1) (* (sqrt -6) PI))) (/ 0 (/ 4/3 (* (sqrt -1) PI)))) (* 0 (/ (* 2/3 (/ 1 (* (sqrt -1) PI))) (/ 4/3 (* (sqrt -1) PI)))) (* (- (* 3/4 (/ (* (sqrt -1) PI) (sqrt -6))) (* 3/8 (* (sqrt -6) (* (sqrt -1) PI)))) (/ 0 (/ 4/3 (* (sqrt -1) PI)))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* 3/4 (* (sqrt -1) (* (sqrt -6) PI)))) (+ (* (/ 4/3 (* (sqrt -6) (* (pow (sqrt -1) 2) PI))) (/ 0 (* 3/4 (* (sqrt -1) (* (sqrt -6) PI))))) (* 0 (/ (- (* 3/4 (/ (* (sqrt -1) PI) (sqrt -6))) (* 3/8 (* (sqrt -6) (* (sqrt -1) PI)))) (* 3/4 (* (sqrt -1) (* (sqrt -6) PI))))) (* (- (+ (* 2/3 (/ 1 (* (sqrt -6) (* (pow (sqrt -1) 2) PI)))) (* 2/3 (/ 1 (* (pow (sqrt -1) 2) (* (sqrt -6) PI))))) (* 4/3 (/ 1 (* (pow (sqrt -1) 2) (* (pow (sqrt -6) 3) PI))))) (/ 0 (* 3/4 (* (sqrt -1) (* (sqrt -6) PI))))))) 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 (/ (- 0 (pow (/ 1/2 (sqrt -1)) 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt -1))) into (/ -1/8 (pow (sqrt -1) 3)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt -1)) (/ (/ -1/8 (pow (sqrt -1) 3)) (sqrt -1))) (* 0 (/ 0 (sqrt -1))) (* (* 1/2 (/ 1 (sqrt -1))) (/ (/ 1/2 (sqrt -1)) (sqrt -1))) (* 0 (/ 0 (sqrt -1))))) into (+ (* 1/8 (/ 1 (pow (sqrt -1) 5))) (* 1/4 (/ 1 (sqrt -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 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 -6))))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ 1 (sqrt -6)) 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt -6))) into (/ -1/2 (pow (sqrt -6) 3)) * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) 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 (/ (- 0 (pow (/ 1/2 (sqrt -1)) 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt -1))) into (/ -1/8 (pow (sqrt -1) 3)) * [misc]backup-simplify: Simplify (- (/ 0 (sqrt -1)) (+ (* (/ 4/3 (* (sqrt -1) PI)) (/ (/ -1/8 (pow (sqrt -1) 3)) (sqrt -1))) (* 0 (/ 0 (sqrt -1))) (* (* 2/3 (/ 1 (* (sqrt -1) PI))) (/ (/ 1/2 (sqrt -1)) (sqrt -1))) (* 0 (/ 0 (sqrt -1))))) into (+ (* 1/6 (/ 1 (* (pow (sqrt -1) 5) PI))) (* 1/3 (/ 1 (* (sqrt -1) PI)))) * [misc]backup-simplify: Simplify (- (/ (/ -1/2 (pow (sqrt -6) 3)) (/ 4/3 (* (sqrt -1) PI))) (+ (* (* 3/4 (* (sqrt -1) (* (sqrt -6) PI))) (/ (+ (* 1/6 (/ 1 (* (pow (sqrt -1) 5) PI))) (* 1/3 (/ 1 (* (sqrt -1) PI)))) (/ 4/3 (* (sqrt -1) PI)))) (* 0 (/ 0 (/ 4/3 (* (sqrt -1) PI)))) (* (- (* 3/4 (/ (* (sqrt -1) PI) (sqrt -6))) (* 3/8 (* (sqrt -6) (* (sqrt -1) PI)))) (/ (* 2/3 (/ 1 (* (sqrt -1) PI))) (/ 4/3 (* (sqrt -1) PI)))) (* 0 (/ 0 (/ 4/3 (* (sqrt -1) PI)))))) into (- (+ (* 3/32 (/ (* (sqrt -6) PI) (pow (sqrt -1) 3))) (+ (* 3/8 (/ (* (sqrt -1) PI) (pow (sqrt -6) 3))) (* 3/8 (/ (* (sqrt -1) PI) (sqrt -6)))))) * [misc]backup-simplify: Simplify (- (/ (+ (* 1/8 (/ 1 (pow (sqrt -1) 5))) (* 1/4 (/ 1 (sqrt -1)))) (* 3/4 (* (sqrt -1) (* (sqrt -6) PI)))) (+ (* (/ 4/3 (* (sqrt -6) (* (pow (sqrt -1) 2) PI))) (/ (- (+ (* 3/32 (/ (* (sqrt -6) PI) (pow (sqrt -1) 3))) (+ (* 3/8 (/ (* (sqrt -1) PI) (pow (sqrt -6) 3))) (* 3/8 (/ (* (sqrt -1) PI) (sqrt -6)))))) (* 3/4 (* (sqrt -1) (* (sqrt -6) PI))))) (* 0 (/ 0 (* 3/4 (* (sqrt -1) (* (sqrt -6) PI))))) (* (- (+ (* 2/3 (/ 1 (* (sqrt -6) (* (pow (sqrt -1) 2) PI)))) (* 2/3 (/ 1 (* (pow (sqrt -1) 2) (* (sqrt -6) PI))))) (* 4/3 (/ 1 (* (pow (sqrt -1) 2) (* (pow (sqrt -6) 3) PI))))) (/ (- (* 3/4 (/ (* (sqrt -1) PI) (sqrt -6))) (* 3/8 (* (sqrt -6) (* (sqrt -1) PI)))) (* 3/4 (* (sqrt -1) (* (sqrt -6) PI))))) (* 0 (/ 0 (* 3/4 (* (sqrt -1) (* (sqrt -6) PI))))))) into (- (+ (/ 1 (* (pow (sqrt -1) 2) (* (sqrt -6) PI))) (+ (* 4/3 (/ 1 (* (pow (sqrt -6) 5) (* (pow (sqrt -1) 2) PI)))) (+ (* 1/6 (/ 1 (* (sqrt -6) (* (pow (sqrt -1) 6) PI)))) (+ (* 2/3 (/ 1 (* (pow (sqrt -1) 2) (* (pow (sqrt -6) 5) PI)))) (* 1/6 (/ 1 (* (pow (sqrt -1) 6) (* (sqrt -6) PI)))))))) (* 4/3 (/ 1 (* (pow (sqrt -6) 3) (* (pow (sqrt -1) 2) PI))))) * [misc]backup-simplify: Simplify (- (+ (/ 1 (* (pow (sqrt -1) 2) (* (sqrt -6) PI))) (+ (* 4/3 (/ 1 (* (pow (sqrt -6) 5) (* (pow (sqrt -1) 2) PI)))) (+ (* 1/6 (/ 1 (* (sqrt -6) (* (pow (sqrt -1) 6) PI)))) (+ (* 2/3 (/ 1 (* (pow (sqrt -1) 2) (* (pow (sqrt -6) 5) PI)))) (* 1/6 (/ 1 (* (pow (sqrt -1) 6) (* (sqrt -6) PI)))))))) (* 4/3 (/ 1 (* (pow (sqrt -6) 3) (* (pow (sqrt -1) 2) PI))))) into (- (+ (* 2/3 (/ 1 (* (pow (sqrt -1) 2) (* (pow (sqrt -6) 5) PI)))) (+ (/ 1 (* (pow (sqrt -1) 2) (* (sqrt -6) PI))) (+ (* 1/6 (/ 1 (* (sqrt -6) (* (pow (sqrt -1) 6) PI)))) (+ (* 1/6 (/ 1 (* (pow (sqrt -1) 6) (* (sqrt -6) PI)))) (* 4/3 (/ 1 (* (pow (sqrt -6) 5) (* (pow (sqrt -1) 2) PI)))))))) (* 4/3 (/ 1 (* (pow (sqrt -6) 3) (* (pow (sqrt -1) 2) PI))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* 2/3 (/ 1 (* (pow (sqrt -1) 2) (* (pow (sqrt -6) 5) PI)))) (+ (/ 1 (* (pow (sqrt -1) 2) (* (sqrt -6) PI))) (+ (* 1/6 (/ 1 (* (sqrt -6) (* (pow (sqrt -1) 6) PI)))) (+ (* 1/6 (/ 1 (* (pow (sqrt -1) 6) (* (sqrt -6) PI)))) (* 4/3 (/ 1 (* (pow (sqrt -6) 5) (* (pow (sqrt -1) 2) PI)))))))) (* 4/3 (/ 1 (* (pow (sqrt -6) 3) (* (pow (sqrt -1) 2) PI))))) (pow (/ 1 v) 7)) (+ (* (- (+ (* 2/3 (/ 1 (* (sqrt -6) (* (pow (sqrt -1) 2) PI)))) (* 2/3 (/ 1 (* (pow (sqrt -1) 2) (* (sqrt -6) PI))))) (* 4/3 (/ 1 (* (pow (sqrt -1) 2) (* (pow (sqrt -6) 3) PI))))) (pow (/ 1 v) 5)) (* (/ 4/3 (* (sqrt -6) (* (pow (sqrt -1) 2) PI))) (pow (/ 1 v) 3)))) into (- (+ (* 4/3 (/ 1 (* (sqrt -6) (* (pow v 3) (* (pow (sqrt -1) 2) PI))))) (+ (* 2/3 (/ 1 (* (pow (sqrt -1) 2) (* (pow v 5) (* (sqrt -6) PI))))) (+ (/ 1 (* (pow v 7) (* (sqrt -6) (* (pow (sqrt -1) 2) PI)))) (+ (* 2/3 (/ 1 (* (pow v 7) (* (pow (sqrt -6) 5) (* (pow (sqrt -1) 2) PI))))) (+ (* 2/3 (/ 1 (* (sqrt -6) (* (pow v 5) (* (pow (sqrt -1) 2) PI))))) (+ (* 4/3 (/ 1 (* (pow (sqrt -1) 2) (* (pow v 7) (* (pow (sqrt -6) 5) PI))))) (+ (* 1/6 (/ 1 (* (pow (sqrt -1) 6) (* (pow v 7) (* (sqrt -6) PI))))) (* 1/6 (/ 1 (* (pow v 7) (* (sqrt -6) (* (pow (sqrt -1) 6) PI)))))))))))) (+ (* 4/3 (/ 1 (* (pow (sqrt -6) 3) (* (pow v 5) (* (pow (sqrt -1) 2) PI))))) (* 4/3 (/ 1 (* (pow (sqrt -1) 2) (* (pow v 7) (* (pow (sqrt -6) 3) PI))))))) * [misc]approximate: Taking taylor expansion of (/ (/ 1 (sqrt (- 1 (* (/ 1 (- v)) (/ 1 (- v)))))) (/ (sqrt (+ 2 (* (* (/ 1 (- v)) (/ 1 (- v))) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* (/ 1 (- v)) (/ 1 (- v)))))))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (/ (/ 1 (sqrt (- 1 (* (/ 1 (- v)) (/ 1 (- v)))))) (/ (sqrt (+ 2 (* (* (/ 1 (- v)) (/ 1 (- v))) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* (/ 1 (- v)) (/ 1 (- v)))))))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (- 1 (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [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 -1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (sqrt -1) into (sqrt -1) * [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 (* 2 (sqrt -1))) into 0 * [misc]backup-simplify: Simplify (/ 1 (sqrt -1)) into (/ 1 (sqrt -1)) * [misc]taylor: Taking taylor expansion of (/ (sqrt (+ 2 (* (* (/ 1 (- v)) (/ 1 (- v))) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* (/ 1 (- v)) (/ 1 (- v))))))) in v * [misc]taylor: Taking taylor expansion of (sqrt (+ 2 (* (* (/ 1 (- v)) (/ 1 (- v))) -6))) in v * [misc]taylor: Taking taylor expansion of (+ 2 (* (* (/ 1 (- v)) (/ 1 (- v))) -6)) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- v)) (/ 1 (- v))) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 1 -6) into -6 * [misc]backup-simplify: Simplify (+ 0 -6) into -6 * [misc]backup-simplify: Simplify (sqrt -6) into (sqrt -6) * [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 (+ (* 1 0) (* 0 -6)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -6))) into 0 * [misc]taylor: Taking taylor expansion of (/ (/ 4/3 PI) (sqrt (- 1 (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (/ 4/3 PI) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of PI in v * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (/ 4/3 PI) into (/ 4/3 PI) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [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 -1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (sqrt -1) into (sqrt -1) * [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 (* 2 (sqrt -1))) into 0 * [misc]backup-simplify: Simplify (/ (/ 4/3 PI) (sqrt -1)) into (/ 4/3 (* (sqrt -1) PI)) * [misc]backup-simplify: Simplify (/ (sqrt -6) (/ 4/3 (* (sqrt -1) PI))) into (* 3/4 (* (sqrt -1) (* (sqrt -6) PI))) * [misc]backup-simplify: Simplify (/ (/ 1 (sqrt -1)) (* 3/4 (* (sqrt -1) (* (sqrt -6) PI)))) into (/ 4/3 (* (sqrt -6) (* (pow (sqrt -1) 2) PI))) * [misc]taylor: Taking taylor expansion of (/ (/ 1 (sqrt (- 1 (* (/ 1 (- v)) (/ 1 (- v)))))) (/ (sqrt (+ 2 (* (* (/ 1 (- v)) (/ 1 (- v))) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* (/ 1 (- v)) (/ 1 (- v)))))))) in v * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (- 1 (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [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 -1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (sqrt -1) into (sqrt -1) * [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 (* 2 (sqrt -1))) into 0 * [misc]backup-simplify: Simplify (/ 1 (sqrt -1)) into (/ 1 (sqrt -1)) * [misc]taylor: Taking taylor expansion of (/ (sqrt (+ 2 (* (* (/ 1 (- v)) (/ 1 (- v))) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* (/ 1 (- v)) (/ 1 (- v))))))) in v * [misc]taylor: Taking taylor expansion of (sqrt (+ 2 (* (* (/ 1 (- v)) (/ 1 (- v))) -6))) in v * [misc]taylor: Taking taylor expansion of (+ 2 (* (* (/ 1 (- v)) (/ 1 (- v))) -6)) in v * [misc]taylor: Taking taylor expansion of 2 in v * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- v)) (/ 1 (- v))) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 1 -6) into -6 * [misc]backup-simplify: Simplify (+ 0 -6) into -6 * [misc]backup-simplify: Simplify (sqrt -6) into (sqrt -6) * [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 (+ (* 1 0) (* 0 -6)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt -6))) into 0 * [misc]taylor: Taking taylor expansion of (/ (/ 4/3 PI) (sqrt (- 1 (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (/ 4/3 PI) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of PI in v * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (/ 4/3 PI) into (/ 4/3 PI) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [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 -1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (sqrt -1) into (sqrt -1) * [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 (* 2 (sqrt -1))) into 0 * [misc]backup-simplify: Simplify (/ (/ 4/3 PI) (sqrt -1)) into (/ 4/3 (* (sqrt -1) PI)) * [misc]backup-simplify: Simplify (/ (sqrt -6) (/ 4/3 (* (sqrt -1) PI))) into (* 3/4 (* (sqrt -1) (* (sqrt -6) PI))) * [misc]backup-simplify: Simplify (/ (/ 1 (sqrt -1)) (* 3/4 (* (sqrt -1) (* (sqrt -6) PI)))) into (/ 4/3 (* (sqrt -6) (* (pow (sqrt -1) 2) PI))) * [misc]backup-simplify: Simplify (/ 4/3 (* (sqrt -6) (* (pow (sqrt -1) 2) PI))) into (/ 4/3 (* (sqrt -6) (* (pow (sqrt -1) 2) PI))) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt -1)) (/ 0 (sqrt -1))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt -1)) (+ (* (/ 4/3 (* (sqrt -1) PI)) (/ 0 (sqrt -1))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (/ 4/3 (* (sqrt -1) PI))) (+ (* (* 3/4 (* (sqrt -1) (* (sqrt -6) PI))) (/ 0 (/ 4/3 (* (sqrt -1) PI)))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* 3/4 (* (sqrt -1) (* (sqrt -6) PI)))) (+ (* (/ 4/3 (* (sqrt -6) (* (pow (sqrt -1) 2) PI))) (/ 0 (* 3/4 (* (sqrt -1) (* (sqrt -6) PI))))))) 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 (/ (- 1 (pow 0 2) (+)) (* 2 (sqrt -1))) into (/ 1/2 (sqrt -1)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt -1)) (/ (/ 1/2 (sqrt -1)) (sqrt -1))) (* 0 (/ 0 (sqrt -1))))) into (* 1/2 (/ 1 (sqrt -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 (+ (* 1 0) (+ (* 0 0) (* 0 -6))) into 0 * [misc]backup-simplify: Simplify (+ 2 0) into 2 * [misc]backup-simplify: Simplify (/ (- 2 (pow 0 2) (+)) (* 2 (sqrt -6))) into (/ 1 (sqrt -6)) * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)))) 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 (/ (- 1 (pow 0 2) (+)) (* 2 (sqrt -1))) into (/ 1/2 (sqrt -1)) * [misc]backup-simplify: Simplify (- (/ 0 (sqrt -1)) (+ (* (/ 4/3 (* (sqrt -1) PI)) (/ (/ 1/2 (sqrt -1)) (sqrt -1))) (* 0 (/ 0 (sqrt -1))))) into (* 2/3 (/ 1 (* (sqrt -1) PI))) * [misc]backup-simplify: Simplify (- (/ (/ 1 (sqrt -6)) (/ 4/3 (* (sqrt -1) PI))) (+ (* (* 3/4 (* (sqrt -1) (* (sqrt -6) PI))) (/ (* 2/3 (/ 1 (* (sqrt -1) PI))) (/ 4/3 (* (sqrt -1) PI)))) (* 0 (/ 0 (/ 4/3 (* (sqrt -1) PI)))))) into (- (* 3/4 (/ (* (sqrt -1) PI) (sqrt -6))) (* 3/8 (* (sqrt -6) (* (sqrt -1) PI)))) * [misc]backup-simplify: Simplify (- (/ (* 1/2 (/ 1 (sqrt -1))) (* 3/4 (* (sqrt -1) (* (sqrt -6) PI)))) (+ (* (/ 4/3 (* (sqrt -6) (* (pow (sqrt -1) 2) PI))) (/ (- (* 3/4 (/ (* (sqrt -1) PI) (sqrt -6))) (* 3/8 (* (sqrt -6) (* (sqrt -1) PI)))) (* 3/4 (* (sqrt -1) (* (sqrt -6) PI))))) (* 0 (/ 0 (* 3/4 (* (sqrt -1) (* (sqrt -6) PI))))))) into (- (+ (* 2/3 (/ 1 (* (sqrt -6) (* (pow (sqrt -1) 2) PI)))) (* 2/3 (/ 1 (* (pow (sqrt -1) 2) (* (sqrt -6) PI))))) (* 4/3 (/ 1 (* (pow (sqrt -1) 2) (* (pow (sqrt -6) 3) PI))))) * [misc]backup-simplify: Simplify (- (+ (* 2/3 (/ 1 (* (sqrt -6) (* (pow (sqrt -1) 2) PI)))) (* 2/3 (/ 1 (* (pow (sqrt -1) 2) (* (sqrt -6) PI))))) (* 4/3 (/ 1 (* (pow (sqrt -1) 2) (* (pow (sqrt -6) 3) PI))))) into (- (+ (* 2/3 (/ 1 (* (sqrt -6) (* (pow (sqrt -1) 2) PI)))) (* 2/3 (/ 1 (* (pow (sqrt -1) 2) (* (sqrt -6) PI))))) (* 4/3 (/ 1 (* (pow (sqrt -1) 2) (* (pow (sqrt -6) 3) PI))))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]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 (+ (* 2 (* 0 (/ 1/2 (sqrt -1)))))) (* 2 (sqrt -1))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt -1)) (/ 0 (sqrt -1))) (* 0 (/ (/ 1/2 (sqrt -1)) (sqrt -1))) (* (* 1/2 (/ 1 (sqrt -1))) (/ 0 (sqrt -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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (/ 1 (sqrt -6)))))) (* 2 (sqrt -6))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) 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 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (/ 1/2 (sqrt -1)))))) (* 2 (sqrt -1))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt -1)) (+ (* (/ 4/3 (* (sqrt -1) PI)) (/ 0 (sqrt -1))) (* 0 (/ (/ 1/2 (sqrt -1)) (sqrt -1))) (* (* 2/3 (/ 1 (* (sqrt -1) PI))) (/ 0 (sqrt -1))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (/ 4/3 (* (sqrt -1) PI))) (+ (* (* 3/4 (* (sqrt -1) (* (sqrt -6) PI))) (/ 0 (/ 4/3 (* (sqrt -1) PI)))) (* 0 (/ (* 2/3 (/ 1 (* (sqrt -1) PI))) (/ 4/3 (* (sqrt -1) PI)))) (* (- (* 3/4 (/ (* (sqrt -1) PI) (sqrt -6))) (* 3/8 (* (sqrt -6) (* (sqrt -1) PI)))) (/ 0 (/ 4/3 (* (sqrt -1) PI)))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* 3/4 (* (sqrt -1) (* (sqrt -6) PI)))) (+ (* (/ 4/3 (* (sqrt -6) (* (pow (sqrt -1) 2) PI))) (/ 0 (* 3/4 (* (sqrt -1) (* (sqrt -6) PI))))) (* 0 (/ (- (* 3/4 (/ (* (sqrt -1) PI) (sqrt -6))) (* 3/8 (* (sqrt -6) (* (sqrt -1) PI)))) (* 3/4 (* (sqrt -1) (* (sqrt -6) PI))))) (* (- (+ (* 2/3 (/ 1 (* (sqrt -6) (* (pow (sqrt -1) 2) PI)))) (* 2/3 (/ 1 (* (pow (sqrt -1) 2) (* (sqrt -6) PI))))) (* 4/3 (/ 1 (* (pow (sqrt -1) 2) (* (pow (sqrt -6) 3) PI))))) (/ 0 (* 3/4 (* (sqrt -1) (* (sqrt -6) PI))))))) 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 (pow (/ 1/2 (sqrt -1)) 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt -1))) into (/ -1/8 (pow (sqrt -1) 3)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt -1)) (/ (/ -1/8 (pow (sqrt -1) 3)) (sqrt -1))) (* 0 (/ 0 (sqrt -1))) (* (* 1/2 (/ 1 (sqrt -1))) (/ (/ 1/2 (sqrt -1)) (sqrt -1))) (* 0 (/ 0 (sqrt -1))))) into (+ (* 1/8 (/ 1 (pow (sqrt -1) 5))) (* 1/4 (/ 1 (sqrt -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)))) 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 -6))))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ 1 (sqrt -6)) 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt -6))) into (/ -1/2 (pow (sqrt -6) 3)) * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) 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 (pow (/ 1/2 (sqrt -1)) 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt -1))) into (/ -1/8 (pow (sqrt -1) 3)) * [misc]backup-simplify: Simplify (- (/ 0 (sqrt -1)) (+ (* (/ 4/3 (* (sqrt -1) PI)) (/ (/ -1/8 (pow (sqrt -1) 3)) (sqrt -1))) (* 0 (/ 0 (sqrt -1))) (* (* 2/3 (/ 1 (* (sqrt -1) PI))) (/ (/ 1/2 (sqrt -1)) (sqrt -1))) (* 0 (/ 0 (sqrt -1))))) into (+ (* 1/6 (/ 1 (* (pow (sqrt -1) 5) PI))) (* 1/3 (/ 1 (* (sqrt -1) PI)))) * [misc]backup-simplify: Simplify (- (/ (/ -1/2 (pow (sqrt -6) 3)) (/ 4/3 (* (sqrt -1) PI))) (+ (* (* 3/4 (* (sqrt -1) (* (sqrt -6) PI))) (/ (+ (* 1/6 (/ 1 (* (pow (sqrt -1) 5) PI))) (* 1/3 (/ 1 (* (sqrt -1) PI)))) (/ 4/3 (* (sqrt -1) PI)))) (* 0 (/ 0 (/ 4/3 (* (sqrt -1) PI)))) (* (- (* 3/4 (/ (* (sqrt -1) PI) (sqrt -6))) (* 3/8 (* (sqrt -6) (* (sqrt -1) PI)))) (/ (* 2/3 (/ 1 (* (sqrt -1) PI))) (/ 4/3 (* (sqrt -1) PI)))) (* 0 (/ 0 (/ 4/3 (* (sqrt -1) PI)))))) into (- (+ (* 3/32 (/ (* (sqrt -6) PI) (pow (sqrt -1) 3))) (+ (* 3/8 (/ (* (sqrt -1) PI) (pow (sqrt -6) 3))) (* 3/8 (/ (* (sqrt -1) PI) (sqrt -6)))))) * [misc]backup-simplify: Simplify (- (/ (+ (* 1/8 (/ 1 (pow (sqrt -1) 5))) (* 1/4 (/ 1 (sqrt -1)))) (* 3/4 (* (sqrt -1) (* (sqrt -6) PI)))) (+ (* (/ 4/3 (* (sqrt -6) (* (pow (sqrt -1) 2) PI))) (/ (- (+ (* 3/32 (/ (* (sqrt -6) PI) (pow (sqrt -1) 3))) (+ (* 3/8 (/ (* (sqrt -1) PI) (pow (sqrt -6) 3))) (* 3/8 (/ (* (sqrt -1) PI) (sqrt -6)))))) (* 3/4 (* (sqrt -1) (* (sqrt -6) PI))))) (* 0 (/ 0 (* 3/4 (* (sqrt -1) (* (sqrt -6) PI))))) (* (- (+ (* 2/3 (/ 1 (* (sqrt -6) (* (pow (sqrt -1) 2) PI)))) (* 2/3 (/ 1 (* (pow (sqrt -1) 2) (* (sqrt -6) PI))))) (* 4/3 (/ 1 (* (pow (sqrt -1) 2) (* (pow (sqrt -6) 3) PI))))) (/ (- (* 3/4 (/ (* (sqrt -1) PI) (sqrt -6))) (* 3/8 (* (sqrt -6) (* (sqrt -1) PI)))) (* 3/4 (* (sqrt -1) (* (sqrt -6) PI))))) (* 0 (/ 0 (* 3/4 (* (sqrt -1) (* (sqrt -6) PI))))))) into (- (+ (/ 1 (* (pow (sqrt -1) 2) (* (sqrt -6) PI))) (+ (* 4/3 (/ 1 (* (pow (sqrt -6) 5) (* (pow (sqrt -1) 2) PI)))) (+ (* 1/6 (/ 1 (* (sqrt -6) (* (pow (sqrt -1) 6) PI)))) (+ (* 2/3 (/ 1 (* (pow (sqrt -1) 2) (* (pow (sqrt -6) 5) PI)))) (* 1/6 (/ 1 (* (pow (sqrt -1) 6) (* (sqrt -6) PI)))))))) (* 4/3 (/ 1 (* (pow (sqrt -6) 3) (* (pow (sqrt -1) 2) PI))))) * [misc]backup-simplify: Simplify (- (+ (/ 1 (* (pow (sqrt -1) 2) (* (sqrt -6) PI))) (+ (* 4/3 (/ 1 (* (pow (sqrt -6) 5) (* (pow (sqrt -1) 2) PI)))) (+ (* 1/6 (/ 1 (* (sqrt -6) (* (pow (sqrt -1) 6) PI)))) (+ (* 2/3 (/ 1 (* (pow (sqrt -1) 2) (* (pow (sqrt -6) 5) PI)))) (* 1/6 (/ 1 (* (pow (sqrt -1) 6) (* (sqrt -6) PI)))))))) (* 4/3 (/ 1 (* (pow (sqrt -6) 3) (* (pow (sqrt -1) 2) PI))))) into (- (+ (* 2/3 (/ 1 (* (pow (sqrt -1) 2) (* (pow (sqrt -6) 5) PI)))) (+ (/ 1 (* (pow (sqrt -1) 2) (* (sqrt -6) PI))) (+ (* 1/6 (/ 1 (* (sqrt -6) (* (pow (sqrt -1) 6) PI)))) (+ (* 1/6 (/ 1 (* (pow (sqrt -1) 6) (* (sqrt -6) PI)))) (* 4/3 (/ 1 (* (pow (sqrt -6) 5) (* (pow (sqrt -1) 2) PI)))))))) (* 4/3 (/ 1 (* (pow (sqrt -6) 3) (* (pow (sqrt -1) 2) PI))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* 2/3 (/ 1 (* (pow (sqrt -1) 2) (* (pow (sqrt -6) 5) PI)))) (+ (/ 1 (* (pow (sqrt -1) 2) (* (sqrt -6) PI))) (+ (* 1/6 (/ 1 (* (sqrt -6) (* (pow (sqrt -1) 6) PI)))) (+ (* 1/6 (/ 1 (* (pow (sqrt -1) 6) (* (sqrt -6) PI)))) (* 4/3 (/ 1 (* (pow (sqrt -6) 5) (* (pow (sqrt -1) 2) PI)))))))) (* 4/3 (/ 1 (* (pow (sqrt -6) 3) (* (pow (sqrt -1) 2) PI))))) (pow (/ 1 (- v)) 7)) (+ (* (- (+ (* 2/3 (/ 1 (* (sqrt -6) (* (pow (sqrt -1) 2) PI)))) (* 2/3 (/ 1 (* (pow (sqrt -1) 2) (* (sqrt -6) PI))))) (* 4/3 (/ 1 (* (pow (sqrt -1) 2) (* (pow (sqrt -6) 3) PI))))) (pow (/ 1 (- v)) 5)) (* (/ 4/3 (* (sqrt -6) (* (pow (sqrt -1) 2) PI))) (pow (/ 1 (- v)) 3)))) into (- (+ (* 4/3 (/ 1 (* (pow (sqrt -6) 3) (* (pow v 7) (* (pow (sqrt -1) 2) PI))))) (* 4/3 (/ 1 (* (pow (sqrt -1) 2) (* (pow v 5) (* (pow (sqrt -6) 3) PI)))))) (+ (* 4/3 (/ 1 (* (sqrt -6) (* (pow v 3) (* (pow (sqrt -1) 2) PI))))) (+ (* 2/3 (/ 1 (* (sqrt -6) (* (pow v 5) (* (pow (sqrt -1) 2) PI))))) (+ (/ 1 (* (pow (sqrt -1) 2) (* (pow v 7) (* (sqrt -6) PI)))) (+ (* 1/6 (/ 1 (* (sqrt -6) (* (pow v 7) (* (pow (sqrt -1) 6) PI))))) (+ (* 4/3 (/ 1 (* (pow (sqrt -6) 5) (* (pow v 7) (* (pow (sqrt -1) 2) PI))))) (+ (* 2/3 (/ 1 (* (pow (sqrt -1) 2) (* (pow v 7) (* (pow (sqrt -6) 5) PI))))) (+ (* 2/3 (/ 1 (* (pow (sqrt -1) 2) (* (pow v 5) (* (sqrt -6) PI))))) (* 1/6 (/ 1 (* (pow (sqrt -1) 6) (* (pow v 7) (* (sqrt -6) PI))))))))))))) * * * * [misc]progress: [ 3 / 4 ] generating series at (2 2 1 1 2) * [misc]approximate: Taking taylor expansion of (* (* v v) -6) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (* v v) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]taylor: Taking taylor expansion of (* (* v v) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]backup-simplify: Simplify (* 0 0) into 0 * [misc]backup-simplify: Simplify (* 0 -6) 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 -6)) 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 (+ (* 0 0) (+ (* 0 0) (* 1 -6))) into -6 * [misc]backup-simplify: Simplify -6 into -6 * [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 -6)))) 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 0) (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 -6))))) 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 (+ (* 0 0) (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6)))))) 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 0) (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6))))))) 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 (+ (* 0 0) (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6)))))))) 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 (+ (* 0 0) (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6))))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* -6 (pow v 2)) into (* -6 (pow v 2)) * [misc]approximate: Taking taylor expansion of (* (* (/ 1 v) (/ 1 v)) -6) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (* (/ 1 v) (/ 1 v)) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]taylor: Taking taylor expansion of (* (* (/ 1 v) (/ 1 v)) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (* 1 -6) into -6 * [misc]backup-simplify: Simplify -6 into -6 * [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 (+ (* 1 0) (* 0 -6)) 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 (+ (* 1 0) (+ (* 0 0) (* 0 -6))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6)))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6))))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6)))))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* -6 (pow (/ 1 (/ 1 v)) 2)) into (* -6 (pow v 2)) * [misc]approximate: Taking taylor expansion of (* (* (/ 1 (- v)) (/ 1 (- v))) -6) in (v) around 0 * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- v)) (/ 1 (- v))) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- v)) (/ 1 (- v))) -6) 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 -6 in v * [misc]backup-simplify: Simplify -6 into -6 * [misc]backup-simplify: Simplify (* -1 -1) into 1 * [misc]backup-simplify: Simplify (* 1 -6) into -6 * [misc]backup-simplify: Simplify -6 into -6 * [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 (+ (* 1 0) (* 0 -6)) 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 (+ (* 1 0) (+ (* 0 0) (* 0 -6))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6)))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6))))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6)))))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -6))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* -6 (pow (/ 1 (/ 1 (- v))) 2)) into (* -6 (pow v 2)) * * * * [misc]progress: [ 4 / 4 ] generating series at (2 2 2) * [misc]approximate: Taking taylor expansion of (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) in v * [misc]taylor: Taking taylor expansion of (/ 4/3 PI) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of PI in v * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (/ 4/3 PI) into (/ 4/3 PI) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* v v))) in v * [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 (* 0 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 (- 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 (/ (/ 4/3 PI) 1) into (/ 4/3 PI) * [misc]taylor: Taking taylor expansion of (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) in v * [misc]taylor: Taking taylor expansion of (/ 4/3 PI) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of PI in v * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (/ 4/3 PI) into (/ 4/3 PI) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* v v))) in v * [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 (* 0 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 (- 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 (/ (/ 4/3 PI) 1) into (/ 4/3 PI) * [misc]backup-simplify: Simplify (/ 4/3 PI) into (/ 4/3 PI) * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (/ 4/3 PI) (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)))) 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 (/ (- -1 (pow 0 2) (+)) (* 2 1)) into -1/2 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (/ 4/3 PI) (/ -1/2 1)) (* 0 (/ 0 1)))) into (* 2/3 (/ 1 PI)) * [misc]backup-simplify: Simplify (* 2/3 (/ 1 PI)) into (/ 2/3 PI) * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) 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 (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 -1/2)))) (* 2 1)) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (/ 4/3 PI) (/ 0 1)) (* 0 (/ -1/2 1)) (* (* 2/3 (/ 1 PI)) (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) 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 (pow -1/2 2) (+ (* 2 (* 0 0)))) (* 2 1)) into -1/8 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (/ 4/3 PI) (/ -1/8 1)) (* 0 (/ 0 1)) (* (* 2/3 (/ 1 PI)) (/ -1/2 1)) (* 0 (/ 0 1)))) into (* 1/2 (/ 1 PI)) * [misc]backup-simplify: Simplify (* 1/2 (/ 1 PI)) into (/ 1/2 PI) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 PI) (pow v 4)) (+ (* (/ 2/3 PI) (pow v 2)) (/ 4/3 PI))) into (+ (* 2/3 (/ (pow v 2) PI)) (+ (* 4/3 (/ 1 PI)) (* 1/2 (/ (pow v 4) PI)))) * [misc]approximate: Taking taylor expansion of (/ (/ 4/3 PI) (sqrt (- 1 (* (/ 1 v) (/ 1 v))))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (/ (/ 4/3 PI) (sqrt (- 1 (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (/ 4/3 PI) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of PI in v * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (/ 4/3 PI) into (/ 4/3 PI) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* (/ 1 v) (/ 1 v)))) in v * [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 1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (sqrt -1) into (sqrt -1) * [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 (* 2 (sqrt -1))) into 0 * [misc]backup-simplify: Simplify (/ (/ 4/3 PI) (sqrt -1)) into (/ 4/3 (* (sqrt -1) PI)) * [misc]taylor: Taking taylor expansion of (/ (/ 4/3 PI) (sqrt (- 1 (* (/ 1 v) (/ 1 v))))) in v * [misc]taylor: Taking taylor expansion of (/ 4/3 PI) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of PI in v * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (/ 4/3 PI) into (/ 4/3 PI) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* (/ 1 v) (/ 1 v)))) in v * [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 1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (sqrt -1) into (sqrt -1) * [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 (* 2 (sqrt -1))) into 0 * [misc]backup-simplify: Simplify (/ (/ 4/3 PI) (sqrt -1)) into (/ 4/3 (* (sqrt -1) PI)) * [misc]backup-simplify: Simplify (/ 4/3 (* (sqrt -1) PI)) into (/ 4/3 (* (sqrt -1) PI)) * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt -1)) (+ (* (/ 4/3 (* (sqrt -1) PI)) (/ 0 (sqrt -1))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)))) 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 (pow 0 2) (+)) (* 2 (sqrt -1))) into (/ 1/2 (sqrt -1)) * [misc]backup-simplify: Simplify (- (/ 0 (sqrt -1)) (+ (* (/ 4/3 (* (sqrt -1) PI)) (/ (/ 1/2 (sqrt -1)) (sqrt -1))) (* 0 (/ 0 (sqrt -1))))) into (* 2/3 (/ 1 (* (sqrt -1) PI))) * [misc]backup-simplify: Simplify (* 2/3 (/ 1 (* (sqrt -1) PI))) into (/ 2/3 (* (sqrt -1) PI)) * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) 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 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (/ 1/2 (sqrt -1)))))) (* 2 (sqrt -1))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt -1)) (+ (* (/ 4/3 (* (sqrt -1) PI)) (/ 0 (sqrt -1))) (* 0 (/ (/ 1/2 (sqrt -1)) (sqrt -1))) (* (* 2/3 (/ 1 (* (sqrt -1) PI))) (/ 0 (sqrt -1))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) 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 (/ (- 0 (pow (/ 1/2 (sqrt -1)) 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt -1))) into (/ -1/8 (pow (sqrt -1) 3)) * [misc]backup-simplify: Simplify (- (/ 0 (sqrt -1)) (+ (* (/ 4/3 (* (sqrt -1) PI)) (/ (/ -1/8 (pow (sqrt -1) 3)) (sqrt -1))) (* 0 (/ 0 (sqrt -1))) (* (* 2/3 (/ 1 (* (sqrt -1) PI))) (/ (/ 1/2 (sqrt -1)) (sqrt -1))) (* 0 (/ 0 (sqrt -1))))) into (+ (* 1/6 (/ 1 (* (pow (sqrt -1) 5) PI))) (* 1/3 (/ 1 (* (sqrt -1) PI)))) * [misc]backup-simplify: Simplify (+ (* 1/6 (/ 1 (* (pow (sqrt -1) 5) PI))) (* 1/3 (/ 1 (* (sqrt -1) PI)))) into (+ (* 1/6 (/ 1 (* (pow (sqrt -1) 5) PI))) (* 1/3 (/ 1 (* (sqrt -1) PI)))) * [misc]backup-simplify: Simplify (+ (* (+ (* 1/6 (/ 1 (* (pow (sqrt -1) 5) PI))) (* 1/3 (/ 1 (* (sqrt -1) PI)))) (pow (/ 1 v) 5)) (+ (* (/ 2/3 (* (sqrt -1) PI)) (pow (/ 1 v) 3)) (* (/ 4/3 (* (sqrt -1) PI)) (/ 1 v)))) into (+ (* 4/3 (/ 1 (* v (* (sqrt -1) PI)))) (+ (* 1/3 (/ 1 (* (pow v 5) (* (sqrt -1) PI)))) (+ (* 2/3 (/ 1 (* (pow v 3) (* (sqrt -1) PI)))) (* 1/6 (/ 1 (* (pow v 5) (* (pow (sqrt -1) 5) PI))))))) * [misc]approximate: Taking taylor expansion of (/ (/ 4/3 PI) (sqrt (- 1 (* (/ 1 (- v)) (/ 1 (- v)))))) in (v) around 0 * [misc]taylor: Taking taylor expansion of (/ (/ 4/3 PI) (sqrt (- 1 (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (/ 4/3 PI) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of PI in v * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (/ 4/3 PI) into (/ 4/3 PI) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [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 -1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (sqrt -1) into (sqrt -1) * [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 (* 2 (sqrt -1))) into 0 * [misc]backup-simplify: Simplify (/ (/ 4/3 PI) (sqrt -1)) into (/ 4/3 (* (sqrt -1) PI)) * [misc]taylor: Taking taylor expansion of (/ (/ 4/3 PI) (sqrt (- 1 (* (/ 1 (- v)) (/ 1 (- v)))))) in v * [misc]taylor: Taking taylor expansion of (/ 4/3 PI) in v * [misc]taylor: Taking taylor expansion of 4/3 in v * [misc]backup-simplify: Simplify 4/3 into 4/3 * [misc]taylor: Taking taylor expansion of PI in v * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (/ 4/3 PI) into (/ 4/3 PI) * [misc]taylor: Taking taylor expansion of (sqrt (- 1 (* (/ 1 (- v)) (/ 1 (- v))))) in v * [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 -1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (sqrt -1) into (sqrt -1) * [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 (* 2 (sqrt -1))) into 0 * [misc]backup-simplify: Simplify (/ (/ 4/3 PI) (sqrt -1)) into (/ 4/3 (* (sqrt -1) PI)) * [misc]backup-simplify: Simplify (/ 4/3 (* (sqrt -1) PI)) into (/ 4/3 (* (sqrt -1) PI)) * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt -1)) (+ (* (/ 4/3 (* (sqrt -1) PI)) (/ 0 (sqrt -1))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)))) 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 (/ (- 1 (pow 0 2) (+)) (* 2 (sqrt -1))) into (/ 1/2 (sqrt -1)) * [misc]backup-simplify: Simplify (- (/ 0 (sqrt -1)) (+ (* (/ 4/3 (* (sqrt -1) PI)) (/ (/ 1/2 (sqrt -1)) (sqrt -1))) (* 0 (/ 0 (sqrt -1))))) into (* 2/3 (/ 1 (* (sqrt -1) PI))) * [misc]backup-simplify: Simplify (* 2/3 (/ 1 (* (sqrt -1) PI))) into (/ 2/3 (* (sqrt -1) PI)) * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) 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 0) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 (/ 1/2 (sqrt -1)))))) (* 2 (sqrt -1))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt -1)) (+ (* (/ 4/3 (* (sqrt -1) PI)) (/ 0 (sqrt -1))) (* 0 (/ (/ 1/2 (sqrt -1)) (sqrt -1))) (* (* 2/3 (/ 1 (* (sqrt -1) PI))) (/ 0 (sqrt -1))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 4/3 PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) 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 (pow (/ 1/2 (sqrt -1)) 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt -1))) into (/ -1/8 (pow (sqrt -1) 3)) * [misc]backup-simplify: Simplify (- (/ 0 (sqrt -1)) (+ (* (/ 4/3 (* (sqrt -1) PI)) (/ (/ -1/8 (pow (sqrt -1) 3)) (sqrt -1))) (* 0 (/ 0 (sqrt -1))) (* (* 2/3 (/ 1 (* (sqrt -1) PI))) (/ (/ 1/2 (sqrt -1)) (sqrt -1))) (* 0 (/ 0 (sqrt -1))))) into (+ (* 1/6 (/ 1 (* (pow (sqrt -1) 5) PI))) (* 1/3 (/ 1 (* (sqrt -1) PI)))) * [misc]backup-simplify: Simplify (+ (* 1/6 (/ 1 (* (pow (sqrt -1) 5) PI))) (* 1/3 (/ 1 (* (sqrt -1) PI)))) into (+ (* 1/6 (/ 1 (* (pow (sqrt -1) 5) PI))) (* 1/3 (/ 1 (* (sqrt -1) PI)))) * [misc]backup-simplify: Simplify (+ (* (+ (* 1/6 (/ 1 (* (pow (sqrt -1) 5) PI))) (* 1/3 (/ 1 (* (sqrt -1) PI)))) (pow (/ 1 (- v)) 5)) (+ (* (/ 2/3 (* (sqrt -1) PI)) (pow (/ 1 (- v)) 3)) (* (/ 4/3 (* (sqrt -1) PI)) (/ 1 (- v))))) into (- (+ (* 4/3 (/ 1 (* v (* (sqrt -1) PI)))) (+ (* 1/3 (/ 1 (* (pow v 5) (* (sqrt -1) PI)))) (+ (* 2/3 (/ 1 (* (pow v 3) (* (sqrt -1) PI)))) (* 1/6 (/ 1 (* (pow v 5) (* (pow (sqrt -1) 5) PI)))))))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 2 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 3 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 4 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 5 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 6 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 7 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 8 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 9 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 10 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 11 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 12 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (log (sqrt (- 1 (* v v))))) (- (log (sqrt (+ 2 (* (* v v) -6)))) (- (log (/ 4/3 PI)) (log (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (189 enodes) * [exit]simplify: Simplified to (- (- (- (log (sqrt (- 1 (* v v))))) (- (log (sqrt (- 1 (* v v)))) (log (/ 4/3 PI)))) (log (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (exp (- (- (- (log (sqrt (- 1 (* v v))))) (- (log (sqrt (- 1 (* v v)))) (log (/ 4/3 PI)))) (log (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 13 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (log (sqrt (- 1 (* v v))))) (- (log (sqrt (+ 2 (* (* v v) -6)))) (log (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (114 enodes) * * [misc]simplify: iters left: 2 (295 enodes) * [exit]simplify: Simplified to (- (log (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (+ (log (sqrt (- 1 (* v v)))) (log (sqrt (+ (* (* -6 v) v) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (exp (- (log (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (+ (log (sqrt (- 1 (* v v)))) (log (sqrt (+ (* (* -6 v) v) 2))))))) * * * * [misc]progress: [ 14 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (log (sqrt (- 1 (* v v))))) (log (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (112 enodes) * * [misc]simplify: iters left: 2 (209 enodes) * [exit]simplify: Simplified to (- (log (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (log (* (sqrt (+ (* (* v v) -6) 2)) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (exp (- (log (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (log (* (sqrt (+ (* (* v v) -6) 2)) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 15 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (/ 1 (sqrt (- 1 (* v v))))) (- (log (sqrt (+ 2 (* (* v v) -6)))) (- (log (/ 4/3 PI)) (log (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (211 enodes) * [exit]simplify: Simplified to (- (- (log (/ 4/3 PI)) (+ (log (sqrt (- 1 (* v v)))) (log (sqrt (- 1 (* v v)))))) (log (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (exp (- (- (log (/ 4/3 PI)) (+ (log (sqrt (- 1 (* v v)))) (log (sqrt (- 1 (* v v)))))) (log (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 16 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (/ 1 (sqrt (- 1 (* v v))))) (- (log (sqrt (+ 2 (* (* v v) -6)))) (log (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (128 enodes) * * [misc]simplify: iters left: 2 (387 enodes) * [exit]simplify: Simplified to (- (log (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (+ (log (sqrt (+ (* (* -6 v) v) 2))) (log (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (exp (- (log (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (+ (log (sqrt (+ (* (* -6 v) v) 2))) (log (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 17 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (/ 1 (sqrt (- 1 (* v v))))) (log (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (242 enodes) * [exit]simplify: Simplified to (- (log (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (log (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (exp (- (log (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (log (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 18 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 19 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 20 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (sqrt (- 1 (* v v))))) (/ (* (* (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 2 (* (* v v) -6)))) (/ (* (* (/ 4/3 PI) (/ 4/3 PI)) (/ 4/3 PI)) (* (* (sqrt (- 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (64 enodes) * * [misc]simplify: iters left: 4 (249 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 (- 1 (* v v))) (sqrt (- 1 (* v v)))) (/ (+ (* (* v -6) v) 2) (/ (/ (/ 16/9 PI) PI) (- 1 (* v v))))) (/ (sqrt (+ (* (* v -6) v) 2)) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (cbrt (/ (/ (/ (/ 1 (- 1 (* v v))) (sqrt (- 1 (* v v)))) (/ (+ (* (* v -6) v) 2) (/ (/ (/ 16/9 PI) PI) (- 1 (* v v))))) (/ (sqrt (+ (* (* v -6) v) 2)) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 21 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (sqrt (- 1 (* v v))))) (/ (* (* (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 2 (* (* v v) -6)))) (* (* (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (59 enodes) * * [misc]simplify: iters left: 4 (210 enodes) * [exit]simplify: Simplified to (* (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (sqrt (- 1 (* v v)))) (* (+ (* v (* v -6)) 2) (sqrt (- 1 (* v v))))) (/ (* (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* v (* v -6)) 2)) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (cbrt (* (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (sqrt (- 1 (* v v)))) (* (+ (* v (* v -6)) 2) (sqrt (- 1 (* v v))))) (/ (* (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* v (* v -6)) 2)) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 22 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (sqrt (- 1 (* v v))))) (* (* (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (54 enodes) * * [misc]simplify: iters left: 4 (170 enodes) * [exit]simplify: Simplified to (pow (/ (* (/ 1 (sqrt (- 1 (* v v)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (+ (* v (* v -6)) 2))) 3) * [misc]simplify: Simplified (2 1) to (λ (v) (cbrt (pow (/ (* (/ 1 (sqrt (- 1 (* v v)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (+ (* v (* v -6)) 2))) 3))) * * * * [misc]progress: [ 23 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 24 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 25 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 26 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 27 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (78 enodes) * * [misc]simplify: iters left: 2 (100 enodes) * * [misc]simplify: iters left: 1 (106 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ (* v (* v -6)) 2))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ (* v (* v -6)) 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ (* v (* v -6)) 2))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ (* v (* v -6)) 2)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (83 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ (* (* -6 v) v) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ (* (* -6 v) v) 2))))))) * * * * [misc]progress: [ 28 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (83 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ (* v (* v -6)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ (* v (* v -6)) 2))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (83 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ (* (* -6 v) v) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ (* (* -6 v) v) 2))))))) * * * * [misc]progress: [ 29 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (153 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * * [misc]simplify: iters left: 1 (392 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 30 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (159 enodes) * * [misc]simplify: iters left: 1 (188 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 31 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (111 enodes) * * [misc]simplify: iters left: 3 (342 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 32 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (233 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (fabs (cbrt (- 1 (* v v)))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (fabs (cbrt (- 1 (* v v)))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (fabs (cbrt (- 1 (* v v)))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ (* (* v v) -6) 2))))))) * * * * [misc]progress: [ 33 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (230 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (/ (/ (sqrt (sqrt (- 1 (* v v)))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (/ (/ (sqrt (sqrt (- 1 (* v v)))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 34 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (241 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ (* (* v -6) v) 2))) (cbrt (/ 4/3 PI)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ (* (* v -6) v) 2))) (cbrt (/ 4/3 PI))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ (* (* v -6) v) 2))) (cbrt (/ 4/3 PI)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ (* (* v -6) v) 2))) (cbrt (/ 4/3 PI))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ (* (* v -6) v) 2))) (cbrt (/ 4/3 PI)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ (* (* v -6) v) 2))) (cbrt (/ 4/3 PI))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 35 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (230 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (/ (/ (sqrt (sqrt (- 1 (* v v)))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (/ (/ (sqrt (sqrt (- 1 (* v v)))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 36 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (85 enodes) * * [misc]simplify: iters left: 3 (241 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 4/3 PI)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 4/3 PI))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 4/3 PI)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 4/3 PI))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 4/3 PI)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 4/3 PI))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 37 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (202 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (cbrt (sqrt (- 1 (* v v))))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (cbrt (sqrt (- 1 (* v v))))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (* (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 38 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (331 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (* (/ (cbrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (* (/ (cbrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (* (/ (cbrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (+ (* (* v v) -6) 2))))))) * * * * [misc]progress: [ 39 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (152 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) (/ (sqrt (sqrt (- 1 (* v v)))) (sqrt (/ 4/3 PI)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) (/ (sqrt (sqrt (- 1 (* v v)))) (sqrt (/ 4/3 PI)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 40 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (154 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 4/3 PI)) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (sqrt (/ 4/3 PI)) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ (* v (* -6 v)) 2))) (sqrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (sqrt (/ 4/3 PI)) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ (* v (* -6 v)) 2))) (sqrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 41 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (152 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) (/ (sqrt (sqrt (- 1 (* v v)))) (sqrt (/ 4/3 PI)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) (/ (sqrt (sqrt (- 1 (* v v)))) (sqrt (/ 4/3 PI)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 42 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (497 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (sqrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (sqrt (/ 4/3 PI))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ (* v (* -6 v)) 2))) (sqrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (sqrt (/ 4/3 PI))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ (* v (* -6 v)) 2))) (sqrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 43 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (192 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) (cbrt (sqrt (- 1 (* v v))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) (cbrt (sqrt (- 1 (* v v))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (* (/ (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) (cbrt (sqrt (- 1 (* v v))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) (cbrt (sqrt (- 1 (* v v)))))) (* (/ (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 44 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * * [misc]simplify: iters left: 2 (467 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (fabs (cbrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (264 enodes) * [exit]simplify: Simplified to (/ (* (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (fabs (cbrt (- 1 (* v v))))) (/ (* (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 45 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (474 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2))))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2))))) (sqrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (* (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2))))) (sqrt (sqrt (- 1 (* v v))))) (* (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 46 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (94 enodes) * * [misc]simplify: iters left: 2 (239 enodes) * * [misc]simplify: iters left: 1 (439 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 47 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (474 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2))))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2))))) (sqrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (* (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2))))) (sqrt (sqrt (- 1 (* v v))))) (* (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 48 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 1))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 49 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (79 enodes) * * [misc]simplify: iters left: 3 (199 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) 4/3)) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) 4/3)) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* (* -6 v) v) 2))) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* (* -6 v) v) 2))) PI)))) * * * * [misc]progress: [ 50 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (152 enodes) * * [misc]simplify: iters left: 2 (330 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) (/ (fabs (cbrt (- 1 (* v v)))) 4/3)) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) (/ (fabs (cbrt (- 1 (* v v)))) 4/3)) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) PI) (* (sqrt (cbrt (- 1 (* v v)))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) (/ (fabs (cbrt (- 1 (* v v)))) 4/3)) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) PI) (* (sqrt (cbrt (- 1 (* v v)))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))))) * * * * [misc]progress: [ 51 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (149 enodes) * * [misc]simplify: iters left: 2 (327 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (* (/ (cbrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (* (/ (cbrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* (* -6 v) v) 2))) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* (* -6 v) v) 2))) PI)))) * * * * [misc]progress: [ 52 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (112 enodes) * * [misc]simplify: iters left: 2 (321 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2))))) 4/3) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2))))) 4/3) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (119 enodes) * * [misc]simplify: iters left: 2 (276 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (* PI (cbrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2))))) 4/3) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (* PI (cbrt (sqrt (+ (* v (* -6 v)) 2))))))) * * * * [misc]progress: [ 53 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (149 enodes) * * [misc]simplify: iters left: 2 (327 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (* (/ (cbrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (* (/ (cbrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* (* -6 v) v) 2))) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* (* -6 v) v) 2))) PI)))) * * * * [misc]progress: [ 54 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 1))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (144 enodes) * * [misc]simplify: iters left: 1 (186 enodes) * [exit]simplify: Simplified to (* 4/3 (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* 4/3 (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (119 enodes) * * [misc]simplify: iters left: 2 (276 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (* PI (cbrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* 4/3 (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (* PI (cbrt (sqrt (+ (* v (* -6 v)) 2))))))) * * * * [misc]progress: [ 55 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) 1)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (272 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 56 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (149 enodes) * * [misc]simplify: iters left: 2 (327 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (* (/ (cbrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (* (/ (cbrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (107 enodes) * * [misc]simplify: iters left: 1 (153 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 PI))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 57 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (53 enodes) * * [misc]simplify: iters left: 4 (113 enodes) * * [misc]simplify: iters left: 3 (286 enodes) * [exit]simplify: Simplified to (* (/ (/ 4/3 PI) (sqrt (- 1 (* (pow v 3) (pow v 3))))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ 4/3 PI) (sqrt (- 1 (* (pow v 3) (pow v 3))))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (111 enodes) * * [misc]simplify: iters left: 3 (187 enodes) * * [misc]simplify: iters left: 2 (298 enodes) * * [misc]simplify: iters left: 1 (427 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ (pow v 4) (+ (* v v) 1))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) (/ (* (sqrt (+ (pow v 4) (+ (* v v) 1))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 58 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (252 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (/ (/ (sqrt (- 1 (pow v 4))) (/ 4/3 PI)) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (/ (/ (sqrt (- 1 (pow v 4))) (/ 4/3 PI)) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (* v v))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (/ (/ (sqrt (- 1 (pow v 4))) (/ 4/3 PI)) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) (/ (* (sqrt (+ 1 (* v v))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 59 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (87 enodes) * * [misc]simplify: iters left: 2 (126 enodes) * * [misc]simplify: iters left: 1 (157 enodes) * [exit]simplify: Simplified to (/ (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) (fabs (cbrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) (fabs (cbrt (+ (* (* v -6) v) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) (fabs (cbrt (+ (* (* v -6) v) 2)))) (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 60 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (84 enodes) * [exit]simplify: Simplified to (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* v -6)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* v -6)) 2))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* v -6)) 2))))) (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 61 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (223 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (fabs (cbrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (fabs (cbrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (fabs (cbrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 62 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (74 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (294 enodes) * [exit]simplify: Simplified to (* (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v -6) v) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v -6) v) 2))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v -6) v) 2))))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (+ (* (* v v) -6) 2))))))) * * * * [misc]progress: [ 63 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (292 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v)))))) (/ (fabs (cbrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v)))))) (/ (fabs (cbrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v)))))) (/ (fabs (cbrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (* (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 64 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * * [misc]simplify: iters left: 2 (472 enodes) * [exit]simplify: Simplified to (* (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* v -6)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* v -6)) 2))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ (* v (* -6 v)) 2))) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* v -6)) 2))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ (* v (* -6 v)) 2))) (cbrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 65 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (292 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v)))))) (/ (fabs (cbrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v)))))) (/ (fabs (cbrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v)))))) (/ (fabs (cbrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (* (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 66 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (166 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v -6) v) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v -6) v) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ (* v (* -6 v)) 2))) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v -6) v) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ (* v (* -6 v)) 2))) (cbrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 67 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (280 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (+ (* v (* v -6)) 2)))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (+ (* v (* v -6)) 2)))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (+ (* v (* v -6)) 2)))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))))) (/ (* (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 68 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (164 enodes) * * [misc]simplify: iters left: 1 (234 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (+ (* (* v v) -6) 2))))))) * * * * [misc]progress: [ 69 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (161 enodes) * * [misc]simplify: iters left: 1 (231 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (fabs (cbrt (+ (* (* v -6) v) 2))) (/ (sqrt (sqrt (- 1 (* v v)))) (sqrt (/ 4/3 PI))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (fabs (cbrt (+ (* (* v -6) v) 2))) (/ (sqrt (sqrt (- 1 (* v v)))) (sqrt (/ 4/3 PI))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (fabs (cbrt (+ (* (* v -6) v) 2))) (/ (sqrt (sqrt (- 1 (* v v)))) (sqrt (/ 4/3 PI))))) (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 70 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (102 enodes) * * [misc]simplify: iters left: 2 (207 enodes) * * [misc]simplify: iters left: 1 (288 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v -6) v) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v -6) v) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ 4/3 PI)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ (* v (* -6 v)) 2))) (sqrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v -6) v) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ 4/3 PI)))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ (* v (* -6 v)) 2))) (sqrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 71 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (161 enodes) * * [misc]simplify: iters left: 1 (231 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (fabs (cbrt (+ (* (* v -6) v) 2))) (/ (sqrt (sqrt (- 1 (* v v)))) (sqrt (/ 4/3 PI))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (fabs (cbrt (+ (* (* v -6) v) 2))) (/ (sqrt (sqrt (- 1 (* v v)))) (sqrt (/ 4/3 PI))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (fabs (cbrt (+ (* (* v -6) v) 2))) (/ (sqrt (sqrt (- 1 (* v v)))) (sqrt (/ 4/3 PI))))) (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 72 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (113 enodes) * * [misc]simplify: iters left: 2 (280 enodes) * * [misc]simplify: iters left: 1 (412 enodes) * [exit]simplify: Simplified to (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ 4/3 PI))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* v -6)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ 4/3 PI))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* v -6)) 2))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ (* v (* -6 v)) 2))) (sqrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ 4/3 PI))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* v -6)) 2))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ (* v (* -6 v)) 2))) (sqrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 73 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (136 enodes) * * [misc]simplify: iters left: 2 (340 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (* (/ (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* -6 v)) 2)))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2))))) (* (/ (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* -6 v)) 2)))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 74 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (195 enodes) * * [misc]simplify: iters left: 1 (305 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* v -6)) 2)))) (/ (fabs (cbrt (- 1 (* v v)))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* v -6)) 2)))) (/ (fabs (cbrt (- 1 (* v v)))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (264 enodes) * [exit]simplify: Simplified to (/ (* (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* v -6)) 2)))) (/ (fabs (cbrt (- 1 (* v v)))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (* (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 75 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (102 enodes) * * [misc]simplify: iters left: 2 (201 enodes) * * [misc]simplify: iters left: 1 (342 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* v -6)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* v -6)) 2))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (* (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* -6 v)) 2)))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* v -6)) 2))))) (* (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* -6 v)) 2)))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 76 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (105 enodes) * * [misc]simplify: iters left: 1 (166 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (fabs (cbrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (fabs (cbrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (fabs (cbrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 77 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (102 enodes) * * [misc]simplify: iters left: 2 (201 enodes) * * [misc]simplify: iters left: 1 (342 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* v -6)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* v -6)) 2))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (* (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* -6 v)) 2)))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* v -6)) 2))))) (* (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* -6 v)) 2)))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 78 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 1))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (61 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (fabs (cbrt (+ (* (* v -6) v) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (fabs (cbrt (+ (* (* v -6) v) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (fabs (cbrt (+ (* (* v -6) v) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 79 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (134 enodes) * * [misc]simplify: iters left: 2 (278 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v)))))) (/ 4/3 (fabs (cbrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v)))))) (/ 4/3 (fabs (cbrt (+ (* (* v v) -6) 2))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (cbrt (+ (* (* -6 v) v) 2))) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v)))))) (/ 4/3 (fabs (cbrt (+ (* (* v v) -6) 2))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (cbrt (+ (* (* -6 v) v) 2))) PI)))) * * * * [misc]progress: [ 80 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (161 enodes) * * [misc]simplify: iters left: 1 (233 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (fabs (cbrt (+ (* (* v -6) v) 2))) (/ (fabs (cbrt (- 1 (* v v)))) 4/3))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (fabs (cbrt (+ (* (* v -6) v) 2))) (/ (fabs (cbrt (- 1 (* v v)))) 4/3))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) PI) (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (cbrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (fabs (cbrt (+ (* (* v -6) v) 2))) (/ (fabs (cbrt (- 1 (* v v)))) 4/3))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) PI) (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (cbrt (+ (* v (* -6 v)) 2))))))) * * * * [misc]progress: [ 81 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (158 enodes) * * [misc]simplify: iters left: 1 (228 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (fabs (cbrt (+ (* (* v v) -6) 2))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (fabs (cbrt (+ (* (* v v) -6) 2))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (cbrt (+ (* (* -6 v) v) 2))) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (fabs (cbrt (+ (* (* v v) -6) 2))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (cbrt (+ (* (* -6 v) v) 2))) PI)))) * * * * [misc]progress: [ 82 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (162 enodes) * * [misc]simplify: iters left: 1 (229 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (fabs (cbrt (+ (* (* v v) -6) 2))) 4/3)) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (fabs (cbrt (+ (* (* v v) -6) 2))) 4/3)) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (119 enodes) * * [misc]simplify: iters left: 2 (276 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (* PI (sqrt (cbrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (fabs (cbrt (+ (* (* v v) -6) 2))) 4/3)) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (* PI (sqrt (cbrt (+ (* v (* -6 v)) 2))))))) * * * * [misc]progress: [ 83 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (158 enodes) * * [misc]simplify: iters left: 1 (228 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (fabs (cbrt (+ (* (* v v) -6) 2))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (fabs (cbrt (+ (* (* v v) -6) 2))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (cbrt (+ (* (* -6 v) v) 2))) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (fabs (cbrt (+ (* (* v v) -6) 2))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (cbrt (+ (* (* -6 v) v) 2))) PI)))) * * * * [misc]progress: [ 84 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 1))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (84 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* v -6)) 2)))) (* 4/3 (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* v -6)) 2)))) (* 4/3 (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (119 enodes) * * [misc]simplify: iters left: 2 (276 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (* PI (sqrt (cbrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* v -6)) 2)))) (* 4/3 (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (* PI (sqrt (cbrt (+ (* v (* -6 v)) 2))))))) * * * * [misc]progress: [ 85 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) 1)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (82 enodes) * * [misc]simplify: iters left: 1 (86 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* v -6)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* v -6)) 2))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* v -6)) 2))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 86 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (158 enodes) * * [misc]simplify: iters left: 1 (228 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (fabs (cbrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (fabs (cbrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (107 enodes) * * [misc]simplify: iters left: 1 (153 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (fabs (cbrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 87 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (100 enodes) * * [misc]simplify: iters left: 3 (219 enodes) * * [misc]simplify: iters left: 2 (418 enodes) * [exit]simplify: Simplified to (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (111 enodes) * * [misc]simplify: iters left: 3 (187 enodes) * * [misc]simplify: iters left: 2 (298 enodes) * * [misc]simplify: iters left: 1 (427 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ (pow v 4) (+ (* v v) 1))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (* (sqrt (+ (pow v 4) (+ (* v v) 1))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 88 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (185 enodes) * * [misc]simplify: iters left: 2 (385 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (- 1 (pow v 4))) (/ 4/3 PI))) (/ (fabs (cbrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (- 1 (pow v 4))) (/ 4/3 PI))) (/ (fabs (cbrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (* v v))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (- 1 (pow v 4))) (/ 4/3 PI))) (/ (fabs (cbrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (* (sqrt (+ 1 (* v v))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 89 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (85 enodes) * * [misc]simplify: iters left: 2 (124 enodes) * * [misc]simplify: iters left: 1 (157 enodes) * [exit]simplify: Simplified to (/ (* (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 90 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (82 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 91 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (219 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (/ (cbrt (sqrt (- 1 (* v v)))) (cbrt (/ 4/3 PI))) (/ (cbrt (sqrt (- 1 (* v v)))) (cbrt (/ 4/3 PI))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (/ (cbrt (sqrt (- 1 (* v v)))) (cbrt (/ 4/3 PI))) (/ (cbrt (sqrt (- 1 (* v v)))) (cbrt (/ 4/3 PI))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 92 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (292 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (+ (* (* v v) -6) 2))))))) * * * * [misc]progress: [ 93 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (289 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ (* v (* v -6)) 2))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ (* v (* v -6)) 2))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 94 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (114 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * [exit]simplify: Simplified to (* (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 95 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (289 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ (* v (* v -6)) 2))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ (* v (* v -6)) 2))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 96 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (166 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI)))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI)))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI)))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 97 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (135 enodes) * * [misc]simplify: iters left: 2 (280 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ (* v (* v -6)) 2))) (sqrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ (* v (* v -6)) 2))) (sqrt (/ 4/3 PI)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (* (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 98 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (102 enodes) * * [misc]simplify: iters left: 2 (162 enodes) * * [misc]simplify: iters left: 1 (232 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ (* (* v v) -6) 2))))))) * * * * [misc]progress: [ 99 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (99 enodes) * * [misc]simplify: iters left: 2 (159 enodes) * * [misc]simplify: iters left: 1 (229 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 100 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (100 enodes) * * [misc]simplify: iters left: 2 (204 enodes) * * [misc]simplify: iters left: 1 (334 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (sqrt (/ 4/3 PI)) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (sqrt (/ 4/3 PI)) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) (sqrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (sqrt (/ 4/3 PI)) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) (sqrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 101 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (99 enodes) * * [misc]simplify: iters left: 2 (159 enodes) * * [misc]simplify: iters left: 1 (229 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 102 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (113 enodes) * * [misc]simplify: iters left: 2 (287 enodes) * * [misc]simplify: iters left: 1 (455 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (/ 4/3 PI)) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (sqrt (/ 4/3 PI)) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) (sqrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (sqrt (/ 4/3 PI)) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) (sqrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 103 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (343 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (* (/ (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2))))) (* (/ (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 104 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (212 enodes) * * [misc]simplify: iters left: 1 (324 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (fabs (cbrt (- 1 (* v v)))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (fabs (cbrt (- 1 (* v v)))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (264 enodes) * [exit]simplify: Simplified to (/ (* (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (fabs (cbrt (- 1 (* v v)))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (* (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 105 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (228 enodes) * * [misc]simplify: iters left: 1 (408 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* v -6)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* v -6)) 2))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (* (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* v -6)) 2))))) (* (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 106 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (101 enodes) * * [misc]simplify: iters left: 1 (165 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 107 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (228 enodes) * * [misc]simplify: iters left: 1 (408 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* v -6)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* v -6)) 2))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (* (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* v -6)) 2))))) (* (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 108 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 1))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (72 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 109 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (132 enodes) * * [misc]simplify: iters left: 2 (278 enodes) * [exit]simplify: Simplified to (* (/ 4/3 (sqrt (sqrt (+ (* v (* v -6)) 2)))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ 4/3 (sqrt (sqrt (+ (* v (* v -6)) 2)))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (sqrt (+ (* (* -6 v) v) 2))) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (sqrt (+ (* (* -6 v) v) 2))) PI)))) * * * * [misc]progress: [ 110 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (99 enodes) * * [misc]simplify: iters left: 2 (159 enodes) * * [misc]simplify: iters left: 1 (229 enodes) * [exit]simplify: Simplified to (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) PI) (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) PI) (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* -6 v)) 2))))))) * * * * [misc]progress: [ 111 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (96 enodes) * * [misc]simplify: iters left: 2 (156 enodes) * * [misc]simplify: iters left: 1 (226 enodes) * [exit]simplify: Simplified to (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (sqrt (+ (* (* -6 v) v) 2))) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (sqrt (+ (* (* -6 v) v) 2))) PI)))) * * * * [misc]progress: [ 112 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (69 enodes) * * [misc]simplify: iters left: 2 (154 enodes) * * [misc]simplify: iters left: 1 (244 enodes) * [exit]simplify: Simplified to (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) 4/3) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) 4/3) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (119 enodes) * * [misc]simplify: iters left: 2 (276 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (* PI (sqrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) 4/3) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (* PI (sqrt (sqrt (+ (* v (* -6 v)) 2))))))) * * * * [misc]progress: [ 113 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (96 enodes) * * [misc]simplify: iters left: 2 (156 enodes) * * [misc]simplify: iters left: 1 (226 enodes) * [exit]simplify: Simplified to (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (sqrt (+ (* (* -6 v) v) 2))) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (sqrt (+ (* (* -6 v) v) 2))) PI)))) * * * * [misc]progress: [ 114 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 1))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (72 enodes) * * [misc]simplify: iters left: 1 (82 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ (* v (* v -6)) 2))) 4/3)) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ (* v (* v -6)) 2))) 4/3)) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (119 enodes) * * [misc]simplify: iters left: 2 (276 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (* PI (sqrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ (* v (* v -6)) 2))) 4/3)) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (* PI (sqrt (sqrt (+ (* v (* -6 v)) 2))))))) * * * * [misc]progress: [ 115 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) 1)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (61 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 116 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (96 enodes) * * [misc]simplify: iters left: 2 (156 enodes) * * [misc]simplify: iters left: 1 (226 enodes) * [exit]simplify: Simplified to (* (/ (/ 4/3 PI) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ 4/3 PI) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (107 enodes) * * [misc]simplify: iters left: 1 (153 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 117 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (98 enodes) * * [misc]simplify: iters left: 3 (217 enodes) * * [misc]simplify: iters left: 2 (418 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (- 1 (pow v 6))) (/ 4/3 PI)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (- 1 (pow v 6))) (/ 4/3 PI)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (111 enodes) * * [misc]simplify: iters left: 3 (187 enodes) * * [misc]simplify: iters left: 2 (298 enodes) * * [misc]simplify: iters left: 1 (427 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ (pow v 4) (+ (* v v) 1))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (- 1 (pow v 6))) (/ 4/3 PI)))) (/ (* (sqrt (+ (pow v 4) (+ (* v v) 1))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 118 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (183 enodes) * * [misc]simplify: iters left: 2 (388 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (sqrt (sqrt (+ (* v (* v -6)) 2))) (/ (sqrt (- 1 (pow v 4))) (/ 4/3 PI)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (sqrt (sqrt (+ (* v (* v -6)) 2))) (/ (sqrt (- 1 (pow v 4))) (/ 4/3 PI)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (* v v))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (sqrt (sqrt (+ (* v (* v -6)) 2))) (/ (sqrt (- 1 (pow v 4))) (/ 4/3 PI)))) (/ (* (sqrt (+ 1 (* v v))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 119 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt 1) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (75 enodes) * * [misc]simplify: iters left: 2 (160 enodes) * * [misc]simplify: iters left: 1 (444 enodes) * [exit]simplify: Simplified to (* (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 120 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt 1) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (82 enodes) * * [misc]simplify: iters left: 1 (143 enodes) * [exit]simplify: Simplified to (* (* (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 121 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (184 enodes) * [exit]simplify: Simplified to (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (cbrt (sqrt (- 1 (* v v)))))) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (cbrt (sqrt (- 1 (* v v)))))) (cbrt (/ 4/3 PI))))) * * * * [misc]progress: [ 122 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (132 enodes) * * [misc]simplify: iters left: 2 (357 enodes) * [exit]simplify: Simplified to (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI))) (* (/ (cbrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI))) (* (/ (cbrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))) (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI))) (* (/ (cbrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))) (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 123 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (sqrt (- 1 (* v v)))))) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (sqrt (- 1 (* v v)))))) (cbrt (/ 4/3 PI))))) * * * * [misc]progress: [ 124 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (116 enodes) * * [misc]simplify: iters left: 2 (291 enodes) * * [misc]simplify: iters left: 1 (428 enodes) * [exit]simplify: Simplified to (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (94 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI)))) (* (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 125 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (sqrt (- 1 (* v v)))))) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (sqrt (- 1 (* v v)))))) (cbrt (/ 4/3 PI))))) * * * * [misc]progress: [ 126 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (171 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (cbrt (/ 4/3 PI)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (cbrt (/ 4/3 PI))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (cbrt (/ 4/3 PI)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (cbrt (/ 4/3 PI))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (94 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (cbrt (/ 4/3 PI)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (cbrt (/ 4/3 PI))))) (* (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 127 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (121 enodes) * * [misc]simplify: iters left: 2 (418 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ 4/3 PI)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (cbrt (sqrt (- 1 (* v v)))))) (sqrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ 4/3 PI)))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (cbrt (sqrt (- 1 (* v v)))))) (sqrt (/ 4/3 PI))))) * * * * [misc]progress: [ 128 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (- 1 (* v v))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (- 1 (* v v))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ 4/3 PI)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))) (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (- 1 (* v v))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ 4/3 PI)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))) (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 129 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (325 enodes) * [exit]simplify: Simplified to (* (* (sqrt (/ 4/3 PI)) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (sqrt (/ 4/3 PI)) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (sqrt (- 1 (* v v)))))) (sqrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (sqrt (/ 4/3 PI)) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v)))))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (sqrt (- 1 (* v v)))))) (sqrt (/ 4/3 PI))))) * * * * [misc]progress: [ 130 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (95 enodes) * * [misc]simplify: iters left: 1 (121 enodes) * [exit]simplify: Simplified to (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (/ 4/3 PI))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (94 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (/ 4/3 PI))) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 131 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (325 enodes) * [exit]simplify: Simplified to (* (* (sqrt (/ 4/3 PI)) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (sqrt (/ 4/3 PI)) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (sqrt (- 1 (* v v)))))) (sqrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (sqrt (/ 4/3 PI)) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v)))))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (sqrt (- 1 (* v v)))))) (sqrt (/ 4/3 PI))))) * * * * [misc]progress: [ 132 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (73 enodes) * * [misc]simplify: iters left: 2 (100 enodes) * * [misc]simplify: iters left: 1 (119 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ 4/3 PI)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (94 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ 4/3 PI)))) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 133 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt 1) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (96 enodes) * * [misc]simplify: iters left: 2 (265 enodes) * * [misc]simplify: iters left: 1 (479 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (264 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v)))))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 134 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt 1) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (167 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (fabs (cbrt (- 1 (* v v)))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (fabs (cbrt (- 1 (* v v)))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* PI (sqrt (cbrt (- 1 (* v v)))))) (/ 4/3 (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (fabs (cbrt (- 1 (* v v)))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* PI (sqrt (cbrt (- 1 (* v v)))))) (/ 4/3 (sqrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 135 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt 1) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (73 enodes) * * [misc]simplify: iters left: 2 (178 enodes) * * [misc]simplify: iters left: 1 (239 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (264 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (- 1 (* v v))))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 136 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt 1) (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * * [misc]simplify: iters left: 2 (45 enodes) * * [misc]simplify: iters left: 1 (56 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (103 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 137 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt 1) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (73 enodes) * * [misc]simplify: iters left: 2 (178 enodes) * * [misc]simplify: iters left: 1 (239 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (264 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (- 1 (* v v))))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 138 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt 1) (/ 1 1))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (54 enodes) * * [misc]simplify: iters left: 1 (60 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (103 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 139 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt 1) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (452 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* 3/4 (cbrt (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* 3/4 (cbrt (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (120 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* 3/4 (cbrt (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) PI)))) * * * * [misc]progress: [ 140 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt 1) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (95 enodes) * * [misc]simplify: iters left: 2 (209 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* 3/4 (fabs (cbrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* 3/4 (fabs (cbrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (281 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2)))) PI) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* 3/4 (fabs (cbrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2)))) PI))) * * * * [misc]progress: [ 141 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt 1) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (100 enodes) * * [misc]simplify: iters left: 2 (314 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* 4/3 (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* 4/3 (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (120 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* 4/3 (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) PI)))) * * * * [misc]progress: [ 142 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt 1) (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (253 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* 4/3 (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* 4/3 (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (118 enodes) * * [misc]simplify: iters left: 2 (284 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (* PI (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* 4/3 (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (* PI (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 143 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt 1) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (100 enodes) * * [misc]simplify: iters left: 2 (314 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* 4/3 (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* 4/3 (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (120 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* 4/3 (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) PI)))) * * * * [misc]progress: [ 144 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt 1) (/ 4/3 1))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (223 enodes) * [exit]simplify: Simplified to (* (* 4/3 (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* 4/3 (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (118 enodes) * * [misc]simplify: iters left: 2 (284 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (* PI (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* 4/3 (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (* PI (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 145 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt 1) 1)) * * [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 (32 enodes) * * [misc]simplify: iters left: 2 (37 enodes) * * [misc]simplify: iters left: 1 (48 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (103 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 146 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt 1) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (202 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* PI 3/4)) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* PI 3/4)) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (69 enodes) * * [misc]simplify: iters left: 2 (105 enodes) * * [misc]simplify: iters left: 1 (140 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (- 1 (* v v))) (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* PI 3/4)) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (- 1 (* v v))) (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 147 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt 1) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (224 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (- 1 (* (pow v 3) (pow v 3)))) 4/3)) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) PI)) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (- 1 (* (pow v 3) (pow v 3)))) 4/3)) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) PI)) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (165 enodes) * * [misc]simplify: iters left: 2 (276 enodes) * * [misc]simplify: iters left: 1 (348 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* (* -6 v) v) 2)) (sqrt (+ (* v v) (+ 1 (pow v 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (- 1 (* (pow v 3) (pow v 3)))) 4/3)) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) PI)) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* (* -6 v) v) 2)) (sqrt (+ (* v v) (+ 1 (pow v 4)))))))) * * * * [misc]progress: [ 148 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt 1) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (188 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* 3/4 PI)) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* 3/4 PI)) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 4))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 1 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* v (* -6 v)) 2)) (sqrt (+ 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* 3/4 PI)) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 4))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* v (* -6 v)) 2)) (sqrt (+ 1 (* v v))))))) * * * * [misc]progress: [ 149 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (85 enodes) * * [misc]simplify: iters left: 2 (124 enodes) * * [misc]simplify: iters left: 1 (157 enodes) * [exit]simplify: Simplified to (/ (* (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 150 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (82 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 151 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (219 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (/ (cbrt (sqrt (- 1 (* v v)))) (cbrt (/ 4/3 PI))) (/ (cbrt (sqrt (- 1 (* v v)))) (cbrt (/ 4/3 PI))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (/ (cbrt (sqrt (- 1 (* v v)))) (cbrt (/ 4/3 PI))) (/ (cbrt (sqrt (- 1 (* v v)))) (cbrt (/ 4/3 PI))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 152 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (292 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (+ (* (* v v) -6) 2))))))) * * * * [misc]progress: [ 153 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (289 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ (* v (* v -6)) 2))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ (* v (* v -6)) 2))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 154 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (114 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * [exit]simplify: Simplified to (* (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 155 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (289 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ (* v (* v -6)) 2))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ (* v (* v -6)) 2))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 156 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (166 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI)))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI)))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI)))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 157 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (135 enodes) * * [misc]simplify: iters left: 2 (280 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ (* v (* v -6)) 2))) (sqrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ (* v (* v -6)) 2))) (sqrt (/ 4/3 PI)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (* (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 158 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (102 enodes) * * [misc]simplify: iters left: 2 (162 enodes) * * [misc]simplify: iters left: 1 (232 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ (* (* v v) -6) 2))))))) * * * * [misc]progress: [ 159 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (99 enodes) * * [misc]simplify: iters left: 2 (159 enodes) * * [misc]simplify: iters left: 1 (229 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 160 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (100 enodes) * * [misc]simplify: iters left: 2 (204 enodes) * * [misc]simplify: iters left: 1 (334 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (sqrt (/ 4/3 PI)) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (sqrt (/ 4/3 PI)) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) (sqrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (sqrt (/ 4/3 PI)) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) (sqrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 161 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (99 enodes) * * [misc]simplify: iters left: 2 (159 enodes) * * [misc]simplify: iters left: 1 (229 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 162 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (113 enodes) * * [misc]simplify: iters left: 2 (287 enodes) * * [misc]simplify: iters left: 1 (455 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (/ 4/3 PI)) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (sqrt (/ 4/3 PI)) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) (sqrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (sqrt (/ 4/3 PI)) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) (sqrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 163 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (343 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (* (/ (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2))))) (* (/ (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 164 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (212 enodes) * * [misc]simplify: iters left: 1 (324 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (fabs (cbrt (- 1 (* v v)))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (fabs (cbrt (- 1 (* v v)))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (264 enodes) * [exit]simplify: Simplified to (/ (* (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (fabs (cbrt (- 1 (* v v)))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (* (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 165 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (228 enodes) * * [misc]simplify: iters left: 1 (408 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* v -6)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* v -6)) 2))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (* (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* v -6)) 2))))) (* (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 166 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (101 enodes) * * [misc]simplify: iters left: 1 (165 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 167 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (228 enodes) * * [misc]simplify: iters left: 1 (408 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* v -6)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* v -6)) 2))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (* (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* v -6)) 2))))) (* (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 168 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 1))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (72 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 169 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (132 enodes) * * [misc]simplify: iters left: 2 (278 enodes) * [exit]simplify: Simplified to (* (/ 4/3 (sqrt (sqrt (+ (* v (* v -6)) 2)))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ 4/3 (sqrt (sqrt (+ (* v (* v -6)) 2)))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (sqrt (+ (* (* -6 v) v) 2))) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (sqrt (+ (* (* -6 v) v) 2))) PI)))) * * * * [misc]progress: [ 170 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (99 enodes) * * [misc]simplify: iters left: 2 (159 enodes) * * [misc]simplify: iters left: 1 (229 enodes) * [exit]simplify: Simplified to (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) PI) (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) PI) (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* -6 v)) 2))))))) * * * * [misc]progress: [ 171 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (96 enodes) * * [misc]simplify: iters left: 2 (156 enodes) * * [misc]simplify: iters left: 1 (226 enodes) * [exit]simplify: Simplified to (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (sqrt (+ (* (* -6 v) v) 2))) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (sqrt (+ (* (* -6 v) v) 2))) PI)))) * * * * [misc]progress: [ 172 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (69 enodes) * * [misc]simplify: iters left: 2 (154 enodes) * * [misc]simplify: iters left: 1 (244 enodes) * [exit]simplify: Simplified to (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) 4/3) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) 4/3) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (119 enodes) * * [misc]simplify: iters left: 2 (276 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (* PI (sqrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) 4/3) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (* PI (sqrt (sqrt (+ (* v (* -6 v)) 2))))))) * * * * [misc]progress: [ 173 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (96 enodes) * * [misc]simplify: iters left: 2 (156 enodes) * * [misc]simplify: iters left: 1 (226 enodes) * [exit]simplify: Simplified to (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (sqrt (+ (* (* -6 v) v) 2))) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (sqrt (+ (* (* -6 v) v) 2))) PI)))) * * * * [misc]progress: [ 174 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 1))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (72 enodes) * * [misc]simplify: iters left: 1 (82 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ (* v (* v -6)) 2))) 4/3)) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ (* v (* v -6)) 2))) 4/3)) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (119 enodes) * * [misc]simplify: iters left: 2 (276 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (* PI (sqrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ (* v (* v -6)) 2))) 4/3)) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (* PI (sqrt (sqrt (+ (* v (* -6 v)) 2))))))) * * * * [misc]progress: [ 175 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) 1)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (61 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 176 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (96 enodes) * * [misc]simplify: iters left: 2 (156 enodes) * * [misc]simplify: iters left: 1 (226 enodes) * [exit]simplify: Simplified to (* (/ (/ 4/3 PI) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ 4/3 PI) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (107 enodes) * * [misc]simplify: iters left: 1 (153 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 177 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (98 enodes) * * [misc]simplify: iters left: 3 (217 enodes) * * [misc]simplify: iters left: 2 (418 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (- 1 (pow v 6))) (/ 4/3 PI)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (- 1 (pow v 6))) (/ 4/3 PI)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (111 enodes) * * [misc]simplify: iters left: 3 (187 enodes) * * [misc]simplify: iters left: 2 (298 enodes) * * [misc]simplify: iters left: 1 (427 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ (pow v 4) (+ (* v v) 1))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (- 1 (pow v 6))) (/ 4/3 PI)))) (/ (* (sqrt (+ (pow v 4) (+ (* v v) 1))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 178 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (183 enodes) * * [misc]simplify: iters left: 2 (388 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (sqrt (sqrt (+ (* v (* v -6)) 2))) (/ (sqrt (- 1 (pow v 4))) (/ 4/3 PI)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (sqrt (sqrt (+ (* v (* v -6)) 2))) (/ (sqrt (- 1 (pow v 4))) (/ 4/3 PI)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (* v v))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (sqrt (sqrt (+ (* v (* v -6)) 2))) (/ (sqrt (- 1 (pow v 4))) (/ 4/3 PI)))) (/ (* (sqrt (+ 1 (* v v))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 179 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 1 (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (73 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * [exit]simplify: Simplified to (* (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 180 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 1 (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (102 enodes) * * [misc]simplify: iters left: 1 (221 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (* (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 181 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (77 enodes) * * [misc]simplify: iters left: 3 (189 enodes) * [exit]simplify: Simplified to (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (cbrt (sqrt (- 1 (* v v)))))) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (cbrt (sqrt (- 1 (* v v)))))) (cbrt (/ 4/3 PI))))) * * * * [misc]progress: [ 182 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (125 enodes) * * [misc]simplify: iters left: 2 (402 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (- 1 (* v v))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (- 1 (* v v))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))) (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (- 1 (* v v))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))) (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 183 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (136 enodes) * * [misc]simplify: iters left: 2 (487 enodes) * [exit]simplify: Simplified to (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (sqrt (- 1 (* v v)))))) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (sqrt (- 1 (* v v)))))) (cbrt (/ 4/3 PI))))) * * * * [misc]progress: [ 184 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (288 enodes) * * [misc]simplify: iters left: 1 (429 enodes) * [exit]simplify: Simplified to (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (94 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI)))) (* (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 185 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (136 enodes) * * [misc]simplify: iters left: 2 (487 enodes) * [exit]simplify: Simplified to (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (sqrt (- 1 (* v v)))))) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (sqrt (- 1 (* v v)))))) (cbrt (/ 4/3 PI))))) * * * * [misc]progress: [ 186 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (82 enodes) * * [misc]simplify: iters left: 2 (177 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (94 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI)))) (* (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 187 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 1 (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (394 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (cbrt (sqrt (- 1 (* v v)))))) (sqrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (cbrt (sqrt (- 1 (* v v)))))) (sqrt (/ 4/3 PI))))) * * * * [misc]progress: [ 188 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 1 (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (244 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))) (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))) (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 189 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 1 (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (263 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ 4/3 PI))) (/ (sqrt (sqrt (- 1 (* v v)))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ 4/3 PI))) (/ (sqrt (sqrt (- 1 (* v v)))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (sqrt (- 1 (* v v)))))) (sqrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ 4/3 PI))) (/ (sqrt (sqrt (- 1 (* v v)))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (sqrt (- 1 (* v v)))))) (sqrt (/ 4/3 PI))))) * * * * [misc]progress: [ 190 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 1 (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (71 enodes) * * [misc]simplify: iters left: 2 (103 enodes) * * [misc]simplify: iters left: 1 (120 enodes) * [exit]simplify: Simplified to (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (/ 4/3 PI))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (94 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (/ 4/3 PI))) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 191 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 1 (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (263 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ 4/3 PI))) (/ (sqrt (sqrt (- 1 (* v v)))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ 4/3 PI))) (/ (sqrt (sqrt (- 1 (* v v)))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (sqrt (- 1 (* v v)))))) (sqrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ 4/3 PI))) (/ (sqrt (sqrt (- 1 (* v v)))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (sqrt (- 1 (* v v)))))) (sqrt (/ 4/3 PI))))) * * * * [misc]progress: [ 192 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 1 (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (100 enodes) * * [misc]simplify: iters left: 2 (176 enodes) * * [misc]simplify: iters left: 1 (356 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 4/3 PI)) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (sqrt (/ 4/3 PI)) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (94 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (sqrt (/ 4/3 PI)) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 193 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 1 (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (304 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (264 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v)))))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 194 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 1 (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (91 enodes) * * [misc]simplify: iters left: 1 (149 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* PI (sqrt (cbrt (- 1 (* v v)))))) (/ 4/3 (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* PI (sqrt (cbrt (- 1 (* v v)))))) (/ 4/3 (sqrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 195 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 1 (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (85 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (313 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (264 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v)))))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 196 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 1 (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * * [misc]simplify: iters left: 2 (45 enodes) * * [misc]simplify: iters left: 1 (56 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (103 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 197 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 1 (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (85 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (313 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (264 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v)))))) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 198 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 1 (/ 1 1))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * * [misc]simplify: iters left: 2 (31 enodes) * * [misc]simplify: iters left: 1 (38 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (103 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 199 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 1 (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (115 enodes) * * [misc]simplify: iters left: 2 (313 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) 3/4)) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) 3/4)) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (120 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) 3/4)) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) PI)))) * * * * [misc]progress: [ 200 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 1 (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (225 enodes) * [exit]simplify: Simplified to (* (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (281 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2)))) PI) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2)))) PI))) * * * * [misc]progress: [ 201 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 1 (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (85 enodes) * * [misc]simplify: iters left: 2 (168 enodes) * [exit]simplify: Simplified to (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (120 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v)))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) PI)))) * * * * [misc]progress: [ 202 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 1 (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (168 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) 3/4) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) 3/4) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (118 enodes) * * [misc]simplify: iters left: 2 (284 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (* PI (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) 3/4) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (* PI (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 203 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 1 (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (85 enodes) * * [misc]simplify: iters left: 2 (168 enodes) * [exit]simplify: Simplified to (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (120 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v)))))) (/ (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) PI)))) * * * * [misc]progress: [ 204 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 1 (/ 4/3 1))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * * [misc]simplify: iters left: 2 (57 enodes) * * [misc]simplify: iters left: 1 (143 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) 3/4)) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) 3/4)) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (118 enodes) * * [misc]simplify: iters left: 2 (284 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (* PI (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) 3/4)) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (* PI (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 205 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 1 1)) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * * [misc]simplify: iters left: 2 (30 enodes) * * [misc]simplify: iters left: 1 (37 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (103 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 206 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 1 (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (85 enodes) * * [misc]simplify: iters left: 2 (168 enodes) * * [misc]simplify: iters left: 1 (453 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* 3/4 PI) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* 3/4 PI) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (69 enodes) * * [misc]simplify: iters left: 2 (105 enodes) * * [misc]simplify: iters left: 1 (140 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (- 1 (* v v))) (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* 3/4 PI) (cbrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (- 1 (* v v))) (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 207 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 1 (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (218 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (- 1 (pow (* v v) 3))) (/ 4/3 PI))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (- 1 (pow (* v v) 3))) (/ 4/3 PI))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (165 enodes) * * [misc]simplify: iters left: 2 (276 enodes) * * [misc]simplify: iters left: 1 (348 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* (* -6 v) v) 2)) (sqrt (+ (* v v) (+ 1 (pow v 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (- 1 (pow (* v v) 3))) (/ 4/3 PI))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* (* -6 v) v) 2)) (sqrt (+ (* v v) (+ 1 (pow v 4)))))))) * * * * [misc]progress: [ 208 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ 1 (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (77 enodes) * * [misc]simplify: iters left: 3 (182 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (* 3/4 PI) (sqrt (- 1 (pow v 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (* 3/4 PI) (sqrt (- 1 (pow v 4))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 1 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* v (* -6 v)) 2)) (sqrt (+ 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (* 3/4 PI) (sqrt (- 1 (pow v 4))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* v (* -6 v)) 2)) (sqrt (+ 1 (* v v))))))) * * * * [misc]progress: [ 209 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) 1) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (65 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (103 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 210 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* v -6) v) 2)))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (208 enodes) * * [misc]simplify: iters left: 1 (343 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (+ 2 (* (* v v) -6)))) (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 211 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (95 enodes) * * [misc]simplify: iters left: 2 (155 enodes) * * [misc]simplify: iters left: 1 (225 enodes) * [exit]simplify: Simplified to (* (* (/ 4/3 (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) PI)) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (/ 4/3 (sqrt (+ (* v (* v -6)) 2))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) PI)) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ 4/3 PI))) (/ (cbrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 212 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (80 enodes) * * [misc]simplify: iters left: 1 (86 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (* (sqrt (+ (* v (* -6 v)) 2)) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI))))) (cbrt (* (sqrt (+ (* v (* -6 v)) 2)) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (* (sqrt (+ (* v (* -6 v)) 2)) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI))))) (cbrt (* (sqrt (+ (* v (* -6 v)) 2)) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (83 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ (* (* -6 v) v) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ (* (* -6 v) v) 2))))))) * * * * [misc]progress: [ 213 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (83 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ (* (* -6 v) v) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ (* (* -6 v) v) 2))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (83 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ (* (* -6 v) v) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ (* (* -6 v) v) 2))))))) * * * * [misc]progress: [ 214 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (93 enodes) * * [misc]simplify: iters left: 2 (127 enodes) * * [misc]simplify: iters left: 1 (150 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 215 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (69 enodes) * * [misc]simplify: iters left: 1 (76 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 216 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (96 enodes) * * [misc]simplify: iters left: 3 (251 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ (cbrt (sqrt (+ (* v (* -6 v)) 2))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (/ (cbrt (sqrt (+ (* v (* -6 v)) 2))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ (cbrt (sqrt (+ (* v (* -6 v)) 2))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (/ (cbrt (sqrt (+ (* v (* -6 v)) 2))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 217 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (74 enodes) * * [misc]simplify: iters left: 3 (160 enodes) * * [misc]simplify: iters left: 2 (310 enodes) * [exit]simplify: Simplified to (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ (* (* v v) -6) 2))))))) * * * * [misc]progress: [ 218 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (307 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 219 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (126 enodes) * * [misc]simplify: iters left: 2 (366 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 220 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (307 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 221 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (159 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (cbrt (sqrt (+ (* (* v v) -6) 2))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (cbrt (sqrt (+ (* (* v v) -6) 2))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (cbrt (sqrt (+ (* (* v v) -6) 2))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 222 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (133 enodes) * * [misc]simplify: iters left: 2 (257 enodes) * * [misc]simplify: iters left: 1 (427 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ 4/3 PI))) (* (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ 4/3 PI))) (* (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (* (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 223 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (149 enodes) * * [misc]simplify: iters left: 1 (200 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (+ (* (* v v) -6) 2))))))) * * * * [misc]progress: [ 224 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (94 enodes) * * [misc]simplify: iters left: 2 (146 enodes) * * [misc]simplify: iters left: 1 (198 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 225 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (87 enodes) * * [misc]simplify: iters left: 2 (165 enodes) * * [misc]simplify: iters left: 1 (288 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (cbrt (sqrt (+ (* (* v v) -6) 2))) (sqrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (cbrt (sqrt (+ (* (* v v) -6) 2))) (sqrt (/ 4/3 PI)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ (* v (* -6 v)) 2))) (sqrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (cbrt (sqrt (+ (* (* v v) -6) 2))) (sqrt (/ 4/3 PI)))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ (* v (* -6 v)) 2))) (sqrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 226 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (94 enodes) * * [misc]simplify: iters left: 2 (146 enodes) * * [misc]simplify: iters left: 1 (198 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 227 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (155 enodes) * * [misc]simplify: iters left: 1 (286 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (cbrt (sqrt (+ (* (* v v) -6) 2))) (sqrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (cbrt (sqrt (+ (* (* v v) -6) 2))) (sqrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ (* v (* -6 v)) 2))) (sqrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (cbrt (sqrt (+ (* (* v v) -6) 2))) (sqrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ (* v (* -6 v)) 2))) (sqrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 228 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (346 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (* (cbrt (sqrt (+ (* (* -6 v) v) 2))) (cbrt (sqrt (+ (* (* -6 v) v) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (* (cbrt (sqrt (+ (* (* -6 v) v) 2))) (cbrt (sqrt (+ (* (* -6 v) v) 2))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (* (/ (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (* (cbrt (sqrt (+ (* (* -6 v) v) 2))) (cbrt (sqrt (+ (* (* -6 v) v) 2))))) (* (/ (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 229 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (213 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (264 enodes) * [exit]simplify: Simplified to (/ (* (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (* (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 230 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (95 enodes) * * [misc]simplify: iters left: 2 (208 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (* (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) (* (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 231 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (97 enodes) * * [misc]simplify: iters left: 1 (157 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 232 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (95 enodes) * * [misc]simplify: iters left: 2 (208 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (* (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) (* (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 233 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 1))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* (* -6 v) v) 2))) (cbrt (sqrt (+ (* (* -6 v) v) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* (* -6 v) v) 2))) (cbrt (sqrt (+ (* (* -6 v) v) 2))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* (* -6 v) v) 2))) (cbrt (sqrt (+ (* (* -6 v) v) 2))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 234 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (130 enodes) * * [misc]simplify: iters left: 2 (254 enodes) * * [misc]simplify: iters left: 1 (419 enodes) * [exit]simplify: Simplified to (/ (* 4/3 (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (* (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* 4/3 (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (* (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* (* -6 v) v) 2))) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* (* -6 v) v) 2))) PI)))) * * * * [misc]progress: [ 235 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (94 enodes) * * [misc]simplify: iters left: 2 (146 enodes) * * [misc]simplify: iters left: 1 (199 enodes) * [exit]simplify: Simplified to (* (/ (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) PI) (* (sqrt (cbrt (- 1 (* v v)))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) PI) (* (sqrt (cbrt (- 1 (* v v)))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))))) * * * * [misc]progress: [ 236 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (143 enodes) * * [misc]simplify: iters left: 1 (195 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) (* (cbrt (sqrt (+ (* (* -6 v) v) 2))) (/ (sqrt (sqrt (- 1 (* v v)))) 4/3))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) (* (cbrt (sqrt (+ (* (* -6 v) v) 2))) (/ (sqrt (sqrt (- 1 (* v v)))) 4/3))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* (* -6 v) v) 2))) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* (* -6 v) v) 2))) PI)))) * * * * [misc]progress: [ 237 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (68 enodes) * * [misc]simplify: iters left: 2 (97 enodes) * * [misc]simplify: iters left: 1 (208 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) 4/3) (* (cbrt (sqrt (+ (* (* -6 v) v) 2))) (cbrt (sqrt (+ (* (* -6 v) v) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) 4/3) (* (cbrt (sqrt (+ (* (* -6 v) v) 2))) (cbrt (sqrt (+ (* (* -6 v) v) 2))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (119 enodes) * * [misc]simplify: iters left: 2 (276 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (* PI (cbrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) 4/3) (* (cbrt (sqrt (+ (* (* -6 v) v) 2))) (cbrt (sqrt (+ (* (* -6 v) v) 2))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (* PI (cbrt (sqrt (+ (* v (* -6 v)) 2))))))) * * * * [misc]progress: [ 238 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (143 enodes) * * [misc]simplify: iters left: 1 (195 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) (* (cbrt (sqrt (+ (* (* -6 v) v) 2))) (/ (sqrt (sqrt (- 1 (* v v)))) 4/3))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) (* (cbrt (sqrt (+ (* (* -6 v) v) 2))) (/ (sqrt (sqrt (- 1 (* v v)))) 4/3))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* (* -6 v) v) 2))) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* (* -6 v) v) 2))) PI)))) * * * * [misc]progress: [ 239 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 1))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (64 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (/ 4/3 (cbrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (/ 4/3 (cbrt (sqrt (+ (* v (* -6 v)) 2))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (119 enodes) * * [misc]simplify: iters left: 2 (276 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (* PI (cbrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (/ 4/3 (cbrt (sqrt (+ (* v (* -6 v)) 2))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (* PI (cbrt (sqrt (+ (* v (* -6 v)) 2))))))) * * * * [misc]progress: [ 240 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) 1)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (133 enodes) * * [misc]simplify: iters left: 1 (202 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 241 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (143 enodes) * * [misc]simplify: iters left: 1 (195 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) (* (cbrt (sqrt (+ (* (* -6 v) v) 2))) (/ PI 4/3))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) (* (cbrt (sqrt (+ (* (* -6 v) v) 2))) (/ PI 4/3))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (107 enodes) * * [misc]simplify: iters left: 1 (153 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 PI))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 242 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (98 enodes) * * [misc]simplify: iters left: 3 (214 enodes) * * [misc]simplify: iters left: 2 (379 enodes) * [exit]simplify: Simplified to (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* -6 v) v) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* -6 v) v) 2))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (111 enodes) * * [misc]simplify: iters left: 3 (187 enodes) * * [misc]simplify: iters left: 2 (298 enodes) * * [misc]simplify: iters left: 1 (427 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ (pow v 4) (+ (* v v) 1))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* -6 v) v) 2))))) (/ (* (sqrt (+ (pow v 4) (+ (* v v) 1))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 243 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (180 enodes) * * [misc]simplify: iters left: 2 (348 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* -6 v) v) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* -6 v) v) 2))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (* v v))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* -6 v) v) 2))))) (/ (* (sqrt (+ 1 (* v v))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 244 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (69 enodes) * * [misc]simplify: iters left: 1 (71 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (fabs (cbrt (+ (* v (* -6 v)) 2))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (fabs (cbrt (+ (* v (* -6 v)) 2))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (fabs (cbrt (+ (* v (* -6 v)) 2))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 245 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 246 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (165 enodes) * * [misc]simplify: iters left: 2 (304 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 247 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (150 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v)))))) (/ (cbrt (/ 4/3 PI)) (fabs (cbrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v)))))) (/ (cbrt (/ 4/3 PI)) (fabs (cbrt (+ (* (* v v) -6) 2))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v)))))) (/ (cbrt (/ 4/3 PI)) (fabs (cbrt (+ (* (* v v) -6) 2))))) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (+ (* (* v v) -6) 2))))))) * * * * [misc]progress: [ 248 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (103 enodes) * * [misc]simplify: iters left: 2 (147 enodes) * * [misc]simplify: iters left: 1 (209 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI))) (/ (fabs (cbrt (+ (* (* -6 v) v) 2))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI))) (/ (fabs (cbrt (+ (* (* -6 v) v) 2))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI))) (/ (fabs (cbrt (+ (* (* -6 v) v) 2))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 249 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (228 enodes) * * [misc]simplify: iters left: 1 (339 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (fabs (cbrt (+ (* (* -6 v) v) 2))) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (fabs (cbrt (+ (* (* -6 v) v) 2))) (cbrt (/ 4/3 PI)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ (* v (* -6 v)) 2))) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (fabs (cbrt (+ (* (* -6 v) v) 2))) (cbrt (/ 4/3 PI)))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ (* v (* -6 v)) 2))) (cbrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 250 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (103 enodes) * * [misc]simplify: iters left: 2 (147 enodes) * * [misc]simplify: iters left: 1 (209 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI))) (/ (fabs (cbrt (+ (* (* -6 v) v) 2))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI))) (/ (fabs (cbrt (+ (* (* -6 v) v) 2))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI))) (/ (fabs (cbrt (+ (* (* -6 v) v) 2))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 251 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (117 enodes) * * [misc]simplify: iters left: 2 (288 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ (* v (* -6 v)) 2))) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ (* v (* -6 v)) 2))) (cbrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 252 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (95 enodes) * * [misc]simplify: iters left: 2 (141 enodes) * * [misc]simplify: iters left: 1 (196 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (+ (* (* -6 v) v) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (+ (* (* -6 v) v) 2))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (+ (* (* -6 v) v) 2))))) (/ (* (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 253 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (82 enodes) * * [misc]simplify: iters left: 1 (101 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (- 1 (* v v)))))) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (+ (* (* v v) -6) 2))))))) * * * * [misc]progress: [ 254 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (79 enodes) * * [misc]simplify: iters left: 1 (98 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 255 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ (* v (* -6 v)) 2))) (sqrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ (* v (* -6 v)) 2))) (sqrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 256 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (79 enodes) * * [misc]simplify: iters left: 1 (98 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 257 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (104 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (/ (fabs (cbrt (+ (* (* v v) -6) 2))) (sqrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (/ (fabs (cbrt (+ (* (* v v) -6) 2))) (sqrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ (* v (* -6 v)) 2))) (sqrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (/ (fabs (cbrt (+ (* (* v v) -6) 2))) (sqrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ (* v (* -6 v)) 2))) (sqrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 258 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (102 enodes) * * [misc]simplify: iters left: 2 (172 enodes) * * [misc]simplify: iters left: 1 (306 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (fabs (cbrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (fabs (cbrt (+ (* v (* -6 v)) 2))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (* (/ (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* -6 v)) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (fabs (cbrt (+ (* v (* -6 v)) 2))))) (* (/ (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* -6 v)) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 259 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (73 enodes) * * [misc]simplify: iters left: 2 (93 enodes) * * [misc]simplify: iters left: 1 (116 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (264 enodes) * [exit]simplify: Simplified to (/ (* (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (* (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 260 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (100 enodes) * * [misc]simplify: iters left: 1 (134 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* -6 v) v) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (* (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* -6 v)) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* -6 v) v) 2)))) (* (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* -6 v)) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 261 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * * [misc]simplify: iters left: 2 (44 enodes) * * [misc]simplify: iters left: 1 (52 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* -6 v) v) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* -6 v) v) 2)))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 262 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (100 enodes) * * [misc]simplify: iters left: 1 (134 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* -6 v) v) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (* (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* -6 v)) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* -6 v) v) 2)))) (* (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* -6 v)) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 263 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 1))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * * [misc]simplify: iters left: 2 (42 enodes) * * [misc]simplify: iters left: 1 (44 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 264 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (195 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (/ 4/3 (cbrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (/ 4/3 (cbrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (cbrt (+ (* (* -6 v) v) 2))) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (/ 4/3 (cbrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (cbrt (+ (* (* -6 v) v) 2))) PI)))) * * * * [misc]progress: [ 265 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (79 enodes) * * [misc]simplify: iters left: 1 (98 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ (fabs (cbrt (- 1 (* v v)))) 4/3)) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ (fabs (cbrt (- 1 (* v v)))) 4/3)) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) PI) (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (cbrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ (fabs (cbrt (- 1 (* v v)))) 4/3)) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) PI) (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (cbrt (+ (* v (* -6 v)) 2))))))) * * * * [misc]progress: [ 266 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (cbrt (+ (* (* -6 v) v) 2))) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v)))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (cbrt (+ (* (* -6 v) v) 2))) PI)))) * * * * [misc]progress: [ 267 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * * [misc]simplify: iters left: 2 (54 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) 4/3) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) 4/3) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (119 enodes) * * [misc]simplify: iters left: 2 (276 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (* PI (sqrt (cbrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) 4/3) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (* PI (sqrt (cbrt (+ (* v (* -6 v)) 2))))))) * * * * [misc]progress: [ 268 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (cbrt (+ (* (* -6 v) v) 2))) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v)))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (cbrt (+ (* (* -6 v) v) 2))) PI)))) * * * * [misc]progress: [ 269 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 1))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * * [misc]simplify: iters left: 2 (44 enodes) * * [misc]simplify: iters left: 1 (47 enodes) * [exit]simplify: Simplified to (* 4/3 (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* -6 v) v) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* 4/3 (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* -6 v) v) 2))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (119 enodes) * * [misc]simplify: iters left: 2 (276 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (* PI (sqrt (cbrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* 4/3 (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* -6 v) v) 2))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (* PI (sqrt (cbrt (+ (* v (* -6 v)) 2))))))) * * * * [misc]progress: [ 270 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) 1)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * * [misc]simplify: iters left: 2 (46 enodes) * * [misc]simplify: iters left: 1 (49 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* -6 v) v) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* -6 v) v) 2)))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 271 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ 4/3 PI)) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ 4/3 PI)) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (107 enodes) * * [misc]simplify: iters left: 1 (153 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ 4/3 PI)) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 272 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (174 enodes) * * [misc]simplify: iters left: 2 (253 enodes) * * [misc]simplify: iters left: 1 (339 enodes) * [exit]simplify: Simplified to (* (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) PI)) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) PI)) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (111 enodes) * * [misc]simplify: iters left: 3 (187 enodes) * * [misc]simplify: iters left: 2 (298 enodes) * * [misc]simplify: iters left: 1 (427 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ (pow v 4) (+ (* v v) 1))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) PI)) (/ (* (sqrt (+ (pow v 4) (+ (* v v) 1))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 273 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (79 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (223 enodes) * * [misc]simplify: iters left: 1 (305 enodes) * [exit]simplify: Simplified to (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* -6 v) v) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* -6 v) v) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (* v v))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* -6 v) v) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (* (sqrt (+ 1 (* v v))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 274 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 275 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 276 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (163 enodes) * * [misc]simplify: iters left: 2 (301 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (* (/ (cbrt (sqrt (- 1 (* v v)))) (cbrt (/ 4/3 PI))) (/ (cbrt (sqrt (- 1 (* v v)))) (cbrt (/ 4/3 PI))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (* (/ (cbrt (sqrt (- 1 (* v v)))) (cbrt (/ 4/3 PI))) (/ (cbrt (sqrt (- 1 (* v v)))) (cbrt (/ 4/3 PI))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 277 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (148 enodes) * * [misc]simplify: iters left: 1 (212 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ (cbrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (/ (cbrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI)))) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (+ (* (* v v) -6) 2))))))) * * * * [misc]progress: [ 278 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (146 enodes) * * [misc]simplify: iters left: 1 (210 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 279 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (75 enodes) * * [misc]simplify: iters left: 2 (149 enodes) * * [misc]simplify: iters left: 1 (281 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 280 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (146 enodes) * * [misc]simplify: iters left: 1 (210 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 281 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (115 enodes) * * [misc]simplify: iters left: 2 (331 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI)))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 282 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (93 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (194 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (* (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 283 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (68 enodes) * * [misc]simplify: iters left: 2 (80 enodes) * * [misc]simplify: iters left: 1 (99 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (fabs (cbrt (- 1 (* v v)))) (sqrt (/ 4/3 PI)))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (fabs (cbrt (- 1 (* v v)))) (sqrt (/ 4/3 PI)))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (fabs (cbrt (- 1 (* v v)))) (sqrt (/ 4/3 PI)))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ (* (* v v) -6) 2))))))) * * * * [misc]progress: [ 284 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 285 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (99 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) (sqrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ (* (* v v) -6) 2))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) (sqrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 286 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 287 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (85 enodes) * * [misc]simplify: iters left: 1 (129 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ 4/3 PI))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ 4/3 PI))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) (sqrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ 4/3 PI))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) (sqrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 288 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (96 enodes) * * [misc]simplify: iters left: 2 (175 enodes) * * [misc]simplify: iters left: 1 (325 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (* (/ (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (* (/ (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 289 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (75 enodes) * * [misc]simplify: iters left: 2 (99 enodes) * * [misc]simplify: iters left: 1 (115 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (fabs (cbrt (- 1 (* v v))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (264 enodes) * [exit]simplify: Simplified to (/ (* (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (fabs (cbrt (- 1 (* v v))))) (/ (* (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 290 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (72 enodes) * * [misc]simplify: iters left: 2 (122 enodes) * * [misc]simplify: iters left: 1 (170 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (* (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (sqrt (sqrt (- 1 (* v v))))) (* (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 291 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (65 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 292 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (72 enodes) * * [misc]simplify: iters left: 2 (122 enodes) * * [misc]simplify: iters left: 1 (170 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (* (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (sqrt (sqrt (- 1 (* v v))))) (* (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 293 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 1))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (42 enodes) * * [misc]simplify: iters left: 1 (46 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 294 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (134 enodes) * * [misc]simplify: iters left: 1 (194 enodes) * [exit]simplify: Simplified to (* (/ (/ 4/3 (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ 4/3 (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (sqrt (+ (* (* -6 v) v) 2))) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (sqrt (+ (* (* -6 v) v) 2))) PI)))) * * * * [misc]progress: [ 295 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) 4/3)) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) 4/3)) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) PI) (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) 4/3)) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) PI) (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* -6 v)) 2))))))) * * * * [misc]progress: [ 296 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (93 enodes) * [exit]simplify: Simplified to (/ (* (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (sqrt (+ (* (* -6 v) v) 2))) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (sqrt (+ (* (* -6 v) v) 2))) PI)))) * * * * [misc]progress: [ 297 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (52 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) 4/3)) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) 4/3)) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (119 enodes) * * [misc]simplify: iters left: 2 (276 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (* PI (sqrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) 4/3)) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (* PI (sqrt (sqrt (+ (* v (* -6 v)) 2))))))) * * * * [misc]progress: [ 298 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (93 enodes) * [exit]simplify: Simplified to (/ (* (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (sqrt (+ (* (* -6 v) v) 2))) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (sqrt (+ (* (* -6 v) v) 2))) PI)))) * * * * [misc]progress: [ 299 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 1))) * * [misc]simplify: iters left: 6 (17 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 (42 enodes) * * [misc]simplify: iters left: 1 (45 enodes) * [exit]simplify: Simplified to (* (/ 4/3 (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ 4/3 (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (119 enodes) * * [misc]simplify: iters left: 2 (276 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (* PI (sqrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ 4/3 (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (* PI (sqrt (sqrt (+ (* v (* -6 v)) 2))))))) * * * * [misc]progress: [ 300 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) 1)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 301 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (93 enodes) * [exit]simplify: Simplified to (/ (* (/ 4/3 PI) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (/ 4/3 PI) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (107 enodes) * * [misc]simplify: iters left: 1 (153 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 302 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (172 enodes) * * [misc]simplify: iters left: 2 (254 enodes) * * [misc]simplify: iters left: 1 (337 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (111 enodes) * * [misc]simplify: iters left: 3 (187 enodes) * * [misc]simplify: iters left: 2 (298 enodes) * * [misc]simplify: iters left: 1 (427 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ (pow v 4) (+ (* v v) 1))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6))))) (/ (* (sqrt (+ (pow v 4) (+ (* v v) 1))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 303 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (77 enodes) * * [misc]simplify: iters left: 3 (136 enodes) * * [misc]simplify: iters left: 2 (212 enodes) * * [misc]simplify: iters left: 1 (294 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (* v v))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) (/ (* (sqrt (+ 1 (* v v))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 304 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt 1) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (83 enodes) * [exit]simplify: Simplified to (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 305 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt 1) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (52 enodes) * * [misc]simplify: iters left: 1 (55 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (* (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 306 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (385 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (cbrt (sqrt (- 1 (* v v)))))) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v))))))) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (cbrt (sqrt (- 1 (* v v)))))) (cbrt (/ 4/3 PI))))) * * * * [misc]progress: [ 307 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (170 enodes) * * [misc]simplify: iters left: 1 (276 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))) (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v)))))) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))) (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 308 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (102 enodes) * * [misc]simplify: iters left: 2 (234 enodes) * * [misc]simplify: iters left: 1 (475 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (sqrt (- 1 (* v v)))))) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (sqrt (- 1 (* v v)))))) (cbrt (/ 4/3 PI))))) * * * * [misc]progress: [ 309 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (116 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (94 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI)))) (* (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 310 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (102 enodes) * * [misc]simplify: iters left: 2 (234 enodes) * * [misc]simplify: iters left: 1 (475 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (sqrt (- 1 (* v v)))))) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (sqrt (- 1 (* v v)))))) (cbrt (/ 4/3 PI))))) * * * * [misc]progress: [ 311 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (117 enodes) * * [misc]simplify: iters left: 2 (259 enodes) * * [misc]simplify: iters left: 1 (312 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (94 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI)))) (* (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 312 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (85 enodes) * * [misc]simplify: iters left: 2 (184 enodes) * * [misc]simplify: iters left: 1 (360 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (cbrt (sqrt (- 1 (* v v)))))) (sqrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (cbrt (sqrt (- 1 (* v v)))))) (sqrt (/ 4/3 PI))))) * * * * [misc]progress: [ 313 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (102 enodes) * * [misc]simplify: iters left: 1 (130 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))) (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))) (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 314 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (73 enodes) * * [misc]simplify: iters left: 2 (121 enodes) * * [misc]simplify: iters left: 1 (169 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (sqrt (- 1 (* v v)))))) (sqrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (sqrt (- 1 (* v v)))))) (sqrt (/ 4/3 PI))))) * * * * [misc]progress: [ 315 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (61 enodes) * * [misc]simplify: iters left: 1 (64 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 4/3 PI)) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (sqrt (/ 4/3 PI)) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (94 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (sqrt (/ 4/3 PI)) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 316 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (73 enodes) * * [misc]simplify: iters left: 2 (121 enodes) * * [misc]simplify: iters left: 1 (169 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (sqrt (- 1 (* v v)))))) (sqrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (sqrt (- 1 (* v v)))))) (sqrt (/ 4/3 PI))))) * * * * [misc]progress: [ 317 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (59 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 4/3 PI)) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (sqrt (/ 4/3 PI)) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (94 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (sqrt (/ 4/3 PI)) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 318 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt 1) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (72 enodes) * * [misc]simplify: iters left: 2 (139 enodes) * * [misc]simplify: iters left: 1 (221 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (264 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 319 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt 1) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (56 enodes) * * [misc]simplify: iters left: 2 (68 enodes) * * [misc]simplify: iters left: 1 (77 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (- 1 (* v v))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* PI (sqrt (cbrt (- 1 (* v v)))))) (/ 4/3 (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (- 1 (* v v))))) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* PI (sqrt (cbrt (- 1 (* v v)))))) (/ 4/3 (sqrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 320 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt 1) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (56 enodes) * * [misc]simplify: iters left: 2 (80 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (264 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 321 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt 1) (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (103 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 322 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt 1) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (56 enodes) * * [misc]simplify: iters left: 2 (80 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (264 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 323 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt 1) (/ 1 1))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (103 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 324 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt 1) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (87 enodes) * * [misc]simplify: iters left: 2 (176 enodes) * * [misc]simplify: iters left: 1 (288 enodes) * [exit]simplify: Simplified to (* (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (120 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) PI)))) * * * * [misc]progress: [ 325 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt 1) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (68 enodes) * * [misc]simplify: iters left: 1 (85 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 4/3 (fabs (cbrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 4/3 (fabs (cbrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (281 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2)))) PI) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 4/3 (fabs (cbrt (- 1 (* v v)))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2)))) PI))) * * * * [misc]progress: [ 326 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt 1) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (96 enodes) * * [misc]simplify: iters left: 1 (104 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (120 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v)))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) PI)))) * * * * [misc]progress: [ 327 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt 1) (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (* 4/3 (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* 4/3 (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (118 enodes) * * [misc]simplify: iters left: 2 (284 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (* PI (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* 4/3 (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (* PI (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 328 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt 1) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (96 enodes) * * [misc]simplify: iters left: 1 (104 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (120 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v)))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) PI)))) * * * * [misc]progress: [ 329 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt 1) (/ 4/3 1))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) 4/3) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) 4/3) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (118 enodes) * * [misc]simplify: iters left: 2 (284 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (* PI (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) 4/3) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (* PI (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 330 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt 1) 1)) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * * [misc]simplify: iters left: 2 (24 enodes) * * [misc]simplify: iters left: 1 (26 enodes) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (103 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 331 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt 1) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (56 enodes) * * [misc]simplify: iters left: 2 (69 enodes) * * [misc]simplify: iters left: 1 (80 enodes) * [exit]simplify: Simplified to (* (/ 4/3 PI) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ 4/3 PI) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (69 enodes) * * [misc]simplify: iters left: 2 (105 enodes) * * [misc]simplify: iters left: 1 (140 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (- 1 (* v v))) (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ 4/3 PI) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (- 1 (* v v))) (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 332 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt 1) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (77 enodes) * * [misc]simplify: iters left: 3 (176 enodes) * * [misc]simplify: iters left: 2 (297 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (* (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (165 enodes) * * [misc]simplify: iters left: 2 (276 enodes) * * [misc]simplify: iters left: 1 (348 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* (* -6 v) v) 2)) (sqrt (+ (* v v) (+ 1 (pow v 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* (* -6 v) v) 2)) (sqrt (+ (* v v) (+ 1 (pow v 4)))))))) * * * * [misc]progress: [ 333 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt 1) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (256 enodes) * * [misc]simplify: iters left: 1 (403 enodes) * [exit]simplify: Simplified to (* (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 1 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* v (* -6 v)) 2)) (sqrt (+ 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* v (* -6 v)) 2)) (sqrt (+ 1 (* v v))))))) * * * * [misc]progress: [ 334 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 335 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 336 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (163 enodes) * * [misc]simplify: iters left: 2 (301 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (* (/ (cbrt (sqrt (- 1 (* v v)))) (cbrt (/ 4/3 PI))) (/ (cbrt (sqrt (- 1 (* v v)))) (cbrt (/ 4/3 PI))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (* (/ (cbrt (sqrt (- 1 (* v v)))) (cbrt (/ 4/3 PI))) (/ (cbrt (sqrt (- 1 (* v v)))) (cbrt (/ 4/3 PI))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 337 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (148 enodes) * * [misc]simplify: iters left: 1 (212 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ (cbrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (/ (cbrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 4/3 PI)))) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (+ (* (* v v) -6) 2))))))) * * * * [misc]progress: [ 338 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (146 enodes) * * [misc]simplify: iters left: 1 (210 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 339 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (75 enodes) * * [misc]simplify: iters left: 2 (149 enodes) * * [misc]simplify: iters left: 1 (281 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 340 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (146 enodes) * * [misc]simplify: iters left: 1 (210 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 341 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (115 enodes) * * [misc]simplify: iters left: 2 (331 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI)))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 342 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (93 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (194 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (* (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 343 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (68 enodes) * * [misc]simplify: iters left: 2 (80 enodes) * * [misc]simplify: iters left: 1 (99 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (fabs (cbrt (- 1 (* v v)))) (sqrt (/ 4/3 PI)))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (fabs (cbrt (- 1 (* v v)))) (sqrt (/ 4/3 PI)))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (fabs (cbrt (- 1 (* v v)))) (sqrt (/ 4/3 PI)))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (cbrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ (* (* v v) -6) 2))))))) * * * * [misc]progress: [ 344 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 345 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (99 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) (sqrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ (* (* v v) -6) 2))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) (sqrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 346 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 347 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (85 enodes) * * [misc]simplify: iters left: 1 (129 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ 4/3 PI))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ 4/3 PI))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) (sqrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (/ 4/3 PI))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) (sqrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 348 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (96 enodes) * * [misc]simplify: iters left: 2 (175 enodes) * * [misc]simplify: iters left: 1 (325 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (* (/ (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (* (/ (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 349 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (75 enodes) * * [misc]simplify: iters left: 2 (99 enodes) * * [misc]simplify: iters left: 1 (115 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (fabs (cbrt (- 1 (* v v))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (264 enodes) * [exit]simplify: Simplified to (/ (* (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (fabs (cbrt (- 1 (* v v))))) (/ (* (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 350 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (72 enodes) * * [misc]simplify: iters left: 2 (122 enodes) * * [misc]simplify: iters left: 1 (170 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (* (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (sqrt (sqrt (- 1 (* v v))))) (* (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 351 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (65 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 352 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (72 enodes) * * [misc]simplify: iters left: 2 (122 enodes) * * [misc]simplify: iters left: 1 (170 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (* (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (sqrt (sqrt (- 1 (* v v))))) (* (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 353 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 1))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (42 enodes) * * [misc]simplify: iters left: 1 (46 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 354 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (134 enodes) * * [misc]simplify: iters left: 1 (194 enodes) * [exit]simplify: Simplified to (* (/ (/ 4/3 (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ 4/3 (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (sqrt (+ (* (* -6 v) v) 2))) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (sqrt (+ (* (* -6 v) v) 2))) PI)))) * * * * [misc]progress: [ 355 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) 4/3)) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) 4/3)) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) PI) (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) 4/3)) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) PI) (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* -6 v)) 2))))))) * * * * [misc]progress: [ 356 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (93 enodes) * [exit]simplify: Simplified to (/ (* (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (sqrt (+ (* (* -6 v) v) 2))) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (sqrt (+ (* (* -6 v) v) 2))) PI)))) * * * * [misc]progress: [ 357 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (52 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) 4/3)) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) 4/3)) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (119 enodes) * * [misc]simplify: iters left: 2 (276 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (* PI (sqrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* v (* -6 v)) 2))) 4/3)) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (* PI (sqrt (sqrt (+ (* v (* -6 v)) 2))))))) * * * * [misc]progress: [ 358 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (93 enodes) * [exit]simplify: Simplified to (/ (* (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (sqrt (+ (* (* -6 v) v) 2))) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (sqrt (+ (* (* -6 v) v) 2))) PI)))) * * * * [misc]progress: [ 359 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 1))) * * [misc]simplify: iters left: 6 (17 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 (42 enodes) * * [misc]simplify: iters left: 1 (45 enodes) * [exit]simplify: Simplified to (* (/ 4/3 (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ 4/3 (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (119 enodes) * * [misc]simplify: iters left: 2 (276 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (* PI (sqrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ 4/3 (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) (* PI (sqrt (sqrt (+ (* v (* -6 v)) 2))))))) * * * * [misc]progress: [ 360 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) 1)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (/ PI 4/3) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 361 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (93 enodes) * [exit]simplify: Simplified to (/ (* (/ 4/3 PI) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (/ 4/3 PI) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (107 enodes) * * [misc]simplify: iters left: 1 (153 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 362 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (172 enodes) * * [misc]simplify: iters left: 2 (254 enodes) * * [misc]simplify: iters left: 1 (337 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (111 enodes) * * [misc]simplify: iters left: 3 (187 enodes) * * [misc]simplify: iters left: 2 (298 enodes) * * [misc]simplify: iters left: 1 (427 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ (pow v 4) (+ (* v v) 1))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6))))) (/ (* (sqrt (+ (pow v 4) (+ (* v v) 1))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 363 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (77 enodes) * * [misc]simplify: iters left: 3 (136 enodes) * * [misc]simplify: iters left: 2 (212 enodes) * * [misc]simplify: iters left: 1 (294 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (* v v))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) (/ (* (sqrt (+ 1 (* v v))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 364 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (58 enodes) * * [misc]simplify: iters left: 1 (63 enodes) * [exit]simplify: Simplified to (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 365 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * * [misc]simplify: iters left: 2 (44 enodes) * * [misc]simplify: iters left: 1 (49 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (* (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 366 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (134 enodes) * * [misc]simplify: iters left: 2 (384 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v))))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (cbrt (sqrt (- 1 (* v v)))))) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v))))))) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (cbrt (sqrt (- 1 (* v v)))))) (cbrt (/ 4/3 PI))))) * * * * [misc]progress: [ 367 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (146 enodes) * * [misc]simplify: iters left: 1 (226 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))) (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v)))))) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))) (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 368 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (96 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (444 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (sqrt (- 1 (* v v)))))) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (sqrt (- 1 (* v v)))))) (cbrt (/ 4/3 PI))))) * * * * [misc]progress: [ 369 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (109 enodes) * * [misc]simplify: iters left: 1 (126 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (94 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI)))) (* (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 370 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (96 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (444 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (sqrt (- 1 (* v v)))))) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (sqrt (- 1 (* v v)))))) (cbrt (/ 4/3 PI))))) * * * * [misc]progress: [ 371 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (96 enodes) * * [misc]simplify: iters left: 1 (111 enodes) * [exit]simplify: Simplified to (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (94 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (* (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 372 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (84 enodes) * * [misc]simplify: iters left: 2 (176 enodes) * * [misc]simplify: iters left: 1 (364 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (cbrt (sqrt (- 1 (* v v)))))) (sqrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v)))))) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (cbrt (sqrt (- 1 (* v v)))))) (sqrt (/ 4/3 PI))))) * * * * [misc]progress: [ 373 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (82 enodes) * * [misc]simplify: iters left: 1 (101 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))) (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v)))))) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))) (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 374 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (69 enodes) * * [misc]simplify: iters left: 2 (101 enodes) * * [misc]simplify: iters left: 1 (126 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (- 1 (* v v)))) (sqrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (- 1 (* v v)))) (sqrt (/ 4/3 PI)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (sqrt (- 1 (* v v)))))) (sqrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (- 1 (* v v)))) (sqrt (/ 4/3 PI)))) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (sqrt (- 1 (* v v)))))) (sqrt (/ 4/3 PI))))) * * * * [misc]progress: [ 375 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (56 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (62 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 4/3 PI)) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (sqrt (/ 4/3 PI)) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (94 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (sqrt (/ 4/3 PI)) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 376 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (69 enodes) * * [misc]simplify: iters left: 2 (101 enodes) * * [misc]simplify: iters left: 1 (126 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (- 1 (* v v)))) (sqrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (- 1 (* v v)))) (sqrt (/ 4/3 PI)))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (sqrt (- 1 (* v v)))))) (sqrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (- 1 (* v v)))) (sqrt (/ 4/3 PI)))) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) (sqrt (sqrt (- 1 (* v v)))))) (sqrt (/ 4/3 PI))))) * * * * [misc]progress: [ 377 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (52 enodes) * * [misc]simplify: iters left: 1 (55 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 4/3 PI)) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (sqrt (/ 4/3 PI)) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (94 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (sqrt (/ 4/3 PI)) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 378 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [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 (64 enodes) * * [misc]simplify: iters left: 2 (100 enodes) * * [misc]simplify: iters left: 1 (190 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (264 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 379 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (53 enodes) * * [misc]simplify: iters left: 1 (65 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (- 1 (* v v))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* PI (sqrt (cbrt (- 1 (* v v)))))) (/ 4/3 (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (fabs (cbrt (- 1 (* v v))))) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* PI (sqrt (cbrt (- 1 (* v v)))))) (/ 4/3 (sqrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 380 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (66 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (264 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 381 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * * [misc]simplify: iters left: 2 (35 enodes) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (103 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 382 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (66 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (264 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* -6 v) v) 2))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 383 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (/ 1 1))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (103 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 384 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (75 enodes) * * [misc]simplify: iters left: 2 (111 enodes) * * [misc]simplify: iters left: 1 (207 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) 3/4) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) 3/4) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (120 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) 3/4) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) PI)))) * * * * [misc]progress: [ 385 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (64 enodes) * * [misc]simplify: iters left: 1 (83 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 4/3 (fabs (cbrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 4/3 (fabs (cbrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (281 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2)))) PI) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 4/3 (fabs (cbrt (- 1 (* v v)))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2)))) PI))) * * * * [misc]progress: [ 386 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (61 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* 3/4 (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* 3/4 (sqrt (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (120 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* 3/4 (sqrt (sqrt (- 1 (* v v)))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) PI)))) * * * * [misc]progress: [ 387 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (* 4/3 (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* 4/3 (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (118 enodes) * * [misc]simplify: iters left: 2 (284 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (* PI (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* 4/3 (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (* PI (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 388 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (61 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* 3/4 (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* 3/4 (sqrt (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (120 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* 3/4 (sqrt (sqrt (- 1 (* v v)))))) (/ (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* v (* -6 v)) 2)) PI)))) * * * * [misc]progress: [ 389 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (/ 4/3 1))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (* 4/3 (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* 4/3 (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (118 enodes) * * [misc]simplify: iters left: 2 (284 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (* PI (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* 4/3 (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (* PI (sqrt (- 1 (* v v)))) (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 390 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 1)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (103 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 391 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (61 enodes) * * [misc]simplify: iters left: 1 (79 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* 3/4 PI)) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* 3/4 PI)) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (69 enodes) * * [misc]simplify: iters left: 2 (105 enodes) * * [misc]simplify: iters left: 1 (140 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (- 1 (* v v))) (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* 3/4 PI)) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (- 1 (* v v))) (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 392 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (172 enodes) * * [misc]simplify: iters left: 2 (277 enodes) * * [misc]simplify: iters left: 1 (411 enodes) * [exit]simplify: Simplified to (* (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (165 enodes) * * [misc]simplify: iters left: 2 (276 enodes) * * [misc]simplify: iters left: 1 (348 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* (* -6 v) v) 2)) (sqrt (+ (* v v) (+ 1 (pow v 4)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* (* -6 v) v) 2)) (sqrt (+ (* v v) (+ 1 (pow v 4)))))))) * * * * [misc]progress: [ 393 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (138 enodes) * * [misc]simplify: iters left: 2 (253 enodes) * * [misc]simplify: iters left: 1 (376 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 1 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* v (* -6 v)) 2)) (sqrt (+ 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* v (* -6 v)) 2)) (sqrt (+ 1 (* v v))))))) * * * * [misc]progress: [ 394 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) 1) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (103 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* -6 v)) 2)))))) * * * * [misc]progress: [ 395 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* v v) -6) 2))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ (* (* v v) -6) 2))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ 1 (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (208 enodes) * * [misc]simplify: iters left: 1 (343 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (+ 2 (* (* v v) -6)))) (* (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 396 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (92 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* -6 v) v) 2)) (/ PI 4/3))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* -6 v) v) 2)) (/ PI 4/3))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ 4/3 PI))) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 397 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (* (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (84 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v))))))) (cbrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (cbrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v))))))) (cbrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (81 enodes) * * [misc]simplify: iters left: 1 (87 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (* v v)))) (cbrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ (* v (* v -6)) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (* (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (cbrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ (* v (* v -6)) 2))))))) * * * * [misc]progress: [ 398 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (56 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (81 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ 2 (* (* -6 v) v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ 2 (* (* -6 v) v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (sqrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (sqrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (81 enodes) * * [misc]simplify: iters left: 1 (87 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (* v v)))) (sqrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ (* v (* v -6)) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (sqrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ (* v (* v -6)) 2))))))) * * * * [misc]progress: [ 399 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (191 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (145 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 400 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (108 enodes) * * [misc]simplify: iters left: 1 (188 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (145 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 401 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (247 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 402 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (441 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (/ (cbrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (/ (cbrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (111 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (452 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (/ (cbrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 403 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (153 enodes) * * [misc]simplify: iters left: 2 (436 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 404 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (114 enodes) * * [misc]simplify: iters left: 2 (424 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 405 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (153 enodes) * * [misc]simplify: iters left: 2 (436 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 406 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (111 enodes) * * [misc]simplify: iters left: 2 (342 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 407 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (326 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (* (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (* (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (* (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 408 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (94 enodes) * * [misc]simplify: iters left: 2 (184 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (111 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (452 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 409 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (179 enodes) * * [misc]simplify: iters left: 1 (491 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* v (* -6 v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* v (* -6 v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* v (* -6 v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 410 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (75 enodes) * * [misc]simplify: iters left: 2 (201 enodes) * * [misc]simplify: iters left: 1 (390 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 411 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (179 enodes) * * [misc]simplify: iters left: 1 (491 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* v (* -6 v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* v (* -6 v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* v (* -6 v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 412 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (76 enodes) * * [misc]simplify: iters left: 2 (185 enodes) * * [misc]simplify: iters left: 1 (405 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 413 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (118 enodes) * * [misc]simplify: iters left: 2 (297 enodes) * [exit]simplify: Simplified to (* (/ (/ 1 (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ 1 (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (397 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 414 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (85 enodes) * * [misc]simplify: iters left: 2 (127 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (fabs (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (fabs (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (159 enodes) * * [misc]simplify: iters left: 2 (396 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (fabs (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 415 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (83 enodes) * * [misc]simplify: iters left: 2 (125 enodes) * * [misc]simplify: iters left: 1 (296 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (* (sqrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (* (sqrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (397 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (* (sqrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 416 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (335 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 417 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (83 enodes) * * [misc]simplify: iters left: 2 (125 enodes) * * [misc]simplify: iters left: 1 (296 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (* (sqrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (* (sqrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (397 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (* (sqrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 418 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 1))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (50 enodes) * * [misc]simplify: iters left: 1 (62 enodes) * [exit]simplify: Simplified to (/ 1 (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (335 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 419 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (126 enodes) * * [misc]simplify: iters left: 2 (261 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (* (cbrt (sqrt (+ 2 (* v (* -6 v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (* (cbrt (sqrt (+ 2 (* v (* -6 v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (474 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (* (cbrt (sqrt (+ 2 (* v (* -6 v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 420 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (152 enodes) * * [misc]simplify: iters left: 1 (404 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (169 enodes) * * [misc]simplify: iters left: 2 (481 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 421 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (148 enodes) * * [misc]simplify: iters left: 1 (394 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (* (sqrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (* (sqrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (474 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (* (sqrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 422 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (85 enodes) * * [misc]simplify: iters left: 1 (151 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (411 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (- 1 (* v v))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ 1 PI) (- 1 (* v v))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 423 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (148 enodes) * * [misc]simplify: iters left: 1 (394 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (* (sqrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (* (sqrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (474 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (* (sqrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 424 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 1))) * * [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 (40 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * * [misc]simplify: iters left: 1 (61 enodes) * [exit]simplify: Simplified to (/ 4/3 (* (cbrt (sqrt (+ 2 (* v (* -6 v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (* (cbrt (sqrt (+ 2 (* v (* -6 v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (411 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (- 1 (* v v))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (* (cbrt (sqrt (+ 2 (* v (* -6 v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ (/ 1 PI) (- 1 (* v v))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 425 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) 1)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (88 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (* (/ 1 (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ 1 (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (335 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) 1)) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 426 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (81 enodes) * * [misc]simplify: iters left: 2 (143 enodes) * * [misc]simplify: iters left: 1 (389 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (* (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (* (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (131 enodes) * * [misc]simplify: iters left: 1 (158 enodes) * [exit]simplify: Simplified to (/ (/ 1 (- 1 (* v v))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (* (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) (/ (/ 1 (- 1 (* v v))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 427 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (199 enodes) * * [misc]simplify: iters left: 2 (386 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (- 1 (pow v 6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (- 1 (pow v 6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (111 enodes) * * [misc]simplify: iters left: 3 (186 enodes) * * [misc]simplify: iters left: 2 (313 enodes) * * [misc]simplify: iters left: 1 (421 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (pow v 4) (+ (* v v) 1))) (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (- 1 (pow v 6))))) (/ (/ (sqrt (+ (pow v 4) (+ (* v v) 1))) (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 428 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (172 enodes) * * [misc]simplify: iters left: 2 (354 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (79 enodes) * * [misc]simplify: iters left: 1 (135 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 429 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (87 enodes) * * [misc]simplify: iters left: 1 (120 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (145 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* v -6) v) 2)))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* v -6) v) 2)))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 430 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (61 enodes) * * [misc]simplify: iters left: 1 (65 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (145 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* v -6) v) 2)))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* v -6) v) 2)))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 431 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (169 enodes) * * [misc]simplify: iters left: 2 (451 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 432 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (103 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (433 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (111 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (452 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 433 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * * [misc]simplify: iters left: 1 (412 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 434 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (157 enodes) * * [misc]simplify: iters left: 1 (221 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (cbrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (cbrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 435 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * * [misc]simplify: iters left: 1 (412 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 436 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (72 enodes) * * [misc]simplify: iters left: 2 (147 enodes) * * [misc]simplify: iters left: 1 (195 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (cbrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (+ 2 (* (* v v) -6))))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (cbrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 437 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (93 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (339 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 438 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (97 enodes) * * [misc]simplify: iters left: 1 (138 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (111 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (452 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 439 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (68 enodes) * * [misc]simplify: iters left: 2 (95 enodes) * * [misc]simplify: iters left: 1 (136 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 440 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (81 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (cbrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (+ 2 (* (* v v) -6))))) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (cbrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 441 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (68 enodes) * * [misc]simplify: iters left: 2 (95 enodes) * * [misc]simplify: iters left: 1 (136 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 442 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (68 enodes) * * [misc]simplify: iters left: 1 (72 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (cbrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (cbrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 443 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (93 enodes) * * [misc]simplify: iters left: 2 (132 enodes) * * [misc]simplify: iters left: 1 (148 enodes) * [exit]simplify: Simplified to (* (/ (/ 1 (cbrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ 1 (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ 1 (cbrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ 1 (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (397 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (/ 1 (cbrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ 1 (cbrt (sqrt (- 1 (* v v)))))) (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 444 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (68 enodes) * [exit]simplify: Simplified to (/ (/ 1 (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (159 enodes) * * [misc]simplify: iters left: 2 (396 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* v v) -6))))) (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 445 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (75 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (397 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 446 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * * [misc]simplify: iters left: 2 (32 enodes) * * [misc]simplify: iters left: 1 (36 enodes) * [exit]simplify: Simplified to (/ 1 (fabs (cbrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (335 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 447 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (75 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (397 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 448 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 1))) * * [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) * [exit]simplify: Simplified to (/ 1 (fabs (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (335 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 449 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (138 enodes) * * [misc]simplify: iters left: 1 (237 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (fabs (cbrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (fabs (cbrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (474 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (fabs (cbrt (+ 2 (* (* v v) -6))))) (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 450 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (88 enodes) * * [misc]simplify: iters left: 1 (124 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (169 enodes) * * [misc]simplify: iters left: 2 (481 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 451 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (122 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (474 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 452 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (41 enodes) * * [misc]simplify: iters left: 1 (50 enodes) * [exit]simplify: Simplified to (/ 4/3 (fabs (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (411 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (cbrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (cbrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 453 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (122 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (474 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 454 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 1))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * * [misc]simplify: iters left: 2 (38 enodes) * * [misc]simplify: iters left: 1 (43 enodes) * [exit]simplify: Simplified to (/ 4/3 (fabs (cbrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (411 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (cbrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (cbrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 455 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) 1)) * * [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 (/ 1 (fabs (cbrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (fabs (cbrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (335 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (fabs (cbrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 456 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (114 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (fabs (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (131 enodes) * * [misc]simplify: iters left: 1 (158 enodes) * [exit]simplify: Simplified to (/ (/ 1 (- 1 (* v v))) (sqrt (cbrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (- 1 (* v v))) (sqrt (cbrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 457 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (161 enodes) * * [misc]simplify: iters left: 2 (245 enodes) * * [misc]simplify: iters left: 1 (400 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (111 enodes) * * [misc]simplify: iters left: 3 (186 enodes) * * [misc]simplify: iters left: 2 (313 enodes) * * [misc]simplify: iters left: 1 (421 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (pow v 4) (+ (* v v) 1))) (sqrt (- 1 (* v v)))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ (sqrt (+ (pow v 4) (+ (* v v) 1))) (sqrt (- 1 (* v v)))) (sqrt (cbrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 458 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (134 enodes) * * [misc]simplify: iters left: 2 (214 enodes) * * [misc]simplify: iters left: 1 (368 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (79 enodes) * * [misc]simplify: iters left: 1 (135 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 459 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (85 enodes) * * [misc]simplify: iters left: 1 (134 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (145 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (/ (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 460 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (145 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 461 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (165 enodes) * * [misc]simplify: iters left: 2 (470 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 462 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (111 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (452 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 463 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (99 enodes) * * [misc]simplify: iters left: 2 (215 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 464 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (160 enodes) * * [misc]simplify: iters left: 1 (299 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 465 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (99 enodes) * * [misc]simplify: iters left: 2 (215 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 466 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (82 enodes) * * [misc]simplify: iters left: 2 (224 enodes) * * [misc]simplify: iters left: 1 (434 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 467 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (179 enodes) * * [misc]simplify: iters left: 1 (438 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 468 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (68 enodes) * * [misc]simplify: iters left: 2 (95 enodes) * * [misc]simplify: iters left: 1 (169 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (111 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (452 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 469 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (93 enodes) * * [misc]simplify: iters left: 1 (160 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 470 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (79 enodes) * * [misc]simplify: iters left: 1 (106 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 471 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (93 enodes) * * [misc]simplify: iters left: 1 (160 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 472 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (86 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 473 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (124 enodes) * * [misc]simplify: iters left: 1 (176 enodes) * [exit]simplify: Simplified to (* (/ (/ 1 (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ 1 (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ 1 (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ 1 (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (397 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 474 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (69 enodes) * [exit]simplify: Simplified to (/ (/ 1 (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (159 enodes) * * [misc]simplify: iters left: 2 (396 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 475 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (73 enodes) * * [misc]simplify: iters left: 2 (97 enodes) * * [misc]simplify: iters left: 1 (136 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (397 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 476 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * * [misc]simplify: iters left: 2 (34 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (335 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 477 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (73 enodes) * * [misc]simplify: iters left: 2 (97 enodes) * * [misc]simplify: iters left: 1 (136 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (397 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 478 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 1))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * * [misc]simplify: iters left: 2 (30 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (335 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 479 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (308 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (474 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 480 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (149 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (169 enodes) * * [misc]simplify: iters left: 2 (481 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 481 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (84 enodes) * * [misc]simplify: iters left: 1 (147 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (474 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 482 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (39 enodes) * * [misc]simplify: iters left: 1 (48 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (411 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 483 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (84 enodes) * * [misc]simplify: iters left: 1 (147 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (474 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 484 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 1))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * * [misc]simplify: iters left: 2 (36 enodes) * * [misc]simplify: iters left: 1 (41 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (411 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 485 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) 1)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (335 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 486 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (139 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (131 enodes) * * [misc]simplify: iters left: 1 (158 enodes) * [exit]simplify: Simplified to (/ (/ 1 (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 487 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (159 enodes) * * [misc]simplify: iters left: 2 (242 enodes) * * [misc]simplify: iters left: 1 (480 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (111 enodes) * * [misc]simplify: iters left: 3 (186 enodes) * * [misc]simplify: iters left: 2 (313 enodes) * * [misc]simplify: iters left: 1 (421 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (pow v 4) (+ (* v v) 1))) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (sqrt (+ (pow v 4) (+ (* v v) 1))) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 488 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (130 enodes) * * [misc]simplify: iters left: 2 (207 enodes) * * [misc]simplify: iters left: 1 (443 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (79 enodes) * * [misc]simplify: iters left: 1 (135 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 489 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * * [misc]simplify: iters left: 1 (64 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (85 enodes) * * [misc]simplify: iters left: 1 (140 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (* (sqrt (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (* (sqrt (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 490 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * * [misc]simplify: iters left: 2 (32 enodes) * [exit]simplify: Simplified to (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (85 enodes) * * [misc]simplify: iters left: 1 (140 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (* (sqrt (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (* (sqrt (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 491 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (130 enodes) * * [misc]simplify: iters left: 2 (367 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * * [misc]simplify: iters left: 1 (455 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 492 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (80 enodes) * * [misc]simplify: iters left: 2 (185 enodes) * * [misc]simplify: iters left: 1 (265 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (451 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))) (sqrt (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))) (sqrt (cbrt (- 1 (* v v))))))) * * * * [misc]progress: [ 493 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (166 enodes) * * [misc]simplify: iters left: 1 (316 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * * [misc]simplify: iters left: 1 (455 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 494 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (65 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (421 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 495 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (166 enodes) * * [misc]simplify: iters left: 1 (316 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * * [misc]simplify: iters left: 1 (455 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 496 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (421 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 497 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (101 enodes) * * [misc]simplify: iters left: 1 (202 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * * [misc]simplify: iters left: 1 (455 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 498 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (78 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (451 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))) (sqrt (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))) (sqrt (cbrt (- 1 (* v v))))))) * * * * [misc]progress: [ 499 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (54 enodes) * * [misc]simplify: iters left: 1 (60 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * * [misc]simplify: iters left: 1 (455 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 500 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (sqrt (/ 4/3 PI)) * [misc]simplify: Simplified (2 1) to (λ (v) (* (sqrt (/ 4/3 PI)) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (421 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (sqrt (/ 4/3 PI)) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 501 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (54 enodes) * * [misc]simplify: iters left: 1 (60 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * * [misc]simplify: iters left: 1 (455 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 502 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * [exit]simplify: Simplified to (sqrt (/ 4/3 PI)) * [misc]simplify: Simplified (2 1) to (λ (v) (* (sqrt (/ 4/3 PI)) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (421 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (sqrt (/ 4/3 PI)) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 503 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (49 enodes) * * [misc]simplify: iters left: 1 (74 enodes) * [exit]simplify: Simplified to (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (395 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (+ (* v (* v -6)) 2))) (* (* (sqrt (- 1 (* v v))) PI) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 4/3 (sqrt (+ (* v (* v -6)) 2))) (* (* (sqrt (- 1 (* v v))) PI) (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 504 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * * [misc]simplify: iters left: 2 (33 enodes) * [exit]simplify: Simplified to (/ 1 (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (fabs (cbrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (397 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (* v v)))) (sqrt (+ (* (* v -6) v) 2))) (* (sqrt (cbrt (- 1 (* v v)))) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (fabs (cbrt (- 1 (* v v))))) (/ (/ (/ 4/3 (sqrt (- 1 (* v v)))) (sqrt (+ (* (* v -6) v) 2))) (* (sqrt (cbrt (- 1 (* v v)))) PI)))) * * * * [misc]progress: [ 505 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * * [misc]simplify: iters left: 2 (31 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (395 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (+ (* v (* v -6)) 2))) (* (* (sqrt (- 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (sqrt (- 1 (* v v))))) (/ (/ 4/3 (sqrt (+ (* v (* v -6)) 2))) (* (* (sqrt (- 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 506 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (5 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 1) to (λ (v) (* 1 (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 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 (136 enodes) * * [misc]simplify: iters left: 2 (338 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* 1 (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 507 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * * [misc]simplify: iters left: 2 (31 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (395 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (+ (* v (* v -6)) 2))) (* (* (sqrt (- 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (sqrt (- 1 (* v v))))) (/ (/ 4/3 (sqrt (+ (* v (* v -6)) 2))) (* (* (sqrt (- 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 508 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ 1 1))) * * [misc]simplify: iters left: 6 (5 enodes) * * [misc]simplify: iters left: 5 (9 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 1) to (λ (v) (* 1 (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 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 (136 enodes) * * [misc]simplify: iters left: 2 (338 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* 1 (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 509 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [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 (48 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (167 enodes) * * [misc]simplify: iters left: 2 (463 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (* (sqrt (+ (* (* v -6) v) 2)) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (* (sqrt (+ (* (* v -6) v) 2)) (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 510 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * * [misc]simplify: iters left: 2 (44 enodes) * [exit]simplify: Simplified to (/ 4/3 (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (470 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (sqrt (+ (* v (* v -6)) 2))) (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (/ (/ (/ 1 PI) (sqrt (+ (* v (* v -6)) 2))) (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 511 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * * [misc]simplify: iters left: 2 (33 enodes) * * [misc]simplify: iters left: 1 (41 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (167 enodes) * * [misc]simplify: iters left: 2 (463 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 512 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * [exit]simplify: Simplified to 4/3 * [misc]simplify: Simplified (2 1) to (λ (v) (* 4/3 (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (415 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* 4/3 (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 513 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * * [misc]simplify: iters left: 2 (33 enodes) * * [misc]simplify: iters left: 1 (41 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (167 enodes) * * [misc]simplify: iters left: 2 (463 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 514 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ 4/3 1))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * [exit]simplify: Simplified to 4/3 * [misc]simplify: Simplified (2 1) to (λ (v) (* 4/3 (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (415 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* 4/3 (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 515 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) 1)) * * [misc]simplify: iters left: 5 (4 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 1) to (λ (v) (* 1 (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 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 (136 enodes) * * [misc]simplify: iters left: 2 (338 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* 1 (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 516 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * * [misc]simplify: iters left: 2 (23 enodes) * * [misc]simplify: iters left: 1 (31 enodes) * [exit]simplify: Simplified to (/ 4/3 PI) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 PI) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (130 enodes) * * [misc]simplify: iters left: 1 (157 enodes) * [exit]simplify: Simplified to (/ (/ 1 (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 PI) (/ (/ 1 (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 517 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (112 enodes) * * [misc]simplify: iters left: 2 (170 enodes) * * [misc]simplify: iters left: 1 (250 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (99 enodes) * * [misc]simplify: iters left: 3 (148 enodes) * * [misc]simplify: iters left: 2 (223 enodes) * * [misc]simplify: iters left: 1 (331 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ 1 (pow v 4)))) (sqrt (+ (* (* v v) -6) 2))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (/ (/ (sqrt (+ (* v v) (+ 1 (pow v 4)))) (sqrt (+ (* (* v v) -6) 2))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 518 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (84 enodes) * * [misc]simplify: iters left: 2 (132 enodes) * * [misc]simplify: iters left: 1 (204 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 1 (* v v))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (132 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 519 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (85 enodes) * * [misc]simplify: iters left: 1 (134 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (145 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (/ (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 520 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (145 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 521 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (165 enodes) * * [misc]simplify: iters left: 2 (470 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 522 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (111 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (452 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 523 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (99 enodes) * * [misc]simplify: iters left: 2 (215 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 524 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (160 enodes) * * [misc]simplify: iters left: 1 (299 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 525 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (99 enodes) * * [misc]simplify: iters left: 2 (215 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 526 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (82 enodes) * * [misc]simplify: iters left: 2 (224 enodes) * * [misc]simplify: iters left: 1 (434 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 527 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (179 enodes) * * [misc]simplify: iters left: 1 (438 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 528 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (68 enodes) * * [misc]simplify: iters left: 2 (95 enodes) * * [misc]simplify: iters left: 1 (169 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (111 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (452 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 529 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (93 enodes) * * [misc]simplify: iters left: 1 (160 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 530 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (79 enodes) * * [misc]simplify: iters left: 1 (106 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 531 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (93 enodes) * * [misc]simplify: iters left: 1 (160 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 532 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (86 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 533 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (124 enodes) * * [misc]simplify: iters left: 1 (176 enodes) * [exit]simplify: Simplified to (* (/ (/ 1 (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ 1 (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ 1 (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ 1 (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (397 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 534 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (69 enodes) * [exit]simplify: Simplified to (/ (/ 1 (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (159 enodes) * * [misc]simplify: iters left: 2 (396 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 535 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (73 enodes) * * [misc]simplify: iters left: 2 (97 enodes) * * [misc]simplify: iters left: 1 (136 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (397 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 536 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * * [misc]simplify: iters left: 2 (34 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (335 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 537 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (73 enodes) * * [misc]simplify: iters left: 2 (97 enodes) * * [misc]simplify: iters left: 1 (136 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (397 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 538 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 1))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * * [misc]simplify: iters left: 2 (30 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (335 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 539 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (308 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (474 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 540 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (149 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (169 enodes) * * [misc]simplify: iters left: 2 (481 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 541 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (84 enodes) * * [misc]simplify: iters left: 1 (147 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (474 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 542 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (39 enodes) * * [misc]simplify: iters left: 1 (48 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (411 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 543 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (84 enodes) * * [misc]simplify: iters left: 1 (147 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (474 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 544 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 1))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * * [misc]simplify: iters left: 2 (36 enodes) * * [misc]simplify: iters left: 1 (41 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (411 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 545 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) 1)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (335 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 546 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (139 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (131 enodes) * * [misc]simplify: iters left: 1 (158 enodes) * [exit]simplify: Simplified to (/ (/ 1 (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 547 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (159 enodes) * * [misc]simplify: iters left: 2 (242 enodes) * * [misc]simplify: iters left: 1 (480 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (111 enodes) * * [misc]simplify: iters left: 3 (186 enodes) * * [misc]simplify: iters left: 2 (313 enodes) * * [misc]simplify: iters left: 1 (421 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (pow v 4) (+ (* v v) 1))) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (sqrt (+ (pow v 4) (+ (* v v) 1))) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 548 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (130 enodes) * * [misc]simplify: iters left: 2 (207 enodes) * * [misc]simplify: iters left: 1 (443 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (79 enodes) * * [misc]simplify: iters left: 1 (135 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 549 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (39 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (85 enodes) * * [misc]simplify: iters left: 1 (140 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (* (sqrt (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (* (sqrt (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 550 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (85 enodes) * * [misc]simplify: iters left: 1 (140 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (* (sqrt (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (* (sqrt (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 551 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (83 enodes) * * [misc]simplify: iters left: 2 (185 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * * [misc]simplify: iters left: 1 (455 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 552 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (112 enodes) * * [misc]simplify: iters left: 1 (195 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (451 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))) (sqrt (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))) (sqrt (cbrt (- 1 (* v v))))))) * * * * [misc]progress: [ 553 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (99 enodes) * * [misc]simplify: iters left: 1 (192 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * * [misc]simplify: iters left: 1 (455 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 554 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * * [misc]simplify: iters left: 2 (44 enodes) * * [misc]simplify: iters left: 1 (59 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (421 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 555 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (99 enodes) * * [misc]simplify: iters left: 1 (192 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * * [misc]simplify: iters left: 1 (455 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 556 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * * [misc]simplify: iters left: 2 (41 enodes) * * [misc]simplify: iters left: 1 (57 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (421 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 557 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (93 enodes) * * [misc]simplify: iters left: 1 (162 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * * [misc]simplify: iters left: 1 (455 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 558 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * * [misc]simplify: iters left: 2 (60 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (451 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))) (sqrt (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))) (sqrt (cbrt (- 1 (* v v))))))) * * * * [misc]progress: [ 559 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * * [misc]simplify: iters left: 1 (455 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 560 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * [exit]simplify: Simplified to (sqrt (/ 4/3 PI)) * [misc]simplify: Simplified (2 1) to (λ (v) (* (sqrt (/ 4/3 PI)) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (421 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (sqrt (/ 4/3 PI)) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 561 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * * [misc]simplify: iters left: 1 (455 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 562 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ (sqrt (/ 4/3 PI)) 1))) * * [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 (sqrt (/ 4/3 PI)) * [misc]simplify: Simplified (2 1) to (λ (v) (* (sqrt (/ 4/3 PI)) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (421 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (sqrt (/ 4/3 PI)) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 563 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * [exit]simplify: Simplified to (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (395 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (+ (* v (* v -6)) 2))) (* (* (sqrt (- 1 (* v v))) PI) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 4/3 (sqrt (+ (* v (* v -6)) 2))) (* (* (sqrt (- 1 (* v v))) PI) (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 564 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * [exit]simplify: Simplified to (/ 1 (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (fabs (cbrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (397 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (* v v)))) (sqrt (+ (* (* v -6) v) 2))) (* (sqrt (cbrt (- 1 (* v v)))) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (fabs (cbrt (- 1 (* v v))))) (/ (/ (/ 4/3 (sqrt (- 1 (* v v)))) (sqrt (+ (* (* v -6) v) 2))) (* (sqrt (cbrt (- 1 (* v v)))) PI)))) * * * * [misc]progress: [ 565 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (395 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (+ (* v (* v -6)) 2))) (* (* (sqrt (- 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (sqrt (- 1 (* v v))))) (/ (/ 4/3 (sqrt (+ (* v (* v -6)) 2))) (* (* (sqrt (- 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 566 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (5 enodes) * * [misc]simplify: iters left: 5 (9 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 1) to (λ (v) (* 1 (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 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 (136 enodes) * * [misc]simplify: iters left: 2 (338 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* 1 (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 567 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (395 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (+ (* v (* v -6)) 2))) (* (* (sqrt (- 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (sqrt (- 1 (* v v))))) (/ (/ 4/3 (sqrt (+ (* v (* v -6)) 2))) (* (* (sqrt (- 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 568 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ 1 1))) * * [misc]simplify: iters left: 6 (4 enodes) * * [misc]simplify: iters left: 5 (6 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 1) to (λ (v) (* 1 (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 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 (136 enodes) * * [misc]simplify: iters left: 2 (338 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* 1 (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 569 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * [exit]simplify: Simplified to (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (167 enodes) * * [misc]simplify: iters left: 2 (463 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (* (sqrt (+ (* (* v -6) v) 2)) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (* (sqrt (+ (* (* v -6) v) 2)) (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 570 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * [exit]simplify: Simplified to (/ 4/3 (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (470 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (sqrt (+ (* v (* v -6)) 2))) (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (/ (/ (/ 1 PI) (sqrt (+ (* v (* v -6)) 2))) (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 571 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (167 enodes) * * [misc]simplify: iters left: 2 (463 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 572 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * [exit]simplify: Simplified to 4/3 * [misc]simplify: Simplified (2 1) to (λ (v) (* 4/3 (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (415 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* 4/3 (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 573 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (167 enodes) * * [misc]simplify: iters left: 2 (463 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 574 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ 4/3 1))) * * [misc]simplify: iters left: 6 (5 enodes) * * [misc]simplify: iters left: 5 (8 enodes) * [exit]simplify: Simplified to 4/3 * [misc]simplify: Simplified (2 1) to (λ (v) (* 4/3 (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (415 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* 4/3 (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 575 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 1)) * * [misc]simplify: iters left: 4 (3 enodes) * * [misc]simplify: iters left: 3 (5 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 1) to (λ (v) (* 1 (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 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 (136 enodes) * * [misc]simplify: iters left: 2 (338 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* 1 (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 576 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * [exit]simplify: Simplified to (/ 4/3 PI) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 PI) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (130 enodes) * * [misc]simplify: iters left: 1 (157 enodes) * [exit]simplify: Simplified to (/ (/ 1 (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 PI) (/ (/ 1 (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 577 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (170 enodes) * * [misc]simplify: iters left: 1 (248 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (99 enodes) * * [misc]simplify: iters left: 3 (148 enodes) * * [misc]simplify: iters left: 2 (223 enodes) * * [misc]simplify: iters left: 1 (331 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ 1 (pow v 4)))) (sqrt (+ (* (* v v) -6) 2))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (/ (/ (sqrt (+ (* v v) (+ 1 (pow v 4)))) (sqrt (+ (* (* v v) -6) 2))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 578 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (83 enodes) * * [misc]simplify: iters left: 2 (139 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 1 (* v v))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (132 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 579 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 1) * * [misc]simplify: iters left: 2 (2 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 1) to (λ (v) (* 1 (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 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 (136 enodes) * * [misc]simplify: iters left: 2 (338 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* 1 (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 580 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (18 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (+ 2 (* (* -6 v) v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (+ 2 (* (* -6 v) v)))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (409 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (- 1 (* v v))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (- 1 (* v v))))) * * * * [misc]progress: [ 581 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (+ 2 (* (* v v) -6))) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (138 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (sqrt (+ 2 (* (* v v) -6)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 (sqrt (- 1 (* v v)))) (sqrt (- 1 (* v v)))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (sqrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (18 enodes) * [exit]simplify: Simplified to (/ 1 (- 1 (* v v))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (- 1 (* v v))))) * * * * [misc]progress: [ 582 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (* (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (84 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v))))))) (cbrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (cbrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v))))))) (cbrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (81 enodes) * * [misc]simplify: iters left: 1 (87 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (* v v)))) (cbrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ (* v (* v -6)) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (* (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (cbrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ (* v (* v -6)) 2))))))) * * * * [misc]progress: [ 583 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (56 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (81 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ 2 (* (* -6 v) v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ 2 (* (* -6 v) v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (sqrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (sqrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (81 enodes) * * [misc]simplify: iters left: 1 (87 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (* v v)))) (sqrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ (* v (* v -6)) 2))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (sqrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ (* v (* v -6)) 2))))))) * * * * [misc]progress: [ 584 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (191 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (145 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 585 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (108 enodes) * * [misc]simplify: iters left: 1 (188 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (145 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 586 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (247 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 587 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (441 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (/ (cbrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (/ (cbrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (111 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (452 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (/ (cbrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 588 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (153 enodes) * * [misc]simplify: iters left: 2 (436 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 589 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (114 enodes) * * [misc]simplify: iters left: 2 (424 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 590 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (153 enodes) * * [misc]simplify: iters left: 2 (436 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 591 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (111 enodes) * * [misc]simplify: iters left: 2 (342 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 592 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (326 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (* (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (* (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (* (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 593 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (94 enodes) * * [misc]simplify: iters left: 2 (184 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (111 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (452 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 594 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (179 enodes) * * [misc]simplify: iters left: 1 (491 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* v (* -6 v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* v (* -6 v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* v (* -6 v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 595 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (75 enodes) * * [misc]simplify: iters left: 2 (201 enodes) * * [misc]simplify: iters left: 1 (390 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 596 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (179 enodes) * * [misc]simplify: iters left: 1 (491 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* v (* -6 v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* v (* -6 v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* v (* -6 v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 597 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (76 enodes) * * [misc]simplify: iters left: 2 (185 enodes) * * [misc]simplify: iters left: 1 (405 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 598 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (118 enodes) * * [misc]simplify: iters left: 2 (297 enodes) * [exit]simplify: Simplified to (* (/ (/ 1 (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ 1 (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (397 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 599 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (85 enodes) * * [misc]simplify: iters left: 2 (127 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (fabs (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (fabs (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (159 enodes) * * [misc]simplify: iters left: 2 (396 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (fabs (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 600 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (83 enodes) * * [misc]simplify: iters left: 2 (125 enodes) * * [misc]simplify: iters left: 1 (296 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (* (sqrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (* (sqrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (397 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (* (sqrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 601 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (335 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 602 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (83 enodes) * * [misc]simplify: iters left: 2 (125 enodes) * * [misc]simplify: iters left: 1 (296 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (* (sqrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (* (sqrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (397 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (cbrt (sqrt (+ 2 (* v (* -6 v)))))) (* (sqrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 603 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 1))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (50 enodes) * * [misc]simplify: iters left: 1 (62 enodes) * [exit]simplify: Simplified to (/ 1 (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (335 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 604 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (126 enodes) * * [misc]simplify: iters left: 2 (261 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (* (cbrt (sqrt (+ 2 (* v (* -6 v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (* (cbrt (sqrt (+ 2 (* v (* -6 v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (474 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (* (cbrt (sqrt (+ 2 (* v (* -6 v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 605 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (152 enodes) * * [misc]simplify: iters left: 1 (404 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (169 enodes) * * [misc]simplify: iters left: 2 (481 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 606 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (148 enodes) * * [misc]simplify: iters left: 1 (394 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (* (sqrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (* (sqrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (474 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (* (sqrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 607 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (85 enodes) * * [misc]simplify: iters left: 1 (151 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (411 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (- 1 (* v v))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ 1 PI) (- 1 (* v v))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 608 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (148 enodes) * * [misc]simplify: iters left: 1 (394 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (* (sqrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (* (sqrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (474 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (* (sqrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 609 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 1))) * * [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 (40 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * * [misc]simplify: iters left: 1 (61 enodes) * [exit]simplify: Simplified to (/ 4/3 (* (cbrt (sqrt (+ 2 (* v (* -6 v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (* (cbrt (sqrt (+ 2 (* v (* -6 v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (411 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (- 1 (* v v))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (* (cbrt (sqrt (+ 2 (* v (* -6 v))))) (cbrt (sqrt (+ 2 (* v (* -6 v))))))) (/ (/ (/ 1 PI) (- 1 (* v v))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 610 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) 1)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (88 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (* (/ 1 (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (cbrt (sqrt (+ 2 (* (* v v) -6)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ 1 (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (cbrt (sqrt (+ 2 (* (* v v) -6)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (335 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) 1)) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 611 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (81 enodes) * * [misc]simplify: iters left: 2 (143 enodes) * * [misc]simplify: iters left: 1 (389 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (* (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (* (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (131 enodes) * * [misc]simplify: iters left: 1 (158 enodes) * [exit]simplify: Simplified to (/ (/ 1 (- 1 (* v v))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (* (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (cbrt (sqrt (+ 2 (* (* -6 v) v)))))) (/ (/ 1 (- 1 (* v v))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 612 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (199 enodes) * * [misc]simplify: iters left: 2 (386 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (- 1 (pow v 6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (- 1 (pow v 6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (111 enodes) * * [misc]simplify: iters left: 3 (186 enodes) * * [misc]simplify: iters left: 2 (313 enodes) * * [misc]simplify: iters left: 1 (421 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (pow v 4) (+ (* v v) 1))) (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (- 1 (pow v 6))))) (/ (/ (sqrt (+ (pow v 4) (+ (* v v) 1))) (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 613 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (172 enodes) * * [misc]simplify: iters left: 2 (354 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (79 enodes) * * [misc]simplify: iters left: 1 (135 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 614 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (87 enodes) * * [misc]simplify: iters left: 1 (120 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (145 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* v -6) v) 2)))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* v -6) v) 2)))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 615 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (61 enodes) * * [misc]simplify: iters left: 1 (65 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (145 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* v -6) v) 2)))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* v -6) v) 2)))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 616 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (169 enodes) * * [misc]simplify: iters left: 2 (451 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 617 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (103 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (433 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (111 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (452 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 618 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * * [misc]simplify: iters left: 1 (412 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 619 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (157 enodes) * * [misc]simplify: iters left: 1 (221 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (cbrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (cbrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 620 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * * [misc]simplify: iters left: 1 (412 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 621 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (72 enodes) * * [misc]simplify: iters left: 2 (147 enodes) * * [misc]simplify: iters left: 1 (195 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (cbrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (+ 2 (* (* v v) -6))))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (cbrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 622 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (93 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (339 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 623 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (97 enodes) * * [misc]simplify: iters left: 1 (138 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (111 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (452 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 624 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (68 enodes) * * [misc]simplify: iters left: 2 (95 enodes) * * [misc]simplify: iters left: 1 (136 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 625 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (81 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (cbrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (+ 2 (* (* v v) -6))))) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (cbrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 626 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (68 enodes) * * [misc]simplify: iters left: 2 (95 enodes) * * [misc]simplify: iters left: 1 (136 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 627 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (68 enodes) * * [misc]simplify: iters left: 1 (72 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (cbrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (cbrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 628 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (93 enodes) * * [misc]simplify: iters left: 2 (132 enodes) * * [misc]simplify: iters left: 1 (148 enodes) * [exit]simplify: Simplified to (* (/ (/ 1 (cbrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ 1 (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ 1 (cbrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ 1 (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (397 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (/ 1 (cbrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ 1 (cbrt (sqrt (- 1 (* v v)))))) (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 629 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (68 enodes) * [exit]simplify: Simplified to (/ (/ 1 (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (159 enodes) * * [misc]simplify: iters left: 2 (396 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* v v) -6))))) (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 630 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (75 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (397 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 631 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * * [misc]simplify: iters left: 2 (32 enodes) * * [misc]simplify: iters left: 1 (36 enodes) * [exit]simplify: Simplified to (/ 1 (fabs (cbrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (335 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 632 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (75 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (397 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 633 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 1))) * * [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) * [exit]simplify: Simplified to (/ 1 (fabs (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (335 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 634 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (138 enodes) * * [misc]simplify: iters left: 1 (237 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (fabs (cbrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (fabs (cbrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (474 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (fabs (cbrt (+ 2 (* (* v v) -6))))) (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 635 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (88 enodes) * * [misc]simplify: iters left: 1 (124 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (169 enodes) * * [misc]simplify: iters left: 2 (481 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (cbrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 636 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (122 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (474 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 637 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (41 enodes) * * [misc]simplify: iters left: 1 (50 enodes) * [exit]simplify: Simplified to (/ 4/3 (fabs (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (411 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (cbrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (cbrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 638 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (122 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (474 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 639 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 1))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * * [misc]simplify: iters left: 2 (38 enodes) * * [misc]simplify: iters left: 1 (43 enodes) * [exit]simplify: Simplified to (/ 4/3 (fabs (cbrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (411 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (cbrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (fabs (cbrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (cbrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 640 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) 1)) * * [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 (/ 1 (fabs (cbrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (fabs (cbrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (335 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (fabs (cbrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 641 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (114 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (fabs (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (131 enodes) * * [misc]simplify: iters left: 1 (158 enodes) * [exit]simplify: Simplified to (/ (/ 1 (- 1 (* v v))) (sqrt (cbrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (- 1 (* v v))) (sqrt (cbrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 642 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (161 enodes) * * [misc]simplify: iters left: 2 (245 enodes) * * [misc]simplify: iters left: 1 (400 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (111 enodes) * * [misc]simplify: iters left: 3 (186 enodes) * * [misc]simplify: iters left: 2 (313 enodes) * * [misc]simplify: iters left: 1 (421 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (pow v 4) (+ (* v v) 1))) (sqrt (- 1 (* v v)))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ (sqrt (+ (pow v 4) (+ (* v v) 1))) (sqrt (- 1 (* v v)))) (sqrt (cbrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 643 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (134 enodes) * * [misc]simplify: iters left: 2 (214 enodes) * * [misc]simplify: iters left: 1 (368 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (79 enodes) * * [misc]simplify: iters left: 1 (135 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (cbrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ 2 (* v (* -6 v)))))) (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (cbrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 644 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (85 enodes) * * [misc]simplify: iters left: 1 (134 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (145 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (/ (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 645 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (145 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 646 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (165 enodes) * * [misc]simplify: iters left: 2 (470 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 647 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (111 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (452 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 648 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (99 enodes) * * [misc]simplify: iters left: 2 (215 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 649 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (160 enodes) * * [misc]simplify: iters left: 1 (299 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 650 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (99 enodes) * * [misc]simplify: iters left: 2 (215 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 651 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (82 enodes) * * [misc]simplify: iters left: 2 (224 enodes) * * [misc]simplify: iters left: 1 (434 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 652 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (179 enodes) * * [misc]simplify: iters left: 1 (438 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 653 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (68 enodes) * * [misc]simplify: iters left: 2 (95 enodes) * * [misc]simplify: iters left: 1 (169 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (111 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (452 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 654 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (93 enodes) * * [misc]simplify: iters left: 1 (160 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 655 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (79 enodes) * * [misc]simplify: iters left: 1 (106 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 656 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (93 enodes) * * [misc]simplify: iters left: 1 (160 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 657 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (86 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 658 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (124 enodes) * * [misc]simplify: iters left: 1 (176 enodes) * [exit]simplify: Simplified to (* (/ (/ 1 (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ 1 (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ 1 (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ 1 (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (397 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 659 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (69 enodes) * [exit]simplify: Simplified to (/ (/ 1 (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (159 enodes) * * [misc]simplify: iters left: 2 (396 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 660 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (73 enodes) * * [misc]simplify: iters left: 2 (97 enodes) * * [misc]simplify: iters left: 1 (136 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (397 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 661 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * * [misc]simplify: iters left: 2 (34 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (335 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 662 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (73 enodes) * * [misc]simplify: iters left: 2 (97 enodes) * * [misc]simplify: iters left: 1 (136 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (397 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 663 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 1))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * * [misc]simplify: iters left: 2 (30 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (335 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 664 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (308 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (474 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 665 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (149 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (169 enodes) * * [misc]simplify: iters left: 2 (481 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 666 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (84 enodes) * * [misc]simplify: iters left: 1 (147 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (474 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 667 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (39 enodes) * * [misc]simplify: iters left: 1 (48 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (411 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 668 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (84 enodes) * * [misc]simplify: iters left: 1 (147 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (474 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 669 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 1))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * * [misc]simplify: iters left: 2 (36 enodes) * * [misc]simplify: iters left: 1 (41 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (411 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 670 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) 1)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (335 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 671 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (139 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (131 enodes) * * [misc]simplify: iters left: 1 (158 enodes) * [exit]simplify: Simplified to (/ (/ 1 (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 672 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (159 enodes) * * [misc]simplify: iters left: 2 (242 enodes) * * [misc]simplify: iters left: 1 (480 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (111 enodes) * * [misc]simplify: iters left: 3 (186 enodes) * * [misc]simplify: iters left: 2 (313 enodes) * * [misc]simplify: iters left: 1 (421 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (pow v 4) (+ (* v v) 1))) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (sqrt (+ (pow v 4) (+ (* v v) 1))) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 673 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (130 enodes) * * [misc]simplify: iters left: 2 (207 enodes) * * [misc]simplify: iters left: 1 (443 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (79 enodes) * * [misc]simplify: iters left: 1 (135 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 674 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * * [misc]simplify: iters left: 1 (64 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (85 enodes) * * [misc]simplify: iters left: 1 (140 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (* (sqrt (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (* (sqrt (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 675 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * * [misc]simplify: iters left: 2 (32 enodes) * [exit]simplify: Simplified to (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (85 enodes) * * [misc]simplify: iters left: 1 (140 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (* (sqrt (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (* (sqrt (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 676 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (130 enodes) * * [misc]simplify: iters left: 2 (367 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * * [misc]simplify: iters left: 1 (455 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 677 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (80 enodes) * * [misc]simplify: iters left: 2 (185 enodes) * * [misc]simplify: iters left: 1 (265 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (451 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))) (sqrt (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))) (sqrt (cbrt (- 1 (* v v))))))) * * * * [misc]progress: [ 678 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (166 enodes) * * [misc]simplify: iters left: 1 (316 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * * [misc]simplify: iters left: 1 (455 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 679 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (65 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (421 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 680 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (166 enodes) * * [misc]simplify: iters left: 1 (316 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * * [misc]simplify: iters left: 1 (455 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 681 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (421 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 682 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (101 enodes) * * [misc]simplify: iters left: 1 (202 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * * [misc]simplify: iters left: 1 (455 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 683 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (78 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (451 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))) (sqrt (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))) (sqrt (cbrt (- 1 (* v v))))))) * * * * [misc]progress: [ 684 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (54 enodes) * * [misc]simplify: iters left: 1 (60 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * * [misc]simplify: iters left: 1 (455 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 685 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (sqrt (/ 4/3 PI)) * [misc]simplify: Simplified (2 1) to (λ (v) (* (sqrt (/ 4/3 PI)) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (421 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (sqrt (/ 4/3 PI)) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 686 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (54 enodes) * * [misc]simplify: iters left: 1 (60 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * * [misc]simplify: iters left: 1 (455 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 687 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * [exit]simplify: Simplified to (sqrt (/ 4/3 PI)) * [misc]simplify: Simplified (2 1) to (λ (v) (* (sqrt (/ 4/3 PI)) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (421 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (sqrt (/ 4/3 PI)) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 688 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (49 enodes) * * [misc]simplify: iters left: 1 (74 enodes) * [exit]simplify: Simplified to (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (395 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (+ (* v (* v -6)) 2))) (* (* (sqrt (- 1 (* v v))) PI) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 4/3 (sqrt (+ (* v (* v -6)) 2))) (* (* (sqrt (- 1 (* v v))) PI) (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 689 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * * [misc]simplify: iters left: 2 (33 enodes) * [exit]simplify: Simplified to (/ 1 (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (fabs (cbrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (397 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (* v v)))) (sqrt (+ (* (* v -6) v) 2))) (* (sqrt (cbrt (- 1 (* v v)))) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (fabs (cbrt (- 1 (* v v))))) (/ (/ (/ 4/3 (sqrt (- 1 (* v v)))) (sqrt (+ (* (* v -6) v) 2))) (* (sqrt (cbrt (- 1 (* v v)))) PI)))) * * * * [misc]progress: [ 690 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * * [misc]simplify: iters left: 2 (31 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (395 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (+ (* v (* v -6)) 2))) (* (* (sqrt (- 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (sqrt (- 1 (* v v))))) (/ (/ 4/3 (sqrt (+ (* v (* v -6)) 2))) (* (* (sqrt (- 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 691 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (5 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 1) to (λ (v) (* 1 (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 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 (136 enodes) * * [misc]simplify: iters left: 2 (338 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* 1 (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 692 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * * [misc]simplify: iters left: 2 (31 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (395 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (+ (* v (* v -6)) 2))) (* (* (sqrt (- 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (sqrt (- 1 (* v v))))) (/ (/ 4/3 (sqrt (+ (* v (* v -6)) 2))) (* (* (sqrt (- 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 693 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ 1 1))) * * [misc]simplify: iters left: 6 (5 enodes) * * [misc]simplify: iters left: 5 (9 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 1) to (λ (v) (* 1 (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 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 (136 enodes) * * [misc]simplify: iters left: 2 (338 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* 1 (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 694 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [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 (48 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (167 enodes) * * [misc]simplify: iters left: 2 (463 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (* (sqrt (+ (* (* v -6) v) 2)) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (* (sqrt (+ (* (* v -6) v) 2)) (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 695 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * * [misc]simplify: iters left: 2 (44 enodes) * [exit]simplify: Simplified to (/ 4/3 (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (470 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (sqrt (+ (* v (* v -6)) 2))) (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (/ (/ (/ 1 PI) (sqrt (+ (* v (* v -6)) 2))) (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 696 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * * [misc]simplify: iters left: 2 (33 enodes) * * [misc]simplify: iters left: 1 (41 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (167 enodes) * * [misc]simplify: iters left: 2 (463 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 697 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * [exit]simplify: Simplified to 4/3 * [misc]simplify: Simplified (2 1) to (λ (v) (* 4/3 (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (415 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* 4/3 (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 698 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * * [misc]simplify: iters left: 2 (33 enodes) * * [misc]simplify: iters left: 1 (41 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (167 enodes) * * [misc]simplify: iters left: 2 (463 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 699 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ 4/3 1))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * [exit]simplify: Simplified to 4/3 * [misc]simplify: Simplified (2 1) to (λ (v) (* 4/3 (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (415 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* 4/3 (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 700 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) 1)) * * [misc]simplify: iters left: 5 (4 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 1) to (λ (v) (* 1 (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 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 (136 enodes) * * [misc]simplify: iters left: 2 (338 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* 1 (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 701 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * * [misc]simplify: iters left: 2 (23 enodes) * * [misc]simplify: iters left: 1 (31 enodes) * [exit]simplify: Simplified to (/ 4/3 PI) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 PI) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (130 enodes) * * [misc]simplify: iters left: 1 (157 enodes) * [exit]simplify: Simplified to (/ (/ 1 (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 PI) (/ (/ 1 (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 702 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (112 enodes) * * [misc]simplify: iters left: 2 (170 enodes) * * [misc]simplify: iters left: 1 (250 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (99 enodes) * * [misc]simplify: iters left: 3 (148 enodes) * * [misc]simplify: iters left: 2 (223 enodes) * * [misc]simplify: iters left: 1 (331 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ 1 (pow v 4)))) (sqrt (+ (* (* v v) -6) 2))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (/ (/ (sqrt (+ (* v v) (+ 1 (pow v 4)))) (sqrt (+ (* (* v v) -6) 2))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 703 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt 1) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (84 enodes) * * [misc]simplify: iters left: 2 (132 enodes) * * [misc]simplify: iters left: 1 (204 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 1 (* v v))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (132 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 704 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (85 enodes) * * [misc]simplify: iters left: 1 (134 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (145 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (/ (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 705 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (145 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 706 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (165 enodes) * * [misc]simplify: iters left: 2 (470 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 707 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (111 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (452 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 708 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (99 enodes) * * [misc]simplify: iters left: 2 (215 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 709 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (160 enodes) * * [misc]simplify: iters left: 1 (299 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 710 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (99 enodes) * * [misc]simplify: iters left: 2 (215 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 711 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (82 enodes) * * [misc]simplify: iters left: 2 (224 enodes) * * [misc]simplify: iters left: 1 (434 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 712 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (179 enodes) * * [misc]simplify: iters left: 1 (438 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 713 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (68 enodes) * * [misc]simplify: iters left: 2 (95 enodes) * * [misc]simplify: iters left: 1 (169 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (111 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (452 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 714 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (93 enodes) * * [misc]simplify: iters left: 1 (160 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 715 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (79 enodes) * * [misc]simplify: iters left: 1 (106 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 716 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (93 enodes) * * [misc]simplify: iters left: 1 (160 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 717 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (86 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 718 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (124 enodes) * * [misc]simplify: iters left: 1 (176 enodes) * [exit]simplify: Simplified to (* (/ (/ 1 (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ 1 (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (/ 1 (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ 1 (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (397 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 719 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (69 enodes) * [exit]simplify: Simplified to (/ (/ 1 (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (159 enodes) * * [misc]simplify: iters left: 2 (396 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 720 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (73 enodes) * * [misc]simplify: iters left: 2 (97 enodes) * * [misc]simplify: iters left: 1 (136 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (397 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 721 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * * [misc]simplify: iters left: 2 (34 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (335 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 722 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (73 enodes) * * [misc]simplify: iters left: 2 (97 enodes) * * [misc]simplify: iters left: 1 (136 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (397 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 723 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 1))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * * [misc]simplify: iters left: 2 (30 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (335 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 724 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (308 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (474 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 725 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (149 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (169 enodes) * * [misc]simplify: iters left: 2 (481 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 726 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (84 enodes) * * [misc]simplify: iters left: 1 (147 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (474 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 727 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (39 enodes) * * [misc]simplify: iters left: 1 (48 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (411 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 728 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (84 enodes) * * [misc]simplify: iters left: 1 (147 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (474 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 729 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 1))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * * [misc]simplify: iters left: 2 (36 enodes) * * [misc]simplify: iters left: 1 (41 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (411 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (sqrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 730 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) 1)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (335 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 731 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (139 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (131 enodes) * * [misc]simplify: iters left: 1 (158 enodes) * [exit]simplify: Simplified to (/ (/ 1 (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) (/ (/ 1 (- 1 (* v v))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 732 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (159 enodes) * * [misc]simplify: iters left: 2 (242 enodes) * * [misc]simplify: iters left: 1 (480 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (111 enodes) * * [misc]simplify: iters left: 3 (186 enodes) * * [misc]simplify: iters left: 2 (313 enodes) * * [misc]simplify: iters left: 1 (421 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (pow v 4) (+ (* v v) 1))) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (sqrt (+ (pow v 4) (+ (* v v) 1))) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 733 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (130 enodes) * * [misc]simplify: iters left: 2 (207 enodes) * * [misc]simplify: iters left: 1 (443 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (79 enodes) * * [misc]simplify: iters left: 1 (135 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 734 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (39 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (85 enodes) * * [misc]simplify: iters left: 1 (140 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (* (sqrt (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (* (sqrt (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 735 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (85 enodes) * * [misc]simplify: iters left: 1 (140 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (* (sqrt (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (* (sqrt (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2)))))) * * * * [misc]progress: [ 736 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (83 enodes) * * [misc]simplify: iters left: 2 (185 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * * [misc]simplify: iters left: 1 (455 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 737 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (112 enodes) * * [misc]simplify: iters left: 1 (195 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (451 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))) (sqrt (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))) (sqrt (cbrt (- 1 (* v v))))))) * * * * [misc]progress: [ 738 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (99 enodes) * * [misc]simplify: iters left: 1 (192 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * * [misc]simplify: iters left: 1 (455 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 739 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * * [misc]simplify: iters left: 2 (44 enodes) * * [misc]simplify: iters left: 1 (59 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (421 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 740 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (99 enodes) * * [misc]simplify: iters left: 1 (192 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * * [misc]simplify: iters left: 1 (455 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 741 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * * [misc]simplify: iters left: 2 (41 enodes) * * [misc]simplify: iters left: 1 (57 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (421 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (/ (/ (cbrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 742 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (93 enodes) * * [misc]simplify: iters left: 1 (162 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * * [misc]simplify: iters left: 1 (455 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 743 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * * [misc]simplify: iters left: 2 (60 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (451 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))) (sqrt (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) (sqrt (+ (* v (* v -6)) 2))) (sqrt (cbrt (- 1 (* v v))))))) * * * * [misc]progress: [ 744 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * * [misc]simplify: iters left: 1 (455 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 745 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * [exit]simplify: Simplified to (sqrt (/ 4/3 PI)) * [misc]simplify: Simplified (2 1) to (λ (v) (* (sqrt (/ 4/3 PI)) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (421 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (sqrt (/ 4/3 PI)) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 746 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * * [misc]simplify: iters left: 1 (455 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 747 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ (sqrt (/ 4/3 PI)) 1))) * * [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 (sqrt (/ 4/3 PI)) * [misc]simplify: Simplified (2 1) to (λ (v) (* (sqrt (/ 4/3 PI)) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (421 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (sqrt (/ 4/3 PI)) (/ (/ (sqrt (/ 4/3 PI)) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 748 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * [exit]simplify: Simplified to (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (395 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (+ (* v (* v -6)) 2))) (* (* (sqrt (- 1 (* v v))) PI) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 4/3 (sqrt (+ (* v (* v -6)) 2))) (* (* (sqrt (- 1 (* v v))) PI) (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 749 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * [exit]simplify: Simplified to (/ 1 (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (fabs (cbrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (397 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (* v v)))) (sqrt (+ (* (* v -6) v) 2))) (* (sqrt (cbrt (- 1 (* v v)))) PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (fabs (cbrt (- 1 (* v v))))) (/ (/ (/ 4/3 (sqrt (- 1 (* v v)))) (sqrt (+ (* (* v -6) v) 2))) (* (sqrt (cbrt (- 1 (* v v)))) PI)))) * * * * [misc]progress: [ 750 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (395 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (+ (* v (* v -6)) 2))) (* (* (sqrt (- 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (sqrt (- 1 (* v v))))) (/ (/ 4/3 (sqrt (+ (* v (* v -6)) 2))) (* (* (sqrt (- 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 751 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (5 enodes) * * [misc]simplify: iters left: 5 (9 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 1) to (λ (v) (* 1 (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 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 (136 enodes) * * [misc]simplify: iters left: 2 (338 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* 1 (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 752 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (395 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (+ (* v (* v -6)) 2))) (* (* (sqrt (- 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (sqrt (- 1 (* v v))))) (/ (/ 4/3 (sqrt (+ (* v (* v -6)) 2))) (* (* (sqrt (- 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 753 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ 1 1))) * * [misc]simplify: iters left: 6 (4 enodes) * * [misc]simplify: iters left: 5 (6 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 1) to (λ (v) (* 1 (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 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 (136 enodes) * * [misc]simplify: iters left: 2 (338 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* 1 (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 754 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * [exit]simplify: Simplified to (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (167 enodes) * * [misc]simplify: iters left: 2 (463 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (* (sqrt (+ (* (* v -6) v) 2)) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (* (sqrt (+ (* (* v -6) v) 2)) (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 755 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * [exit]simplify: Simplified to (/ 4/3 (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (470 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (sqrt (+ (* v (* v -6)) 2))) (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (/ (/ (/ 1 PI) (sqrt (+ (* v (* v -6)) 2))) (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 756 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (167 enodes) * * [misc]simplify: iters left: 2 (463 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 757 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * [exit]simplify: Simplified to 4/3 * [misc]simplify: Simplified (2 1) to (λ (v) (* 4/3 (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (415 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* 4/3 (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 758 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (167 enodes) * * [misc]simplify: iters left: 2 (463 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (/ (/ (/ 1 PI) (sqrt (- 1 (* v v)))) (* (sqrt (+ (* (* v -6) v) 2)) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 759 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ 4/3 1))) * * [misc]simplify: iters left: 6 (5 enodes) * * [misc]simplify: iters left: 5 (8 enodes) * [exit]simplify: Simplified to 4/3 * [misc]simplify: Simplified (2 1) to (λ (v) (* 4/3 (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (415 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* 4/3 (/ (/ (/ 1 PI) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))))) * * * * [misc]progress: [ 760 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 1)) * * [misc]simplify: iters left: 4 (3 enodes) * * [misc]simplify: iters left: 3 (5 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 1) to (λ (v) (* 1 (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 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 (136 enodes) * * [misc]simplify: iters left: 2 (338 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* 1 (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 761 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * [exit]simplify: Simplified to (/ 4/3 PI) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 PI) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (130 enodes) * * [misc]simplify: iters left: 1 (157 enodes) * [exit]simplify: Simplified to (/ (/ 1 (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 PI) (/ (/ 1 (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 762 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (170 enodes) * * [misc]simplify: iters left: 1 (248 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (99 enodes) * * [misc]simplify: iters left: 3 (148 enodes) * * [misc]simplify: iters left: 2 (223 enodes) * * [misc]simplify: iters left: 1 (331 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ 1 (pow v 4)))) (sqrt (+ (* (* v v) -6) 2))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (/ (/ (sqrt (+ (* v v) (+ 1 (pow v 4)))) (sqrt (+ (* (* v v) -6) 2))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 763 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (83 enodes) * * [misc]simplify: iters left: 2 (139 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 1 (* v v))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (132 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 764 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 1) * * [misc]simplify: iters left: 2 (2 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 1) to (λ (v) (* 1 (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 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 (136 enodes) * * [misc]simplify: iters left: 2 (338 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* 1 (/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 765 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (18 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (+ 2 (* (* -6 v) v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (+ 2 (* (* -6 v) v)))) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (409 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (- 1 (* v v))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (- 1 (* v v))))) * * * * [misc]progress: [ 766 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (+ 2 (* (* v v) -6))) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (138 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (sqrt (+ 2 (* (* v v) -6)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 (sqrt (- 1 (* v v)))) (sqrt (- 1 (* v v)))))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- 1 (* v v)))) (sqrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (18 enodes) * [exit]simplify: Simplified to (/ 1 (- 1 (* v v))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (- 1 (* v v))))) * * * * [misc]progress: [ 767 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (* (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (162 enodes) * * [misc]simplify: iters left: 1 (171 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 6)))) (* (cbrt (* (sqrt (+ (* (* v v) -6) 2)) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)))) (cbrt (* (sqrt (+ (* (* v v) -6) 2)) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (* (cbrt (* (sqrt (+ (* (* v v) -6) 2)) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)))) (cbrt (* (sqrt (+ (* (* v v) -6) 2)) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (121 enodes) * * [misc]simplify: iters left: 3 (222 enodes) * * [misc]simplify: iters left: 2 (402 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (cbrt (/ (sqrt (+ (* (* v v) -6) 2)) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (* (cbrt (* (sqrt (+ (* (* v v) -6) 2)) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)))) (cbrt (* (sqrt (+ (* (* v v) -6) 2)) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)))))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (cbrt (/ (sqrt (+ (* (* v v) -6) 2)) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 768 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (sqrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (128 enodes) * * [misc]simplify: iters left: 2 (150 enodes) * * [misc]simplify: iters left: 1 (159 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (/ (sqrt (+ (* (* v v) -6) 2)) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (/ (sqrt (+ (* (* v v) -6) 2)) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (sqrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (sqrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (121 enodes) * * [misc]simplify: iters left: 3 (222 enodes) * * [misc]simplify: iters left: 2 (402 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (/ (sqrt (+ (* (* v v) -6) 2)) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (/ (sqrt (+ (* (* v v) -6) 2)) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (/ (sqrt (+ (* (* v v) -6) 2)) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 769 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (55 enodes) * * [misc]simplify: iters left: 4 (114 enodes) * * [misc]simplify: iters left: 3 (233 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (sqrt (- 1 (pow (* v v) 3)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (sqrt (- 1 (pow (* v v) 3)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (114 enodes) * * [misc]simplify: iters left: 3 (188 enodes) * * [misc]simplify: iters left: 2 (318 enodes) * * [misc]simplify: iters left: 1 (429 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ (* v v) (+ 1 (pow v 4)))) (/ (cbrt (sqrt (+ (* -6 (* v v)) 2))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (sqrt (- 1 (pow (* v v) 3)))) (/ (sqrt (+ (* v v) (+ 1 (pow v 4)))) (/ (cbrt (sqrt (+ (* -6 (* v v)) 2))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 770 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (171 enodes) * * [misc]simplify: iters left: 2 (270 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 6)))) (* (cbrt (sqrt (+ (* (* -6 v) v) 2))) (cbrt (sqrt (+ (* (* -6 v) v) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 6)))) (* (cbrt (sqrt (+ (* (* -6 v) v) 2))) (cbrt (sqrt (+ (* (* -6 v) v) 2))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (114 enodes) * * [misc]simplify: iters left: 3 (188 enodes) * * [misc]simplify: iters left: 2 (318 enodes) * * [misc]simplify: iters left: 1 (429 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ (* v v) (+ 1 (pow v 4)))) (/ (cbrt (sqrt (+ (* -6 (* v v)) 2))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 6)))) (* (cbrt (sqrt (+ (* (* -6 v) v) 2))) (cbrt (sqrt (+ (* (* -6 v) v) 2))))) (/ (sqrt (+ (* v v) (+ 1 (pow v 4)))) (/ (cbrt (sqrt (+ (* -6 (* v v)) 2))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 771 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (28 enodes) * * [misc]simplify: iters left: 5 (59 enodes) * * [misc]simplify: iters left: 4 (139 enodes) * * [misc]simplify: iters left: 3 (432 enodes) * [exit]simplify: Simplified to (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (- 1 (* v (pow v 5)))))) (* (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (- 1 (* v (pow v 5)))))) (* (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (cbrt (sqrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (- 1 (* v (pow v 5)))))) (* (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (cbrt (sqrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 772 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (28 enodes) * * [misc]simplify: iters left: 5 (56 enodes) * * [misc]simplify: iters left: 4 (116 enodes) * * [misc]simplify: iters left: 3 (305 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (/ (sqrt (- 1 (* (pow v 5) v))) (cbrt (/ 4/3 PI)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (cbrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (/ (sqrt (- 1 (* (pow v 5) v))) (cbrt (/ 4/3 PI)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (cbrt (sqrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (cbrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (/ (sqrt (- 1 (* (pow v 5) v))) (cbrt (/ 4/3 PI)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (cbrt (sqrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 773 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (54 enodes) * * [misc]simplify: iters left: 4 (114 enodes) * * [misc]simplify: iters left: 3 (305 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (- 1 (* (pow v 5) v))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (- 1 (* (pow v 5) v))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (cbrt (sqrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (- 1 (* (pow v 5) v))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (cbrt (sqrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 774 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (98 enodes) * * [misc]simplify: iters left: 3 (212 enodes) * [exit]simplify: Simplified to (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow (* v v) 3)))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow (* v v) 3)))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (205 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (/ (sqrt (- 1 (* v v))) (cbrt (/ 4/3 PI)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow (* v v) 3)))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (/ (sqrt (- 1 (* v v))) (cbrt (/ 4/3 PI)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 775 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (54 enodes) * * [misc]simplify: iters left: 4 (114 enodes) * * [misc]simplify: iters left: 3 (305 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (- 1 (* (pow v 5) v))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (- 1 (* (pow v 5) v))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (cbrt (sqrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (- 1 (* (pow v 5) v))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (cbrt (sqrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 776 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (271 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* (pow v 5) v)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* (pow v 5) v)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (/ 4/3 PI)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (205 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (/ (sqrt (- 1 (* v v))) (cbrt (/ 4/3 PI)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* (pow v 5) v)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (/ 4/3 PI)))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (/ (sqrt (- 1 (* v v))) (cbrt (/ 4/3 PI)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 777 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (54 enodes) * * [misc]simplify: iters left: 4 (110 enodes) * * [misc]simplify: iters left: 3 (280 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (- 1 (* (pow v 5) v))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (- 1 (* (pow v 5) v))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (cbrt (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (- 1 (* (pow v 5) v))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (cbrt (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 778 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (53 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (227 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (sqrt (- 1 (* (pow v 5) v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (sqrt (- 1 (* (pow v 5) v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (cbrt (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (sqrt (- 1 (* (pow v 5) v))))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (cbrt (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 779 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (101 enodes) * * [misc]simplify: iters left: 3 (227 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow (* v v) 3)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow (* v v) 3)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (cbrt (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow (* v v) 3)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (cbrt (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 780 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (85 enodes) * * [misc]simplify: iters left: 3 (179 enodes) * * [misc]simplify: iters left: 2 (360 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (sqrt (- 1 (pow v 6))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (sqrt (- 1 (pow v 6))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (205 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (/ (sqrt (- 1 (* v v))) (sqrt (/ 4/3 PI)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (sqrt (- 1 (pow v 6))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (/ (sqrt (- 1 (* v v))) (sqrt (/ 4/3 PI)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 781 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (101 enodes) * * [misc]simplify: iters left: 3 (227 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow (* v v) 3)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow (* v v) 3)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (cbrt (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow (* v v) 3)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (cbrt (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 782 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (189 enodes) * * [misc]simplify: iters left: 2 (352 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (205 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (/ (sqrt (- 1 (* v v))) (sqrt (/ 4/3 PI)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (/ (sqrt (- 1 (* v v))) (sqrt (/ 4/3 PI)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 783 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (106 enodes) * * [misc]simplify: iters left: 3 (253 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (- 1 (* (pow v 5) v)))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (* (pow v 5) v)))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (127 enodes) * * [misc]simplify: iters left: 3 (248 enodes) * * [misc]simplify: iters left: 2 (454 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (* (pow v 5) v)))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))))) * * * * [misc]progress: [ 784 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (99 enodes) * * [misc]simplify: iters left: 3 (212 enodes) * * [misc]simplify: iters left: 2 (437 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (127 enodes) * * [misc]simplify: iters left: 3 (248 enodes) * * [misc]simplify: iters left: 2 (454 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (cbrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (cbrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))))) * * * * [misc]progress: [ 785 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (212 enodes) * * [misc]simplify: iters left: 2 (401 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (127 enodes) * * [misc]simplify: iters left: 3 (248 enodes) * * [misc]simplify: iters left: 2 (454 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))))) * * * * [misc]progress: [ 786 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (149 enodes) * * [misc]simplify: iters left: 2 (206 enodes) * * [misc]simplify: iters left: 1 (318 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (269 enodes) * * [misc]simplify: iters left: 2 (458 enodes) * [exit]simplify: Simplified to (/ (* (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 1 (+ (pow v 4) (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (* (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 1 (+ (pow v 4) (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 787 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (212 enodes) * * [misc]simplify: iters left: 2 (401 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (127 enodes) * * [misc]simplify: iters left: 3 (248 enodes) * * [misc]simplify: iters left: 2 (454 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (sqrt (- 1 (* v v))))) (/ (cbrt (sqrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))))) * * * * [misc]progress: [ 788 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 1))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (186 enodes) * * [misc]simplify: iters left: 1 (260 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (269 enodes) * * [misc]simplify: iters left: 2 (458 enodes) * [exit]simplify: Simplified to (/ (* (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 1 (+ (pow v 4) (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (* (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 1 (+ (pow v 4) (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 789 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (275 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (* (pow v 5) v)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (* (pow v 5) v)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (286 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (cbrt (sqrt (+ (* -6 (* v v)) 2))) (* PI (cbrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (* (pow v 5) v)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (cbrt (sqrt (+ (* -6 (* v v)) 2))) (* PI (cbrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 790 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (100 enodes) * * [misc]simplify: iters left: 3 (226 enodes) * * [misc]simplify: iters left: 2 (410 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (286 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (cbrt (sqrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (cbrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (cbrt (sqrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (cbrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 791 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (98 enodes) * * [misc]simplify: iters left: 3 (224 enodes) * * [misc]simplify: iters left: 2 (407 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (sqrt (sqrt (- 1 (* v v)))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (286 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (cbrt (sqrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (sqrt (sqrt (- 1 (* v v)))))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (cbrt (sqrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 792 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (295 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (cbrt (sqrt (+ (* (* -6 v) v) 2)))) (* (sqrt (- 1 (pow v 6))) (cbrt (sqrt (+ (* (* -6 v) v) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (cbrt (sqrt (+ (* (* -6 v) v) 2)))) (* (sqrt (- 1 (pow v 6))) (cbrt (sqrt (+ (* (* -6 v) v) 2))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (129 enodes) * * [misc]simplify: iters left: 3 (270 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (- 1 (* v v))) PI)) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (cbrt (sqrt (+ (* (* -6 v) v) 2)))) (* (sqrt (- 1 (pow v 6))) (cbrt (sqrt (+ (* (* -6 v) v) 2))))) (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (- 1 (* v v))) PI)) (cbrt (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 793 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (98 enodes) * * [misc]simplify: iters left: 3 (224 enodes) * * [misc]simplify: iters left: 2 (407 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (sqrt (sqrt (- 1 (* v v)))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (286 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (cbrt (sqrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (sqrt (sqrt (- 1 (* v v)))))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (cbrt (sqrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 794 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 1))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (195 enodes) * * [misc]simplify: iters left: 1 (273 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (* (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (* (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (129 enodes) * * [misc]simplify: iters left: 3 (270 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (- 1 (* v v))) PI)) (cbrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (* (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (- 1 (* v v))) PI)) (cbrt (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 795 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) 1)) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (308 enodes) * * [misc]simplify: iters left: 1 (483 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (269 enodes) * * [misc]simplify: iters left: 2 (458 enodes) * [exit]simplify: Simplified to (/ (* (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 1 (+ (pow v 4) (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (cbrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (* (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 1 (+ (pow v 4) (* v v))))) (cbrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 796 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (213 enodes) * * [misc]simplify: iters left: 2 (404 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (cbrt (sqrt (+ (* (* -6 v) v) 2)))) (* (* PI (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (+ (* (* -6 v) v) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (cbrt (sqrt (+ (* (* -6 v) v) 2)))) (* (* PI (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (+ (* (* -6 v) v) 2))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (120 enodes) * * [misc]simplify: iters left: 3 (245 enodes) * * [misc]simplify: iters left: 2 (411 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (cbrt (sqrt (+ (* (* -6 v) v) 2)))) (* (* PI (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (+ (* (* -6 v) v) 2))))) (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 797 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (101 enodes) * * [misc]simplify: iters left: 3 (254 enodes) * [exit]simplify: Simplified to (/ (* (/ 1 (- 1 (* (pow v 3) (pow v 3)))) (/ 4/3 PI)) (* (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (/ 1 (- 1 (* (pow v 3) (pow v 3)))) (/ 4/3 PI)) (* (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (171 enodes) * * [misc]simplify: iters left: 1 (242 enodes) * [exit]simplify: Simplified to (/ (+ 1 (+ (* v v) (pow v 4))) (cbrt (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (/ 1 (- 1 (* (pow v 3) (pow v 3)))) (/ 4/3 PI)) (* (cbrt (sqrt (+ (* v (* -6 v)) 2))) (cbrt (sqrt (+ (* v (* -6 v)) 2))))) (/ (+ 1 (+ (* v v) (pow v 4))) (cbrt (sqrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 798 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (55 enodes) * * [misc]simplify: iters left: 4 (116 enodes) * * [misc]simplify: iters left: 3 (288 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (- 1 (pow (* v v) 3)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (- 1 (pow (* v v) 3)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (135 enodes) * * [misc]simplify: iters left: 2 (211 enodes) * * [misc]simplify: iters left: 1 (266 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ (* v v) 1))) (cbrt (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (- 1 (pow (* v v) 3)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (* (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ (* v v) 1))) (cbrt (sqrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 799 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (162 enodes) * * [misc]simplify: iters left: 2 (273 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (- 1 (pow v 6))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (- 1 (pow v 6))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (114 enodes) * * [misc]simplify: iters left: 3 (188 enodes) * * [misc]simplify: iters left: 2 (318 enodes) * * [misc]simplify: iters left: 1 (429 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ (* v v) (+ 1 (pow v 4)))) (/ (sqrt (cbrt (+ (* -6 (* v v)) 2))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (- 1 (pow v 6))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) (/ (sqrt (+ (* v v) (+ 1 (pow v 4)))) (/ (sqrt (cbrt (+ (* -6 (* v v)) 2))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 800 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (136 enodes) * * [misc]simplify: iters left: 2 (159 enodes) * * [misc]simplify: iters left: 1 (211 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (sqrt (- 1 (pow v 6)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (114 enodes) * * [misc]simplify: iters left: 3 (188 enodes) * * [misc]simplify: iters left: 2 (318 enodes) * * [misc]simplify: iters left: 1 (429 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ (* v v) (+ 1 (pow v 4)))) (/ (sqrt (cbrt (+ (* -6 (* v v)) 2))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ (* v v) (+ 1 (pow v 4)))) (/ (sqrt (cbrt (+ (* -6 (* v v)) 2))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 801 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (28 enodes) * * [misc]simplify: iters left: 5 (58 enodes) * * [misc]simplify: iters left: 4 (120 enodes) * * [misc]simplify: iters left: 3 (313 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (* (fabs (cbrt (+ (* (* -6 v) v) 2))) (sqrt (- 1 (pow (* v v) 3))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (* (fabs (cbrt (+ (* (* -6 v) v) 2))) (sqrt (- 1 (pow (* v v) 3))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (cbrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (* (fabs (cbrt (+ (* (* -6 v) v) 2))) (sqrt (- 1 (pow (* v v) 3))))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (cbrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 802 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (28 enodes) * * [misc]simplify: iters left: 5 (55 enodes) * * [misc]simplify: iters left: 4 (102 enodes) * * [misc]simplify: iters left: 3 (228 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (pow (* v v) 3)))) (fabs (cbrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (pow (* v v) 3)))) (fabs (cbrt (+ (* v (* -6 v)) 2))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (cbrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (pow (* v v) 3)))) (fabs (cbrt (+ (* v (* -6 v)) 2))))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (cbrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 803 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (53 enodes) * * [misc]simplify: iters left: 4 (100 enodes) * * [misc]simplify: iters left: 3 (224 enodes) * [exit]simplify: Simplified to (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* (pow v 5) v)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* (pow v 5) v)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (cbrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* (pow v 5) v)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (cbrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 804 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (277 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (205 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (/ (sqrt (- 1 (* v v))) (cbrt (/ 4/3 PI)))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (/ (sqrt (- 1 (* v v))) (cbrt (/ 4/3 PI)))) (sqrt (cbrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 805 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (53 enodes) * * [misc]simplify: iters left: 4 (100 enodes) * * [misc]simplify: iters left: 3 (224 enodes) * [exit]simplify: Simplified to (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* (pow v 5) v)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* (pow v 5) v)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (cbrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* (pow v 5) v)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (cbrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 806 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (24 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 (337 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ (* (* -6 v) v) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (205 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (/ (sqrt (- 1 (* v v))) (cbrt (/ 4/3 PI)))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ (* (* -6 v) v) 2)))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (/ (sqrt (- 1 (* v v))) (cbrt (/ 4/3 PI)))) (sqrt (cbrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 807 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (53 enodes) * * [misc]simplify: iters left: 4 (98 enodes) * * [misc]simplify: iters left: 3 (219 enodes) * * [misc]simplify: iters left: 2 (465 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (cbrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (cbrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (cbrt (+ (* (* v -6) v) 2))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (cbrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (cbrt (+ (* (* v -6) v) 2))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 808 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (180 enodes) * * [misc]simplify: iters left: 2 (289 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (cbrt (+ (* (* v -6) v) 2))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (cbrt (+ (* (* v -6) v) 2))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 809 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (180 enodes) * * [misc]simplify: iters left: 2 (290 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (cbrt (+ (* (* v -6) v) 2))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (cbrt (+ (* (* v -6) v) 2))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 810 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (77 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (189 enodes) * * [misc]simplify: iters left: 1 (337 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ (* (* -6 v) v) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (205 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (/ (sqrt (- 1 (* v v))) (sqrt (/ 4/3 PI)))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ (* (* -6 v) v) 2)))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (/ (sqrt (- 1 (* v v))) (sqrt (/ 4/3 PI)))) (sqrt (cbrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 811 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (180 enodes) * * [misc]simplify: iters left: 2 (290 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (cbrt (+ (* (* v -6) v) 2))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (cbrt (+ (* (* v -6) v) 2))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 812 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (152 enodes) * * [misc]simplify: iters left: 2 (209 enodes) * * [misc]simplify: iters left: 1 (310 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (205 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (/ (sqrt (- 1 (* v v))) (sqrt (/ 4/3 PI)))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (/ (sqrt (- 1 (* v v))) (sqrt (/ 4/3 PI)))) (sqrt (cbrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 813 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (200 enodes) * * [misc]simplify: iters left: 2 (367 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (cbrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (cbrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (127 enodes) * * [misc]simplify: iters left: 3 (248 enodes) * * [misc]simplify: iters left: 2 (454 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (cbrt (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (cbrt (sqrt (- 1 (* v v))))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (cbrt (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))))) * * * * [misc]progress: [ 814 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (23 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 (209 enodes) * * [misc]simplify: iters left: 1 (275 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* -6 v) v) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (127 enodes) * * [misc]simplify: iters left: 3 (248 enodes) * * [misc]simplify: iters left: 2 (454 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (cbrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* -6 v) v) 2)))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (cbrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))))) * * * * [misc]progress: [ 815 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (163 enodes) * * [misc]simplify: iters left: 2 (240 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (127 enodes) * * [misc]simplify: iters left: 3 (248 enodes) * * [misc]simplify: iters left: 2 (454 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))))) * * * * [misc]progress: [ 816 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (115 enodes) * * [misc]simplify: iters left: 2 (131 enodes) * * [misc]simplify: iters left: 1 (149 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ (* (* -6 v) v) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (269 enodes) * * [misc]simplify: iters left: 2 (458 enodes) * [exit]simplify: Simplified to (/ (* (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 1 (+ (pow v 4) (* v v))))) (sqrt (cbrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ (* (* -6 v) v) 2)))) (/ (* (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 1 (+ (pow v 4) (* v v))))) (sqrt (cbrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 817 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (163 enodes) * * [misc]simplify: iters left: 2 (240 enodes) * * [misc]simplify: iters left: 1 (406 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (127 enodes) * * [misc]simplify: iters left: 3 (248 enodes) * * [misc]simplify: iters left: 2 (454 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (cbrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))))) * * * * [misc]progress: [ 818 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 1))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (103 enodes) * * [misc]simplify: iters left: 2 (112 enodes) * * [misc]simplify: iters left: 1 (121 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (269 enodes) * * [misc]simplify: iters left: 2 (458 enodes) * [exit]simplify: Simplified to (/ (* (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 1 (+ (pow v 4) (* v v))))) (sqrt (cbrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ (* (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 1 (+ (pow v 4) (* v v))))) (sqrt (cbrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 819 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (95 enodes) * * [misc]simplify: iters left: 3 (214 enodes) * * [misc]simplify: iters left: 2 (366 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (* (fabs (cbrt (+ (* (* -6 v) v) 2))) (sqrt (- 1 (pow v 6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (* (fabs (cbrt (+ (* (* -6 v) v) 2))) (sqrt (- 1 (pow v 6))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (286 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (cbrt (+ (* -6 (* v v)) 2))) (* PI (cbrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (* (fabs (cbrt (+ (* (* -6 v) v) 2))) (sqrt (- 1 (pow v 6))))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (cbrt (+ (* -6 (* v v)) 2))) (* PI (cbrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 820 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (177 enodes) * * [misc]simplify: iters left: 2 (232 enodes) * * [misc]simplify: iters left: 1 (375 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (286 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (cbrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (cbrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (cbrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (cbrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 821 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (175 enodes) * * [misc]simplify: iters left: 2 (230 enodes) * * [misc]simplify: iters left: 1 (369 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (286 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (cbrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (cbrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 822 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (157 enodes) * * [misc]simplify: iters left: 1 (185 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (129 enodes) * * [misc]simplify: iters left: 3 (270 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (- 1 (* v v))) PI)) (sqrt (cbrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (- 1 (* v v))) PI)) (sqrt (cbrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 823 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (175 enodes) * * [misc]simplify: iters left: 2 (230 enodes) * * [misc]simplify: iters left: 1 (369 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (286 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (cbrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (cbrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 824 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 1))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (120 enodes) * * [misc]simplify: iters left: 2 (156 enodes) * * [misc]simplify: iters left: 1 (209 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ (* (* -6 v) v) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (129 enodes) * * [misc]simplify: iters left: 3 (270 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (- 1 (* v v))) PI)) (sqrt (cbrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ (* (* -6 v) v) 2)))) (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (- 1 (* v v))) PI)) (sqrt (cbrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 825 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) 1)) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (120 enodes) * * [misc]simplify: iters left: 1 (128 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (269 enodes) * * [misc]simplify: iters left: 2 (458 enodes) * [exit]simplify: Simplified to (/ (* (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 1 (+ (pow v 4) (* v v))))) (sqrt (cbrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (* (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 1 (+ (pow v 4) (* v v))))) (sqrt (cbrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 826 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (227 enodes) * * [misc]simplify: iters left: 1 (359 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) PI) (fabs (cbrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) PI) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (120 enodes) * * [misc]simplify: iters left: 3 (245 enodes) * * [misc]simplify: iters left: 2 (411 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (- 1 (* v v)))) (sqrt (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) PI) (fabs (cbrt (+ (* v (* -6 v)) 2)))) (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (- 1 (* v v)))) (sqrt (cbrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 827 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (196 enodes) * * [misc]simplify: iters left: 2 (410 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (pow v 6))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (- 1 (pow v 6))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (171 enodes) * * [misc]simplify: iters left: 1 (242 enodes) * [exit]simplify: Simplified to (/ (+ 1 (+ (* v v) (pow v 4))) (sqrt (cbrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (- 1 (pow v 6))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (+ 1 (+ (* v v) (pow v 4))) (sqrt (cbrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 828 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (54 enodes) * * [misc]simplify: iters left: 4 (104 enodes) * * [misc]simplify: iters left: 3 (224 enodes) * * [misc]simplify: iters left: 2 (469 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (135 enodes) * * [misc]simplify: iters left: 2 (211 enodes) * * [misc]simplify: iters left: 1 (266 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ (* v v) 1))) (sqrt (cbrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (* (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ (* v v) 1))) (sqrt (cbrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 829 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (160 enodes) * * [misc]simplify: iters left: 2 (273 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 6))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (114 enodes) * * [misc]simplify: iters left: 3 (188 enodes) * * [misc]simplify: iters left: 2 (318 enodes) * * [misc]simplify: iters left: 1 (429 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ (* v v) (+ 1 (pow v 4)))) (/ (sqrt (sqrt (+ (* -6 (* v v)) 2))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 6))))) (/ (sqrt (+ (* v v) (+ 1 (pow v 4)))) (/ (sqrt (sqrt (+ (* -6 (* v v)) 2))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 830 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (134 enodes) * * [misc]simplify: iters left: 2 (159 enodes) * * [misc]simplify: iters left: 1 (216 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (114 enodes) * * [misc]simplify: iters left: 3 (188 enodes) * * [misc]simplify: iters left: 2 (318 enodes) * * [misc]simplify: iters left: 1 (429 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ (* v v) (+ 1 (pow v 4)))) (/ (sqrt (sqrt (+ (* -6 (* v v)) 2))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* v v) (+ 1 (pow v 4)))) (/ (sqrt (sqrt (+ (* -6 (* v v)) 2))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 831 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (56 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (309 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (* (sqrt (sqrt (+ (* (* v v) -6) 2))) (sqrt (- 1 (pow (* v v) 3))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (* (sqrt (sqrt (+ (* (* v v) -6) 2))) (sqrt (- 1 (pow (* v v) 3))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (sqrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (* (sqrt (sqrt (+ (* (* v v) -6) 2))) (sqrt (- 1 (pow (* v v) 3))))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (sqrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 832 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (53 enodes) * * [misc]simplify: iters left: 4 (100 enodes) * * [misc]simplify: iters left: 3 (224 enodes) * [exit]simplify: Simplified to (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (sqrt (- 1 (* (pow v 5) v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (sqrt (- 1 (* (pow v 5) v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (sqrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (sqrt (- 1 (* (pow v 5) v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (sqrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 833 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (98 enodes) * * [misc]simplify: iters left: 3 (224 enodes) * [exit]simplify: Simplified to (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow (* v v) 3)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow (* v v) 3)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (sqrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow (* v v) 3)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (sqrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 834 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (153 enodes) * * [misc]simplify: iters left: 2 (275 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (205 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (/ (sqrt (- 1 (* v v))) (cbrt (/ 4/3 PI)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (/ (sqrt (- 1 (* v v))) (cbrt (/ 4/3 PI)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 835 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (98 enodes) * * [misc]simplify: iters left: 3 (224 enodes) * [exit]simplify: Simplified to (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow (* v v) 3)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow (* v v) 3)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (sqrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow (* v v) 3)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (sqrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 836 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (214 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* (pow v 5) v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* (pow v 5) v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (205 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (/ (sqrt (- 1 (* v v))) (cbrt (/ 4/3 PI)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* (pow v 5) v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (/ (sqrt (- 1 (* v v))) (cbrt (/ 4/3 PI)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 837 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (96 enodes) * * [misc]simplify: iters left: 3 (215 enodes) * * [misc]simplify: iters left: 2 (458 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (- 1 (pow v 6))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (- 1 (pow v 6))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (- 1 (pow v 6))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 838 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (180 enodes) * * [misc]simplify: iters left: 2 (290 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 839 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (178 enodes) * * [misc]simplify: iters left: 2 (288 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 840 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (362 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (205 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (/ (sqrt (- 1 (* v v))) (sqrt (/ 4/3 PI)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (/ (sqrt (- 1 (* v v))) (sqrt (/ 4/3 PI)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 841 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (178 enodes) * * [misc]simplify: iters left: 2 (288 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 842 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (154 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (327 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (205 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (/ (sqrt (- 1 (* v v))) (sqrt (/ 4/3 PI)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (/ (sqrt (- 1 (* v v))) (sqrt (/ 4/3 PI)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 843 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (216 enodes) * * [misc]simplify: iters left: 2 (361 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* -6 v)) 2))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (127 enodes) * * [misc]simplify: iters left: 3 (248 enodes) * * [misc]simplify: iters left: 2 (454 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (cbrt (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* -6 v)) 2))))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (cbrt (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))))) * * * * [misc]progress: [ 844 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (191 enodes) * * [misc]simplify: iters left: 2 (235 enodes) * * [misc]simplify: iters left: 1 (278 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (127 enodes) * * [misc]simplify: iters left: 3 (248 enodes) * * [misc]simplify: iters left: 2 (454 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (cbrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (cbrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))))) * * * * [misc]progress: [ 845 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (187 enodes) * * [misc]simplify: iters left: 2 (290 enodes) * * [misc]simplify: iters left: 1 (476 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (127 enodes) * * [misc]simplify: iters left: 3 (248 enodes) * * [misc]simplify: iters left: 2 (454 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))))) * * * * [misc]progress: [ 846 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (111 enodes) * * [misc]simplify: iters left: 2 (130 enodes) * * [misc]simplify: iters left: 1 (156 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (269 enodes) * * [misc]simplify: iters left: 2 (458 enodes) * [exit]simplify: Simplified to (/ (* (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 1 (+ (pow v 4) (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (* (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 1 (+ (pow v 4) (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 847 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (187 enodes) * * [misc]simplify: iters left: 2 (290 enodes) * * [misc]simplify: iters left: 1 (476 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (127 enodes) * * [misc]simplify: iters left: 3 (248 enodes) * * [misc]simplify: iters left: 2 (454 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))))) * * * * [misc]progress: [ 848 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 1))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (117 enodes) * * [misc]simplify: iters left: 2 (130 enodes) * * [misc]simplify: iters left: 1 (140 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (269 enodes) * * [misc]simplify: iters left: 2 (458 enodes) * [exit]simplify: Simplified to (/ (* (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 1 (+ (pow v 4) (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (* (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 1 (+ (pow v 4) (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 849 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (212 enodes) * * [misc]simplify: iters left: 2 (372 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (sqrt (- 1 (pow v 6))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (sqrt (- 1 (pow v 6))) (cbrt (sqrt (- 1 (* v v)))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (286 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (sqrt (+ (* -6 (* v v)) 2))) (* PI (cbrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (sqrt (- 1 (pow v 6))) (cbrt (sqrt (- 1 (* v v)))))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (sqrt (+ (* -6 (* v v)) 2))) (* PI (cbrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 850 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (175 enodes) * * [misc]simplify: iters left: 2 (232 enodes) * * [misc]simplify: iters left: 1 (369 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (286 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (sqrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (cbrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (sqrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (cbrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 851 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (173 enodes) * * [misc]simplify: iters left: 2 (228 enodes) * * [misc]simplify: iters left: 1 (373 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (286 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (sqrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (sqrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 852 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (126 enodes) * * [misc]simplify: iters left: 2 (155 enodes) * * [misc]simplify: iters left: 1 (183 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (129 enodes) * * [misc]simplify: iters left: 3 (270 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (- 1 (* v v))) PI)) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (- 1 (* v v))) PI)) (sqrt (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 853 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (173 enodes) * * [misc]simplify: iters left: 2 (228 enodes) * * [misc]simplify: iters left: 1 (373 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (286 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (sqrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (sqrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 854 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 1))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (118 enodes) * * [misc]simplify: iters left: 2 (150 enodes) * * [misc]simplify: iters left: 1 (174 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (129 enodes) * * [misc]simplify: iters left: 3 (270 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (- 1 (* v v))) PI)) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (- 1 (* v v))) PI)) (sqrt (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 855 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) 1)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (117 enodes) * * [misc]simplify: iters left: 1 (124 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (269 enodes) * * [misc]simplify: iters left: 2 (458 enodes) * [exit]simplify: Simplified to (/ (* (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 1 (+ (pow v 4) (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (* (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 1 (+ (pow v 4) (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 856 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (79 enodes) * * [misc]simplify: iters left: 3 (166 enodes) * * [misc]simplify: iters left: 2 (224 enodes) * * [misc]simplify: iters left: 1 (369 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) PI) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) PI) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (120 enodes) * * [misc]simplify: iters left: 3 (245 enodes) * * [misc]simplify: iters left: 2 (411 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) PI) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 857 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (194 enodes) * * [misc]simplify: iters left: 2 (410 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (pow v 6))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (- 1 (pow v 6))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (171 enodes) * * [misc]simplify: iters left: 1 (242 enodes) * [exit]simplify: Simplified to (/ (+ 1 (+ (* v v) (pow v 4))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (- 1 (pow v 6))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (+ 1 (+ (* v v) (pow v 4))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 858 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (101 enodes) * * [misc]simplify: iters left: 3 (221 enodes) * * [misc]simplify: iters left: 2 (466 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (* PI (sqrt (- 1 (pow v 4))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (* PI (sqrt (- 1 (pow v 4))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (135 enodes) * * [misc]simplify: iters left: 2 (211 enodes) * * [misc]simplify: iters left: 1 (266 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ (* v v) 1))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (* PI (sqrt (- 1 (pow v 4))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (* (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ (* v v) 1))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 859 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt 1) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (162 enodes) * * [misc]simplify: iters left: 2 (266 enodes) * * [misc]simplify: iters left: 1 (461 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (- 1 (pow v 6)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (119 enodes) * * [misc]simplify: iters left: 3 (210 enodes) * * [misc]simplify: iters left: 2 (380 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ (* (* v v) -6) 2))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (- 1 (pow v 6)))) (* (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ (* (* v v) -6) 2))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 860 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt 1) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (74 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (187 enodes) * * [misc]simplify: iters left: 1 (198 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 6)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (119 enodes) * * [misc]simplify: iters left: 3 (210 enodes) * * [misc]simplify: iters left: 2 (380 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ (* (* v v) -6) 2))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 6)))) (* (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ (* (* v v) -6) 2))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 861 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (110 enodes) * * [misc]simplify: iters left: 3 (247 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* (pow v 3) (pow v 3))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* (pow v 3) (pow v 3))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (205 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (+ (* (* v v) -6) 2))) (/ (cbrt (sqrt (- 1 (* v v)))) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* (pow v 3) (pow v 3))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (+ (* (* v v) -6) 2))) (/ (cbrt (sqrt (- 1 (* v v)))) (cbrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 862 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (204 enodes) * * [misc]simplify: iters left: 2 (394 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (205 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (+ (* (* v v) -6) 2))) (/ (sqrt (cbrt (- 1 (* v v)))) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (+ (* (* v v) -6) 2))) (/ (sqrt (cbrt (- 1 (* v v)))) (cbrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 863 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (227 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow (* v v) 3)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow (* v v) 3)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (205 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (+ (* (* v v) -6) 2))) (/ (sqrt (sqrt (- 1 (* v v)))) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow (* v v) 3)))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (+ (* (* v v) -6) 2))) (/ (sqrt (sqrt (- 1 (* v v)))) (cbrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 864 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (130 enodes) * * [misc]simplify: iters left: 2 (207 enodes) * * [misc]simplify: iters left: 1 (271 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 6)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (123 enodes) * * [misc]simplify: iters left: 3 (227 enodes) * * [misc]simplify: iters left: 2 (396 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (+ (* (* v -6) v) 2)) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (+ (* (* v -6) v) 2)) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 865 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (227 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow (* v v) 3)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow (* v v) 3)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (205 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (+ (* (* v v) -6) 2))) (/ (sqrt (sqrt (- 1 (* v v)))) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow (* v v) 3)))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (+ (* (* v v) -6) 2))) (/ (sqrt (sqrt (- 1 (* v v)))) (cbrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 866 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (250 enodes) * * [misc]simplify: iters left: 1 (495 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 6)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (123 enodes) * * [misc]simplify: iters left: 3 (227 enodes) * * [misc]simplify: iters left: 2 (396 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (+ (* (* v -6) v) 2)) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (+ (* (* v -6) v) 2)) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 867 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (181 enodes) * * [misc]simplify: iters left: 2 (342 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (205 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (+ (* (* v v) -6) 2))) (/ (cbrt (sqrt (- 1 (* v v)))) (sqrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (+ (* (* v v) -6) 2))) (/ (cbrt (sqrt (- 1 (* v v)))) (sqrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 868 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (165 enodes) * * [misc]simplify: iters left: 2 (256 enodes) * * [misc]simplify: iters left: 1 (399 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (205 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (+ (* (* v v) -6) 2))) (/ (sqrt (cbrt (- 1 (* v v)))) (sqrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (+ (* (* v v) -6) 2))) (/ (sqrt (cbrt (- 1 (* v v)))) (sqrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 869 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (179 enodes) * * [misc]simplify: iters left: 2 (327 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (205 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (+ (* (* v v) -6) 2))) (/ (sqrt (sqrt (- 1 (* v v)))) (sqrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (+ (* (* v v) -6) 2))) (/ (sqrt (sqrt (- 1 (* v v)))) (sqrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 870 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (158 enodes) * * [misc]simplify: iters left: 1 (173 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (123 enodes) * * [misc]simplify: iters left: 3 (227 enodes) * * [misc]simplify: iters left: 2 (396 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (+ (* (* v -6) v) 2)) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (+ (* (* v -6) v) 2)) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 871 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (179 enodes) * * [misc]simplify: iters left: 2 (327 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (205 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (+ (* (* v v) -6) 2))) (/ (sqrt (sqrt (- 1 (* v v)))) (sqrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (+ (* (* v v) -6) 2))) (/ (sqrt (sqrt (- 1 (* v v)))) (sqrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 872 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (142 enodes) * * [misc]simplify: iters left: 1 (152 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (123 enodes) * * [misc]simplify: iters left: 3 (227 enodes) * * [misc]simplify: iters left: 2 (396 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (+ (* (* v -6) v) 2)) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (+ (* (* v -6) v) 2)) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 873 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt 1) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (159 enodes) * * [misc]simplify: iters left: 2 (242 enodes) * * [misc]simplify: iters left: 1 (351 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (269 enodes) * * [misc]simplify: iters left: 2 (458 enodes) * [exit]simplify: Simplified to (* (/ (/ 4/3 PI) (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (+ 1 (+ (pow v 4) (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (/ (/ 4/3 PI) (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (+ 1 (+ (pow v 4) (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 874 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt 1) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (134 enodes) * * [misc]simplify: iters left: 2 (158 enodes) * * [misc]simplify: iters left: 1 (168 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (269 enodes) * * [misc]simplify: iters left: 2 (458 enodes) * [exit]simplify: Simplified to (* (/ (/ 4/3 PI) (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (+ 1 (+ (pow v 4) (* v v)))) (sqrt (cbrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (* (/ (/ 4/3 PI) (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (+ 1 (+ (pow v 4) (* v v)))) (sqrt (cbrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 875 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt 1) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (74 enodes) * * [misc]simplify: iters left: 3 (143 enodes) * * [misc]simplify: iters left: 2 (166 enodes) * * [misc]simplify: iters left: 1 (176 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (269 enodes) * * [misc]simplify: iters left: 2 (458 enodes) * [exit]simplify: Simplified to (* (/ (/ 4/3 PI) (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (+ 1 (+ (pow v 4) (* v v)))) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (* (/ (/ 4/3 PI) (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (+ 1 (+ (pow v 4) (* v v)))) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 876 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt 1) (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (98 enodes) * * [misc]simplify: iters left: 1 (101 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (- 1 (pow v 6)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (129 enodes) * * [misc]simplify: iters left: 3 (253 enodes) * * [misc]simplify: iters left: 2 (436 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) PI) (/ (sqrt (+ (* (* v -6) v) 2)) (/ 4/3 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (- 1 (pow v 6)))) (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) PI) (/ (sqrt (+ (* (* v -6) v) 2)) (/ 4/3 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 877 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt 1) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (74 enodes) * * [misc]simplify: iters left: 3 (143 enodes) * * [misc]simplify: iters left: 2 (166 enodes) * * [misc]simplify: iters left: 1 (176 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (269 enodes) * * [misc]simplify: iters left: 2 (458 enodes) * [exit]simplify: Simplified to (* (/ (/ 4/3 PI) (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (+ 1 (+ (pow v 4) (* v v)))) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (* (/ (/ 4/3 PI) (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (+ 1 (+ (pow v 4) (* v v)))) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 878 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt 1) (/ 1 1))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (84 enodes) * * [misc]simplify: iters left: 2 (90 enodes) * * [misc]simplify: iters left: 1 (93 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (- 1 (pow v 6)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (129 enodes) * * [misc]simplify: iters left: 3 (253 enodes) * * [misc]simplify: iters left: 2 (436 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) PI) (/ (sqrt (+ (* (* v -6) v) 2)) (/ 4/3 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (- 1 (pow v 6)))) (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) PI) (/ (sqrt (+ (* (* v -6) v) 2)) (/ 4/3 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 879 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt 1) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [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 (213 enodes) * * [misc]simplify: iters left: 2 (397 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (129 enodes) * * [misc]simplify: iters left: 3 (270 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ (* -6 (* v v)) 2))) (* PI (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ (* -6 (* v v)) 2))) (* PI (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 880 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt 1) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (223 enodes) * * [misc]simplify: iters left: 1 (310 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (129 enodes) * * [misc]simplify: iters left: 3 (270 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (cbrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (cbrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 881 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt 1) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (77 enodes) * * [misc]simplify: iters left: 3 (156 enodes) * * [misc]simplify: iters left: 2 (221 enodes) * * [misc]simplify: iters left: 1 (290 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (129 enodes) * * [misc]simplify: iters left: 3 (270 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 882 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt 1) (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (114 enodes) * * [misc]simplify: iters left: 1 (121 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (- 1 (pow v 6)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (112 enodes) * * [misc]simplify: iters left: 3 (206 enodes) * * [misc]simplify: iters left: 2 (433 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* PI (sqrt (- 1 (* v v))))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (sqrt (- 1 (pow v 6)))) (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* PI (sqrt (- 1 (* v v))))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 883 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt 1) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (77 enodes) * * [misc]simplify: iters left: 3 (156 enodes) * * [misc]simplify: iters left: 2 (221 enodes) * * [misc]simplify: iters left: 1 (290 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (129 enodes) * * [misc]simplify: iters left: 3 (270 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 884 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt 1) (/ 4/3 1))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (129 enodes) * * [misc]simplify: iters left: 1 (133 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (- 1 (pow v 6)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (112 enodes) * * [misc]simplify: iters left: 3 (206 enodes) * * [misc]simplify: iters left: 2 (433 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* PI (sqrt (- 1 (* v v))))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (sqrt (- 1 (pow v 6)))) (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* PI (sqrt (- 1 (* v v))))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 885 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt 1) 1)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (81 enodes) * * [misc]simplify: iters left: 2 (87 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (- 1 (pow v 6)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (129 enodes) * * [misc]simplify: iters left: 3 (253 enodes) * * [misc]simplify: iters left: 2 (436 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) PI) (/ (sqrt (+ (* (* v -6) v) 2)) (/ 4/3 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (- 1 (pow v 6)))) (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) PI) (/ (sqrt (+ (* (* v -6) v) 2)) (/ 4/3 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 886 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt 1) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (154 enodes) * * [misc]simplify: iters left: 2 (238 enodes) * * [misc]simplify: iters left: 1 (346 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (100 enodes) * * [misc]simplify: iters left: 3 (164 enodes) * * [misc]simplify: iters left: 2 (259 enodes) * * [misc]simplify: iters left: 1 (363 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (+ (pow v 4) (* v v)))) (sqrt (+ (* -6 (* v v)) 2))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (/ (/ (sqrt (+ 1 (+ (pow v 4) (* v v)))) (sqrt (+ (* -6 (* v v)) 2))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 887 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt 1) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (222 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (- 1 (* (pow v 3) (pow v 3)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (- 1 (* (pow v 3) (pow v 3)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (99 enodes) * * [misc]simplify: iters left: 3 (192 enodes) * * [misc]simplify: iters left: 2 (334 enodes) * * [misc]simplify: iters left: 1 (492 enodes) * [exit]simplify: Simplified to (/ (+ 1 (+ (pow v 4) (* v v))) (sqrt (+ (* (* v v) -6) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (- 1 (* (pow v 3) (pow v 3)))) (/ (+ 1 (+ (pow v 4) (* v v))) (sqrt (+ (* (* v v) -6) 2))))) * * * * [misc]progress: [ 888 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt 1) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (217 enodes) * * [misc]simplify: iters left: 2 (472 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (* (sqrt (- 1 (pow v 6))) PI)) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (* (sqrt (- 1 (pow v 6))) PI)) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 1 (* v v))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (131 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* v v))) (/ (sqrt (+ 1 (+ (pow v 4) (* v v)))) (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (* (sqrt (- 1 (pow v 6))) PI)) (* (sqrt (+ 1 (* v v))) (/ (sqrt (+ 1 (+ (pow v 4) (* v v)))) (sqrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 889 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (160 enodes) * * [misc]simplify: iters left: 2 (273 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 6))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (114 enodes) * * [misc]simplify: iters left: 3 (188 enodes) * * [misc]simplify: iters left: 2 (318 enodes) * * [misc]simplify: iters left: 1 (429 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ (* v v) (+ 1 (pow v 4)))) (/ (sqrt (sqrt (+ (* -6 (* v v)) 2))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 6))))) (/ (sqrt (+ (* v v) (+ 1 (pow v 4)))) (/ (sqrt (sqrt (+ (* -6 (* v v)) 2))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 890 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (134 enodes) * * [misc]simplify: iters left: 2 (159 enodes) * * [misc]simplify: iters left: 1 (216 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (114 enodes) * * [misc]simplify: iters left: 3 (188 enodes) * * [misc]simplify: iters left: 2 (318 enodes) * * [misc]simplify: iters left: 1 (429 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ (* v v) (+ 1 (pow v 4)))) (/ (sqrt (sqrt (+ (* -6 (* v v)) 2))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* v v) (+ 1 (pow v 4)))) (/ (sqrt (sqrt (+ (* -6 (* v v)) 2))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 891 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (56 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (309 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (* (sqrt (sqrt (+ (* (* v v) -6) 2))) (sqrt (- 1 (pow (* v v) 3))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (* (sqrt (sqrt (+ (* (* v v) -6) 2))) (sqrt (- 1 (pow (* v v) 3))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (sqrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (* (sqrt (sqrt (+ (* (* v v) -6) 2))) (sqrt (- 1 (pow (* v v) 3))))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (sqrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 892 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (53 enodes) * * [misc]simplify: iters left: 4 (100 enodes) * * [misc]simplify: iters left: 3 (224 enodes) * [exit]simplify: Simplified to (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (sqrt (- 1 (* (pow v 5) v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (sqrt (- 1 (* (pow v 5) v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (sqrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (sqrt (- 1 (* (pow v 5) v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (sqrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 893 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (98 enodes) * * [misc]simplify: iters left: 3 (224 enodes) * [exit]simplify: Simplified to (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow (* v v) 3)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow (* v v) 3)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (sqrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow (* v v) 3)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (sqrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 894 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (153 enodes) * * [misc]simplify: iters left: 2 (275 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (205 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (/ (sqrt (- 1 (* v v))) (cbrt (/ 4/3 PI)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (/ (sqrt (- 1 (* v v))) (cbrt (/ 4/3 PI)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 895 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (98 enodes) * * [misc]simplify: iters left: 3 (224 enodes) * [exit]simplify: Simplified to (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow (* v v) 3)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow (* v v) 3)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (sqrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow (* v v) 3)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (sqrt (+ (* (* v -6) v) 2))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 896 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (214 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* (pow v 5) v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* (pow v 5) v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (205 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (/ (sqrt (- 1 (* v v))) (cbrt (/ 4/3 PI)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* (pow v 5) v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (/ (sqrt (- 1 (* v v))) (cbrt (/ 4/3 PI)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 897 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (96 enodes) * * [misc]simplify: iters left: 3 (215 enodes) * * [misc]simplify: iters left: 2 (458 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (- 1 (pow v 6))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (- 1 (pow v 6))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (- 1 (pow v 6))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 898 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (180 enodes) * * [misc]simplify: iters left: 2 (290 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 899 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (178 enodes) * * [misc]simplify: iters left: 2 (288 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 900 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (362 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (205 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (/ (sqrt (- 1 (* v v))) (sqrt (/ 4/3 PI)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (/ (sqrt (- 1 (* v v))) (sqrt (/ 4/3 PI)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 901 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (178 enodes) * * [misc]simplify: iters left: 2 (288 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 902 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (154 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (327 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (205 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (/ (sqrt (- 1 (* v v))) (sqrt (/ 4/3 PI)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (/ (sqrt (- 1 (* v v))) (sqrt (/ 4/3 PI)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 903 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (216 enodes) * * [misc]simplify: iters left: 2 (361 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* -6 v)) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* -6 v)) 2))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (127 enodes) * * [misc]simplify: iters left: 3 (248 enodes) * * [misc]simplify: iters left: 2 (454 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (cbrt (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* v (* -6 v)) 2))))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (cbrt (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))))) * * * * [misc]progress: [ 904 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (191 enodes) * * [misc]simplify: iters left: 2 (235 enodes) * * [misc]simplify: iters left: 1 (278 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (127 enodes) * * [misc]simplify: iters left: 3 (248 enodes) * * [misc]simplify: iters left: 2 (454 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (cbrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (cbrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))))) * * * * [misc]progress: [ 905 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (187 enodes) * * [misc]simplify: iters left: 2 (290 enodes) * * [misc]simplify: iters left: 1 (476 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (127 enodes) * * [misc]simplify: iters left: 3 (248 enodes) * * [misc]simplify: iters left: 2 (454 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))))) * * * * [misc]progress: [ 906 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (111 enodes) * * [misc]simplify: iters left: 2 (130 enodes) * * [misc]simplify: iters left: 1 (156 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (269 enodes) * * [misc]simplify: iters left: 2 (458 enodes) * [exit]simplify: Simplified to (/ (* (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 1 (+ (pow v 4) (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (* (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 1 (+ (pow v 4) (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 907 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (187 enodes) * * [misc]simplify: iters left: 2 (290 enodes) * * [misc]simplify: iters left: 1 (476 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (127 enodes) * * [misc]simplify: iters left: 3 (248 enodes) * * [misc]simplify: iters left: 2 (454 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (sqrt (+ (* (* v v) -6) 2))) (/ 4/3 PI))))) * * * * [misc]progress: [ 908 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 1))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (117 enodes) * * [misc]simplify: iters left: 2 (130 enodes) * * [misc]simplify: iters left: 1 (140 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (269 enodes) * * [misc]simplify: iters left: 2 (458 enodes) * [exit]simplify: Simplified to (/ (* (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 1 (+ (pow v 4) (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (* (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 1 (+ (pow v 4) (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 909 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (212 enodes) * * [misc]simplify: iters left: 2 (372 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (sqrt (- 1 (pow v 6))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (sqrt (- 1 (pow v 6))) (cbrt (sqrt (- 1 (* v v)))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (286 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (sqrt (+ (* -6 (* v v)) 2))) (* PI (cbrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (* (sqrt (- 1 (pow v 6))) (cbrt (sqrt (- 1 (* v v)))))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (sqrt (+ (* -6 (* v v)) 2))) (* PI (cbrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 910 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (175 enodes) * * [misc]simplify: iters left: 2 (232 enodes) * * [misc]simplify: iters left: 1 (369 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (286 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (sqrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (cbrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (sqrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (cbrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 911 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (173 enodes) * * [misc]simplify: iters left: 2 (228 enodes) * * [misc]simplify: iters left: 1 (373 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (286 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (sqrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (sqrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 912 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (126 enodes) * * [misc]simplify: iters left: 2 (155 enodes) * * [misc]simplify: iters left: 1 (183 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (129 enodes) * * [misc]simplify: iters left: 3 (270 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (- 1 (* v v))) PI)) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (- 1 (* v v))) PI)) (sqrt (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 913 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (173 enodes) * * [misc]simplify: iters left: 2 (228 enodes) * * [misc]simplify: iters left: 1 (373 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (286 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (sqrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (sqrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 914 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 1))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (118 enodes) * * [misc]simplify: iters left: 2 (150 enodes) * * [misc]simplify: iters left: 1 (174 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (129 enodes) * * [misc]simplify: iters left: 3 (270 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (- 1 (* v v))) PI)) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* (sqrt (- 1 (* v v))) PI)) (sqrt (sqrt (+ (* (* -6 v) v) 2)))))) * * * * [misc]progress: [ 915 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) 1)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (117 enodes) * * [misc]simplify: iters left: 1 (124 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (269 enodes) * * [misc]simplify: iters left: 2 (458 enodes) * [exit]simplify: Simplified to (/ (* (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 1 (+ (pow v 4) (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (* (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 1 (+ (pow v 4) (* v v))))) (sqrt (sqrt (+ (* (* v -6) v) 2)))))) * * * * [misc]progress: [ 916 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (79 enodes) * * [misc]simplify: iters left: 3 (166 enodes) * * [misc]simplify: iters left: 2 (224 enodes) * * [misc]simplify: iters left: 1 (369 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) PI) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) PI) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (120 enodes) * * [misc]simplify: iters left: 3 (245 enodes) * * [misc]simplify: iters left: 2 (411 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) PI) (sqrt (sqrt (+ (* v (* -6 v)) 2)))) (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))))) * * * * [misc]progress: [ 917 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (194 enodes) * * [misc]simplify: iters left: 2 (410 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (pow v 6))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (- 1 (pow v 6))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (171 enodes) * * [misc]simplify: iters left: 1 (242 enodes) * [exit]simplify: Simplified to (/ (+ 1 (+ (* v v) (pow v 4))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (- 1 (pow v 6))) (sqrt (sqrt (+ (* (* -6 v) v) 2)))) (/ (+ 1 (+ (* v v) (pow v 4))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 918 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (101 enodes) * * [misc]simplify: iters left: 3 (221 enodes) * * [misc]simplify: iters left: 2 (466 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (* PI (sqrt (- 1 (pow v 4))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (* PI (sqrt (- 1 (pow v 4))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (135 enodes) * * [misc]simplify: iters left: 2 (211 enodes) * * [misc]simplify: iters left: 1 (266 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ (* v v) 1))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (* PI (sqrt (- 1 (pow v 4))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (* (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ (* v v) 1))) (sqrt (sqrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 919 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ 1 (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (259 enodes) * * [misc]simplify: iters left: 1 (322 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (119 enodes) * * [misc]simplify: iters left: 3 (210 enodes) * * [misc]simplify: iters left: 2 (380 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ (* (* v v) -6) 2))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (* (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ (* (* v v) -6) 2))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 920 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ 1 (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (134 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (193 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 6)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (119 enodes) * * [misc]simplify: iters left: 3 (210 enodes) * * [misc]simplify: iters left: 2 (380 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ (* (* v v) -6) 2))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 6)))) (* (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ (* (* v v) -6) 2))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 921 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (108 enodes) * * [misc]simplify: iters left: 3 (246 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow (* v v) 3)))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow (* v v) 3)))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (205 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (+ (* (* v v) -6) 2))) (/ (cbrt (sqrt (- 1 (* v v)))) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow (* v v) 3)))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (+ (* (* v v) -6) 2))) (/ (cbrt (sqrt (- 1 (* v v)))) (cbrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 922 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (202 enodes) * * [misc]simplify: iters left: 2 (482 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (205 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (+ (* (* v v) -6) 2))) (/ (sqrt (cbrt (- 1 (* v v)))) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (+ (* (* v v) -6) 2))) (/ (sqrt (cbrt (- 1 (* v v)))) (cbrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 923 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (214 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* (pow v 3) (pow v 3))))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* (pow v 3) (pow v 3))))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (205 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (+ (* (* v v) -6) 2))) (/ (sqrt (sqrt (- 1 (* v v)))) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* (pow v 3) (pow v 3))))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (+ (* (* v v) -6) 2))) (/ (sqrt (sqrt (- 1 (* v v)))) (cbrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 924 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (127 enodes) * * [misc]simplify: iters left: 2 (234 enodes) * * [misc]simplify: iters left: 1 (479 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 6)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (123 enodes) * * [misc]simplify: iters left: 3 (227 enodes) * * [misc]simplify: iters left: 2 (396 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (+ (* (* v -6) v) 2)) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (+ (* (* v -6) v) 2)) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 925 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (214 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* (pow v 3) (pow v 3))))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* (pow v 3) (pow v 3))))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (205 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (+ (* (* v v) -6) 2))) (/ (sqrt (sqrt (- 1 (* v v)))) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (* (pow v 3) (pow v 3))))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (+ (* (* v v) -6) 2))) (/ (sqrt (sqrt (- 1 (* v v)))) (cbrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 926 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (138 enodes) * * [misc]simplify: iters left: 2 (247 enodes) * * [misc]simplify: iters left: 1 (387 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 6)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (123 enodes) * * [misc]simplify: iters left: 3 (227 enodes) * * [misc]simplify: iters left: 2 (396 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (+ (* (* v -6) v) 2)) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (+ (* (* v -6) v) 2)) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 927 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ 1 (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (196 enodes) * * [misc]simplify: iters left: 2 (402 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (205 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (+ (* (* v v) -6) 2))) (/ (cbrt (sqrt (- 1 (* v v)))) (sqrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (+ (* (* v v) -6) 2))) (/ (cbrt (sqrt (- 1 (* v v)))) (sqrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 928 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ 1 (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (159 enodes) * * [misc]simplify: iters left: 2 (245 enodes) * * [misc]simplify: iters left: 1 (370 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (205 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (+ (* (* v v) -6) 2))) (/ (sqrt (cbrt (- 1 (* v v)))) (sqrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (+ (* (* v v) -6) 2))) (/ (sqrt (cbrt (- 1 (* v v)))) (sqrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 929 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ 1 (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (79 enodes) * * [misc]simplify: iters left: 3 (179 enodes) * * [misc]simplify: iters left: 2 (311 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (205 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (+ (* (* v v) -6) 2))) (/ (sqrt (sqrt (- 1 (* v v)))) (sqrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (+ (* (* v v) -6) 2))) (/ (sqrt (sqrt (- 1 (* v v)))) (sqrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 930 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ 1 (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (196 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (123 enodes) * * [misc]simplify: iters left: 3 (227 enodes) * * [misc]simplify: iters left: 2 (396 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (+ (* (* v -6) v) 2)) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (+ (* (* v -6) v) 2)) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 931 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ 1 (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (79 enodes) * * [misc]simplify: iters left: 3 (179 enodes) * * [misc]simplify: iters left: 2 (311 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (205 enodes) * * [misc]simplify: iters left: 2 (332 enodes) * * [misc]simplify: iters left: 1 (420 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (+ (* (* v v) -6) 2))) (/ (sqrt (sqrt (- 1 (* v v)))) (sqrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (sqrt (+ (* v v) (+ (pow v 4) 1))) (sqrt (+ (* (* v v) -6) 2))) (/ (sqrt (sqrt (- 1 (* v v)))) (sqrt (/ 4/3 PI)))))) * * * * [misc]progress: [ 932 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ 1 (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (115 enodes) * * [misc]simplify: iters left: 2 (163 enodes) * * [misc]simplify: iters left: 1 (188 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (123 enodes) * * [misc]simplify: iters left: 3 (227 enodes) * * [misc]simplify: iters left: 2 (396 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (+ (* (* v -6) v) 2)) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (/ (sqrt (+ (* (* v -6) v) 2)) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 933 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ 1 (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (228 enodes) * * [misc]simplify: iters left: 1 (290 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (- 1 (pow v 6))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (- 1 (pow v 6))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (269 enodes) * * [misc]simplify: iters left: 2 (458 enodes) * [exit]simplify: Simplified to (* (/ (/ 4/3 PI) (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (+ 1 (+ (pow v 4) (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (- 1 (pow v 6))))) (* (/ (/ 4/3 PI) (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (+ 1 (+ (pow v 4) (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 934 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ 1 (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (136 enodes) * * [misc]simplify: iters left: 2 (173 enodes) * * [misc]simplify: iters left: 1 (181 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (269 enodes) * * [misc]simplify: iters left: 2 (458 enodes) * [exit]simplify: Simplified to (* (/ (/ 4/3 PI) (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (+ 1 (+ (pow v 4) (* v v)))) (sqrt (cbrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (* (/ (/ 4/3 PI) (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (+ 1 (+ (pow v 4) (* v v)))) (sqrt (cbrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 935 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ 1 (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (132 enodes) * * [misc]simplify: iters left: 2 (162 enodes) * * [misc]simplify: iters left: 1 (166 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (269 enodes) * * [misc]simplify: iters left: 2 (458 enodes) * [exit]simplify: Simplified to (* (/ (/ 4/3 PI) (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (+ 1 (+ (pow v 4) (* v v)))) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (* (/ (/ 4/3 PI) (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (+ 1 (+ (pow v 4) (* v v)))) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 936 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ 1 (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (84 enodes) * * [misc]simplify: iters left: 2 (90 enodes) * * [misc]simplify: iters left: 1 (93 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (- 1 (pow v 6)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (129 enodes) * * [misc]simplify: iters left: 3 (253 enodes) * * [misc]simplify: iters left: 2 (436 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) PI) (/ (sqrt (+ (* (* v -6) v) 2)) (/ 4/3 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (- 1 (pow v 6)))) (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) PI) (/ (sqrt (+ (* (* v -6) v) 2)) (/ 4/3 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 937 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ 1 (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (132 enodes) * * [misc]simplify: iters left: 2 (162 enodes) * * [misc]simplify: iters left: 1 (166 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (132 enodes) * * [misc]simplify: iters left: 3 (269 enodes) * * [misc]simplify: iters left: 2 (458 enodes) * [exit]simplify: Simplified to (* (/ (/ 4/3 PI) (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (+ 1 (+ (pow v 4) (* v v)))) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (* (/ (/ 4/3 PI) (sqrt (+ (* (* v -6) v) 2))) (/ (sqrt (+ 1 (+ (pow v 4) (* v v)))) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 938 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ 1 (/ 1 1))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (78 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (- 1 (pow v 6)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (129 enodes) * * [misc]simplify: iters left: 3 (253 enodes) * * [misc]simplify: iters left: 2 (436 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) PI) (/ (sqrt (+ (* (* v -6) v) 2)) (/ 4/3 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (- 1 (pow v 6)))) (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) PI) (/ (sqrt (+ (* (* v -6) v) 2)) (/ 4/3 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 939 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ 1 (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (186 enodes) * * [misc]simplify: iters left: 2 (367 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (129 enodes) * * [misc]simplify: iters left: 3 (270 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ (* -6 (* v v)) 2))) (* PI (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ (* -6 (* v v)) 2))) (* PI (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 940 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ 1 (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (77 enodes) * * [misc]simplify: iters left: 3 (151 enodes) * * [misc]simplify: iters left: 2 (218 enodes) * * [misc]simplify: iters left: 1 (308 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (129 enodes) * * [misc]simplify: iters left: 3 (270 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (cbrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (fabs (cbrt (- 1 (* v v))))) (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (cbrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 941 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ 1 (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (151 enodes) * * [misc]simplify: iters left: 2 (227 enodes) * * [misc]simplify: iters left: 1 (321 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (129 enodes) * * [misc]simplify: iters left: 3 (270 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 942 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ 1 (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (117 enodes) * * [misc]simplify: iters left: 1 (124 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (- 1 (pow v 6)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (112 enodes) * * [misc]simplify: iters left: 3 (206 enodes) * * [misc]simplify: iters left: 2 (433 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* PI (sqrt (- 1 (* v v))))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (sqrt (- 1 (pow v 6)))) (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* PI (sqrt (- 1 (* v v))))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 943 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ 1 (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (151 enodes) * * [misc]simplify: iters left: 2 (227 enodes) * * [misc]simplify: iters left: 1 (321 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (129 enodes) * * [misc]simplify: iters left: 3 (270 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 6)))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (sqrt (+ (* -6 (* v v)) 2))) (* PI (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 944 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ 1 (/ 4/3 1))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (114 enodes) * * [misc]simplify: iters left: 1 (119 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (- 1 (pow v 6)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (112 enodes) * * [misc]simplify: iters left: 3 (206 enodes) * * [misc]simplify: iters left: 2 (433 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* PI (sqrt (- 1 (* v v))))) (sqrt (+ (* (* v -6) v) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (sqrt (- 1 (pow v 6)))) (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) (* PI (sqrt (- 1 (* v v))))) (sqrt (+ (* (* v -6) v) 2))))) * * * * [misc]progress: [ 945 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ 1 1)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (77 enodes) * * [misc]simplify: iters left: 2 (83 enodes) * * [misc]simplify: iters left: 1 (86 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (- 1 (pow v 6)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (129 enodes) * * [misc]simplify: iters left: 3 (253 enodes) * * [misc]simplify: iters left: 2 (436 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) PI) (/ (sqrt (+ (* (* v -6) v) 2)) (/ 4/3 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (- 1 (pow v 6)))) (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) PI) (/ (sqrt (+ (* (* v -6) v) 2)) (/ 4/3 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 946 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ 1 (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (215 enodes) * * [misc]simplify: iters left: 1 (280 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (100 enodes) * * [misc]simplify: iters left: 3 (164 enodes) * * [misc]simplify: iters left: 2 (259 enodes) * * [misc]simplify: iters left: 1 (363 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (+ (pow v 4) (* v v)))) (sqrt (+ (* -6 (* v v)) 2))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (/ (/ (sqrt (+ 1 (+ (pow v 4) (* v v)))) (sqrt (+ (* -6 (* v v)) 2))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 947 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ 1 (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (79 enodes) * * [misc]simplify: iters left: 3 (206 enodes) * * [misc]simplify: iters left: 2 (465 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (- 1 (pow v 6))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (- 1 (pow v 6))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (99 enodes) * * [misc]simplify: iters left: 3 (192 enodes) * * [misc]simplify: iters left: 2 (334 enodes) * * [misc]simplify: iters left: 1 (492 enodes) * [exit]simplify: Simplified to (/ (+ 1 (+ (pow v 4) (* v v))) (sqrt (+ (* (* v v) -6) 2))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (- 1 (pow v 6))) (/ (+ 1 (+ (pow v 4) (* v v))) (sqrt (+ (* (* v v) -6) 2))))) * * * * [misc]progress: [ 948 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ 1 (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (95 enodes) * * [misc]simplify: iters left: 3 (223 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (- 1 (* (pow v 3) (pow v 3))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (- 1 (* (pow v 3) (pow v 3))))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 1 (* v v))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (131 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (* (sqrt (+ 1 (* v v))) (/ (sqrt (+ 1 (+ (pow v 4) (* v v)))) (sqrt (+ (* -6 (* v v)) 2)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (- 1 (* (pow v 3) (pow v 3))))) (* (sqrt (+ 1 (* v v))) (/ (sqrt (+ 1 (+ (pow v 4) (* v v)))) (sqrt (+ (* -6 (* v v)) 2)))))) * * * * [misc]progress: [ 949 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) 1) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (77 enodes) * * [misc]simplify: iters left: 2 (83 enodes) * * [misc]simplify: iters left: 1 (86 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (- 1 (pow v 6)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (- 1 (pow v 6)))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (129 enodes) * * [misc]simplify: iters left: 3 (253 enodes) * * [misc]simplify: iters left: 2 (436 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) PI) (/ (sqrt (+ (* (* v -6) v) 2)) (/ 4/3 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (- 1 (pow v 6)))) (/ (/ (sqrt (+ 1 (+ (* v v) (pow v 4)))) PI) (/ (sqrt (+ (* (* v -6) v) 2)) (/ 4/3 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 950 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (96 enodes) * * [misc]simplify: iters left: 1 (99 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (+ (* (* -6 v) v) 2))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (+ (* (* -6 v) v) 2))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ 1 (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (/ 1 (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (100 enodes) * * [misc]simplify: iters left: 3 (192 enodes) * * [misc]simplify: iters left: 2 (333 enodes) * * [misc]simplify: iters left: 1 (476 enodes) * [exit]simplify: Simplified to (* (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 1 (+ (* v v) (pow v 4))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 6)))) (sqrt (+ (* (* -6 v) v) 2))) (* (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) (sqrt (+ 1 (+ (* v v) (pow v 4))))))) * * * * [misc]progress: [ 951 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (165 enodes) * * [misc]simplify: iters left: 2 (224 enodes) * * [misc]simplify: iters left: 1 (369 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (sqrt (+ (* (* v v) -6) 2))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (sqrt (+ (* (* v v) -6) 2))) (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (sqrt (- 1 (* v v)))))) * [enter]simplify: Simplifying (/ (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) (sqrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (100 enodes) * * [misc]simplify: iters left: 2 (165 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (+ (pow v 4) (* v v)))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 6)))) (sqrt (+ (* (* v v) -6) 2))) (/ (sqrt (+ 1 (+ (pow v 4) (* v v)))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 952 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (* (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (125 enodes) * * [misc]simplify: iters left: 1 (131 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 4)))) (* (cbrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ (* (* v v) -6) 2)))) (cbrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ (* (* v v) -6) 2)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (* (cbrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ (* (* v v) -6) 2)))) (cbrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ (* (* v v) -6) 2)))))) (/ (sqrt (+ 1 (* v v))) (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (84 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (* v v))) (cbrt (/ (sqrt (+ 2 (* (* -6 v) v))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (* (cbrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ (* (* v v) -6) 2)))) (cbrt (* (/ (sqrt (- 1 (* v v))) (/ 4/3 PI)) (sqrt (+ (* (* v v) -6) 2)))))) (/ (sqrt (+ 1 (* v v))) (cbrt (/ (sqrt (+ 2 (* (* -6 v) v))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 953 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (sqrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (94 enodes) * * [misc]simplify: iters left: 2 (113 enodes) * * [misc]simplify: iters left: 1 (119 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (* (sqrt (+ (* (* v v) -6) 2)) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (* (sqrt (+ (* (* v v) -6) 2)) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI))))) (/ (sqrt (+ 1 (* v v))) (sqrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (sqrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (84 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (* v v))) (sqrt (/ (sqrt (+ 2 (* (* -6 v) v))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (* (sqrt (+ (* (* v v) -6) 2)) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI))))) (/ (sqrt (+ 1 (* v v))) (sqrt (/ (sqrt (+ 2 (* (* -6 v) v))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 954 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (104 enodes) * * [misc]simplify: iters left: 3 (195 enodes) * * [misc]simplify: iters left: 2 (470 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (- 1 (pow v 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (- 1 (pow v 4))))) (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (* v v))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (- 1 (pow v 4))))) (/ (* (sqrt (+ 1 (* v v))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 955 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (135 enodes) * * [misc]simplify: iters left: 2 (232 enodes) * * [misc]simplify: iters left: 1 (469 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 4)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 4)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (* v v))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 4)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (* (sqrt (+ 1 (* v v))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 956 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (55 enodes) * * [misc]simplify: iters left: 4 (129 enodes) * * [misc]simplify: iters left: 3 (400 enodes) * [exit]simplify: Simplified to (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (- 1 (pow v 4))) (cbrt (sqrt (- 1 (* v v)))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (- 1 (pow v 4))) (cbrt (sqrt (- 1 (* v v)))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (- 1 (pow v 4))) (cbrt (sqrt (- 1 (* v v)))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (/ (* (cbrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 957 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (106 enodes) * * [misc]simplify: iters left: 3 (273 enodes) * [exit]simplify: Simplified to (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (sqrt (- 1 (pow v 4)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (sqrt (- 1 (pow v 4)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (sqrt (- 1 (pow v 4)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (/ (* (cbrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 958 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (104 enodes) * * [misc]simplify: iters left: 3 (271 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (sqrt (- 1 (pow v 4))) (sqrt (sqrt (- 1 (* v v)))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (sqrt (- 1 (pow v 4))) (sqrt (sqrt (- 1 (* v v)))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (sqrt (- 1 (pow v 4))) (sqrt (sqrt (- 1 (* v v)))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (/ (* (cbrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 959 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (183 enodes) * [exit]simplify: Simplified to (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (* v v))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (* (sqrt (+ 1 (* v v))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 960 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (104 enodes) * * [misc]simplify: iters left: 3 (271 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (sqrt (- 1 (pow v 4))) (sqrt (sqrt (- 1 (* v v)))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (sqrt (- 1 (pow v 4))) (sqrt (sqrt (- 1 (* v v)))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (sqrt (- 1 (pow v 4))) (sqrt (sqrt (- 1 (* v v)))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (/ (* (cbrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 961 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (243 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (/ 4/3 PI)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (/ 4/3 PI)))) (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (* v v))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (/ 4/3 PI)))) (/ (* (sqrt (+ 1 (* v v))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 962 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (100 enodes) * * [misc]simplify: iters left: 3 (246 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (- 1 (pow v 4))) (cbrt (sqrt (- 1 (* v v)))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (- 1 (pow v 4))) (cbrt (sqrt (- 1 (* v v)))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (/ (* (sqrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (* (sqrt (- 1 (pow v 4))) (cbrt (sqrt (- 1 (* v v)))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (/ (* (sqrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 963 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (193 enodes) * * [misc]simplify: iters left: 2 (463 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (* (sqrt (- 1 (pow v 4))) (fabs (cbrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (* (sqrt (- 1 (pow v 4))) (fabs (cbrt (- 1 (* v v))))))) (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (/ (* (sqrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (* (sqrt (- 1 (pow v 4))) (fabs (cbrt (- 1 (* v v))))))) (/ (/ (* (sqrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 964 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (193 enodes) * * [misc]simplify: iters left: 2 (467 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (/ (* (sqrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (* (sqrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 965 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * * [misc]simplify: iters left: 2 (322 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (* v v))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (* (sqrt (+ 1 (* v v))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 966 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (193 enodes) * * [misc]simplify: iters left: 2 (467 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (/ (* (sqrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (* (sqrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 967 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (160 enodes) * * [misc]simplify: iters left: 2 (321 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (* v v))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (* (sqrt (+ 1 (* v v))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 968 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (96 enodes) * * [misc]simplify: iters left: 3 (226 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (* (sqrt (+ 1 (* v v))) (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (/ (* (sqrt (+ 1 (* v v))) (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 969 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (180 enodes) * * [misc]simplify: iters left: 2 (391 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (* (sqrt (+ 1 (* v v))) (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (/ (* (sqrt (+ 1 (* v v))) (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 970 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (177 enodes) * * [misc]simplify: iters left: 2 (440 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (* (sqrt (+ 1 (* v v))) (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (/ (* (sqrt (+ 1 (* v v))) (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 971 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (103 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (380 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (/ (/ (* 4/3 (sqrt (+ 1 (* v v)))) (* (sqrt (- 1 (* v v))) PI)) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (* 4/3 (sqrt (+ 1 (* v v)))) (* (sqrt (- 1 (* v v))) PI)) (cbrt (sqrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 972 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (177 enodes) * * [misc]simplify: iters left: 2 (440 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (* (sqrt (+ 1 (* v v))) (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (/ (* (sqrt (+ 1 (* v v))) (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 973 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 1))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (117 enodes) * * [misc]simplify: iters left: 2 (151 enodes) * * [misc]simplify: iters left: 1 (237 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 4)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (/ (/ (* 4/3 (sqrt (+ 1 (* v v)))) (* (sqrt (- 1 (* v v))) PI)) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (/ (* 4/3 (sqrt (+ 1 (* v v)))) (* (sqrt (- 1 (* v v))) PI)) (cbrt (sqrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 974 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (241 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))))) (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (284 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))))) (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 975 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (192 enodes) * * [misc]simplify: iters left: 2 (376 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (fabs (cbrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (fabs (cbrt (- 1 (* v v)))))) (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (284 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (fabs (cbrt (- 1 (* v v)))))) (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (cbrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 976 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (188 enodes) * * [misc]simplify: iters left: 2 (364 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (sqrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (sqrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (284 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (sqrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 977 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (268 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (121 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) PI) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) PI) (cbrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 978 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (188 enodes) * * [misc]simplify: iters left: 2 (364 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (sqrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (sqrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (284 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (sqrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 979 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 1))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (116 enodes) * * [misc]simplify: iters left: 2 (158 enodes) * * [misc]simplify: iters left: 1 (233 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (121 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) PI) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) PI) (cbrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 980 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) 1)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (154 enodes) * * [misc]simplify: iters left: 1 (201 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 4)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (/ (/ (* 4/3 (sqrt (+ 1 (* v v)))) (* (sqrt (- 1 (* v v))) PI)) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (/ (* 4/3 (sqrt (+ 1 (* v v)))) (* (sqrt (- 1 (* v v))) PI)) (cbrt (sqrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 981 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (186 enodes) * * [misc]simplify: iters left: 2 (371 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (72 enodes) * * [misc]simplify: iters left: 2 (122 enodes) * * [misc]simplify: iters left: 1 (171 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (cbrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 982 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (55 enodes) * * [misc]simplify: iters left: 4 (116 enodes) * * [misc]simplify: iters left: 3 (286 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (* (sqrt (- 1 (* v (pow v 5)))) PI) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (* (sqrt (- 1 (* v (pow v 5)))) PI) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (131 enodes) * * [misc]simplify: iters left: 2 (211 enodes) * * [misc]simplify: iters left: 1 (248 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ (+ (* v v) 1) (pow v 4))) (sqrt (+ (* v v) 1))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (+ (* (* v v) -6) 2)))) (* (* (sqrt (- 1 (* v (pow v 5)))) PI) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (* (sqrt (+ (+ (* v v) 1) (pow v 4))) (sqrt (+ (* v v) 1))) (cbrt (sqrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 983 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (227 enodes) * [exit]simplify: Simplified to (/ (* (/ 1 (- 1 (pow v 4))) (/ 4/3 PI)) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (/ 1 (- 1 (pow v 4))) (/ 4/3 PI)) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* 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) * * [misc]simplify: iters left: 2 (29 enodes) * [exit]simplify: Simplified to (/ (+ 1 (* v v)) (cbrt (sqrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (/ 1 (- 1 (pow v 4))) (/ 4/3 PI)) (* (cbrt (sqrt (+ (* (* v v) -6) 2))) (cbrt (sqrt (+ (* (* v v) -6) 2))))) (/ (+ 1 (* v v)) (cbrt (sqrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 984 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (130 enodes) * * [misc]simplify: iters left: 2 (242 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 4)))) (/ (fabs (cbrt (+ (* (* v v) -6) 2))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 4)))) (/ (fabs (cbrt (+ (* (* v v) -6) 2))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (* v v))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 4)))) (/ (fabs (cbrt (+ (* (* v v) -6) 2))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) (/ (* (sqrt (+ 1 (* v v))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 985 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (74 enodes) * * [misc]simplify: iters left: 3 (100 enodes) * * [misc]simplify: iters left: 2 (120 enodes) * * [misc]simplify: iters left: 1 (174 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (* v v))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (* (sqrt (+ 1 (* v v))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (cbrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 986 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (54 enodes) * * [misc]simplify: iters left: 4 (110 enodes) * * [misc]simplify: iters left: 3 (279 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (* (fabs (cbrt (+ (* (* v v) -6) 2))) (sqrt (- 1 (pow v 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (* (fabs (cbrt (+ (* (* v v) -6) 2))) (sqrt (- 1 (pow v 4))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (* (fabs (cbrt (+ (* (* v v) -6) 2))) (sqrt (- 1 (pow v 4))))) (/ (/ (* (cbrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 987 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (194 enodes) * [exit]simplify: Simplified to (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (sqrt (- 1 (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (sqrt (- 1 (pow v 4)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (sqrt (- 1 (pow v 4)))) (/ (/ (* (cbrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 988 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (190 enodes) * [exit]simplify: Simplified to (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (* (cbrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 989 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (77 enodes) * * [misc]simplify: iters left: 3 (126 enodes) * * [misc]simplify: iters left: 2 (237 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (* v v))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (* (sqrt (+ 1 (* v v))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 990 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (190 enodes) * [exit]simplify: Simplified to (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (* (cbrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 991 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (85 enodes) * * [misc]simplify: iters left: 3 (186 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (* v v))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (* (sqrt (+ 1 (* v v))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 992 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (183 enodes) * * [misc]simplify: iters left: 2 (426 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (* (sqrt (- 1 (pow v 4))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (* (sqrt (- 1 (pow v 4))) (cbrt (sqrt (- 1 (* v v)))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (/ (* (sqrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (* (sqrt (- 1 (pow v 4))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ (* (sqrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 993 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (148 enodes) * * [misc]simplify: iters left: 2 (258 enodes) * * [misc]simplify: iters left: 1 (487 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (/ (* (sqrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (/ (* (sqrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 994 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (257 enodes) * * [misc]simplify: iters left: 1 (487 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (/ (* (sqrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (/ (* (sqrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 995 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (118 enodes) * * [misc]simplify: iters left: 2 (160 enodes) * * [misc]simplify: iters left: 1 (309 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (* v v))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (* (sqrt (+ 1 (* v v))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 996 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (257 enodes) * * [misc]simplify: iters left: 1 (487 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (/ (* (sqrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (/ (* (sqrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 997 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (77 enodes) * * [misc]simplify: iters left: 3 (121 enodes) * * [misc]simplify: iters left: 2 (171 enodes) * * [misc]simplify: iters left: 1 (267 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (* v v))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (* (sqrt (+ 1 (* v v))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 998 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (166 enodes) * * [misc]simplify: iters left: 2 (321 enodes) * [exit]simplify: Simplified to (/ (* (/ 1 (cbrt (sqrt (- 1 (* v v))))) (/ 1 (cbrt (sqrt (- 1 (* v v)))))) (* (fabs (cbrt (+ (* (* v v) -6) 2))) (sqrt (- 1 (pow v 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (/ 1 (cbrt (sqrt (- 1 (* v v))))) (/ 1 (cbrt (sqrt (- 1 (* v v)))))) (* (fabs (cbrt (+ (* (* v v) -6) 2))) (sqrt (- 1 (pow v 4))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (* (sqrt (+ 1 (* v v))) (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (/ 1 (cbrt (sqrt (- 1 (* v v))))) (/ 1 (cbrt (sqrt (- 1 (* v v)))))) (* (fabs (cbrt (+ (* (* v v) -6) 2))) (sqrt (- 1 (pow v 4))))) (/ (/ (* (sqrt (+ 1 (* v v))) (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 999 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (79 enodes) * * [misc]simplify: iters left: 3 (131 enodes) * * [misc]simplify: iters left: 2 (177 enodes) * * [misc]simplify: iters left: 1 (236 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (* (sqrt (+ 1 (* v v))) (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (/ (* (sqrt (+ 1 (* v v))) (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1000 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (77 enodes) * * [misc]simplify: iters left: 3 (127 enodes) * * [misc]simplify: iters left: 2 (233 enodes) * * [misc]simplify: iters left: 1 (471 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (* (sqrt (+ 1 (* v v))) (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (/ (* (sqrt (+ 1 (* v v))) (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1001 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (86 enodes) * * [misc]simplify: iters left: 2 (102 enodes) * * [misc]simplify: iters left: 1 (125 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (/ (/ (* 4/3 (sqrt (+ 1 (* v v)))) (* (sqrt (- 1 (* v v))) PI)) (sqrt (cbrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (/ (* 4/3 (sqrt (+ 1 (* v v)))) (* (sqrt (- 1 (* v v))) PI)) (sqrt (cbrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 1002 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (77 enodes) * * [misc]simplify: iters left: 3 (127 enodes) * * [misc]simplify: iters left: 2 (233 enodes) * * [misc]simplify: iters left: 1 (471 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (* (sqrt (+ 1 (* v v))) (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (/ (* (sqrt (+ 1 (* v v))) (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1003 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 1))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (83 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (/ (/ (* 4/3 (sqrt (+ 1 (* v v)))) (* (sqrt (- 1 (* v v))) PI)) (sqrt (cbrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (/ (* 4/3 (sqrt (+ 1 (* v v)))) (* (sqrt (- 1 (* v v))) PI)) (sqrt (cbrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 1004 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (85 enodes) * * [misc]simplify: iters left: 3 (182 enodes) * * [misc]simplify: iters left: 2 (339 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (fabs (cbrt (+ (* (* v v) -6) 2))) (sqrt (- 1 (pow v 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (fabs (cbrt (+ (* (* v v) -6) 2))) (sqrt (- 1 (pow v 4))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (284 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (cbrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (fabs (cbrt (+ (* (* v v) -6) 2))) (sqrt (- 1 (pow v 4))))) (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (cbrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 1005 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (200 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (284 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (cbrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (cbrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 1006 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (284 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 1007 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (99 enodes) * * [misc]simplify: iters left: 2 (124 enodes) * * [misc]simplify: iters left: 1 (149 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (121 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) PI) (sqrt (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) PI) (sqrt (cbrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1008 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (284 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (cbrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 1009 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 1))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (93 enodes) * * [misc]simplify: iters left: 2 (126 enodes) * * [misc]simplify: iters left: 1 (170 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (121 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) PI) (sqrt (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) PI) (sqrt (cbrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1010 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) 1)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (77 enodes) * * [misc]simplify: iters left: 2 (80 enodes) * * [misc]simplify: iters left: 1 (85 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (/ (/ (* 4/3 (sqrt (+ 1 (* v v)))) (* (sqrt (- 1 (* v v))) PI)) (sqrt (cbrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (/ (* 4/3 (sqrt (+ 1 (* v v)))) (* (sqrt (- 1 (* v v))) PI)) (sqrt (cbrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 1011 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (196 enodes) * * [misc]simplify: iters left: 1 (323 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (72 enodes) * * [misc]simplify: iters left: 2 (122 enodes) * * [misc]simplify: iters left: 1 (171 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (cbrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (cbrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1012 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (54 enodes) * * [misc]simplify: iters left: 4 (104 enodes) * * [misc]simplify: iters left: 3 (224 enodes) * * [misc]simplify: iters left: 2 (466 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (* (sqrt (- 1 (pow v 6))) PI)) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (* (sqrt (- 1 (pow v 6))) PI)) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (131 enodes) * * [misc]simplify: iters left: 2 (211 enodes) * * [misc]simplify: iters left: 1 (248 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ (+ (* v v) 1) (pow v 4))) (sqrt (+ (* v v) 1))) (sqrt (cbrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (* (sqrt (- 1 (pow v 6))) PI)) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (* (sqrt (+ (+ (* v v) 1) (pow v 4))) (sqrt (+ (* v v) 1))) (sqrt (cbrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 1013 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (167 enodes) * * [misc]simplify: iters left: 2 (382 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (pow v 4))) (fabs (cbrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (- 1 (pow v 4))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* 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) * * [misc]simplify: iters left: 2 (29 enodes) * [exit]simplify: Simplified to (/ (+ 1 (* v v)) (sqrt (cbrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (- 1 (pow v 4))) (fabs (cbrt (+ (* (* v v) -6) 2)))) (/ (+ 1 (* v v)) (sqrt (cbrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 1014 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (126 enodes) * * [misc]simplify: iters left: 2 (234 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 4)))) (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 4)))) (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (* v v))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 4)))) (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) (/ (* (sqrt (+ 1 (* v v))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1015 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (118 enodes) * * [misc]simplify: iters left: 1 (172 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (- 1 (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (- 1 (pow v 4)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (* v v))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (- 1 (pow v 4)))) (/ (* (sqrt (+ 1 (* v v))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1016 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (108 enodes) * * [misc]simplify: iters left: 3 (275 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (* (sqrt (sqrt (+ (* (* v v) -6) 2))) (sqrt (- 1 (pow v 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (* (sqrt (sqrt (+ (* (* v v) -6) 2))) (sqrt (- 1 (pow v 4))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (* (sqrt (sqrt (+ (* (* v v) -6) 2))) (sqrt (- 1 (pow v 4))))) (/ (/ (* (cbrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 1017 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (190 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) (/ (/ (* (cbrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 1018 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (190 enodes) * [exit]simplify: Simplified to (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (* (cbrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 1019 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (393 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (* v v))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (* (sqrt (+ 1 (* v v))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1020 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (190 enodes) * [exit]simplify: Simplified to (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (* (cbrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 1021 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (183 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (* v v))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (* (sqrt (+ 1 (* v v))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1022 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (183 enodes) * * [misc]simplify: iters left: 2 (422 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (* (sqrt (sqrt (+ (* (* v v) -6) 2))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (* (sqrt (sqrt (+ (* (* v v) -6) 2))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (/ (* (sqrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (* (sqrt (sqrt (+ (* (* v v) -6) 2))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))))) (/ (/ (* (sqrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 1023 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (257 enodes) * * [misc]simplify: iters left: 1 (491 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (/ (* (sqrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (* (sqrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 1024 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (79 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (247 enodes) * * [misc]simplify: iters left: 1 (479 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (/ (* (sqrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (* (sqrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 1025 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (114 enodes) * * [misc]simplify: iters left: 2 (152 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (* v v))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (* (sqrt (+ 1 (* v v))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1026 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (79 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (247 enodes) * * [misc]simplify: iters left: 1 (479 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (/ (* (sqrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (* (sqrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 1027 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (125 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (310 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (* v v))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (* (sqrt (+ 1 (* v v))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1028 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (181 enodes) * * [misc]simplify: iters left: 2 (347 enodes) * [exit]simplify: Simplified to (/ (* (/ 1 (cbrt (sqrt (- 1 (* v v))))) (/ 1 (cbrt (sqrt (- 1 (* v v)))))) (* (sqrt (- 1 (pow v 4))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (/ 1 (cbrt (sqrt (- 1 (* v v))))) (/ 1 (cbrt (sqrt (- 1 (* v v)))))) (* (sqrt (- 1 (pow v 4))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (* (sqrt (+ 1 (* v v))) (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (/ 1 (cbrt (sqrt (- 1 (* v v))))) (/ 1 (cbrt (sqrt (- 1 (* v v)))))) (* (sqrt (- 1 (pow v 4))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) (/ (/ (* (sqrt (+ 1 (* v v))) (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1029 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (79 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (233 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (* (sqrt (+ 1 (* v v))) (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (* (sqrt (+ 1 (* v v))) (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1030 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (77 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (233 enodes) * * [misc]simplify: iters left: 1 (381 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (* (sqrt (+ 1 (* v v))) (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (* (sqrt (+ 1 (* v v))) (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1031 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (82 enodes) * * [misc]simplify: iters left: 2 (94 enodes) * * [misc]simplify: iters left: 1 (116 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (/ (/ (* 4/3 (sqrt (+ 1 (* v v)))) (* (sqrt (- 1 (* v v))) PI)) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (* 4/3 (sqrt (+ 1 (* v v)))) (* (sqrt (- 1 (* v v))) PI)) (sqrt (sqrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 1032 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (77 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (233 enodes) * * [misc]simplify: iters left: 1 (381 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (* (sqrt (+ 1 (* v v))) (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (* (sqrt (+ 1 (* v v))) (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1033 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 1))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (96 enodes) * * [misc]simplify: iters left: 1 (103 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (/ (/ (* 4/3 (sqrt (+ 1 (* v v)))) (* (sqrt (- 1 (* v v))) PI)) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (* 4/3 (sqrt (+ 1 (* v v)))) (* (sqrt (- 1 (* v v))) PI)) (sqrt (sqrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 1034 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (178 enodes) * * [misc]simplify: iters left: 2 (327 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (cbrt (sqrt (- 1 (* v v))))) (* (* (sqrt (- 1 (pow v 4))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (cbrt (sqrt (- 1 (* v v))))) (* (* (sqrt (- 1 (pow v 4))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (284 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (cbrt (sqrt (- 1 (* v v))))) (* (* (sqrt (- 1 (pow v 4))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 1035 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (284 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 1036 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (198 enodes) * * [misc]simplify: iters left: 1 (312 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (284 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 1037 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (122 enodes) * * [misc]simplify: iters left: 1 (176 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (121 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) PI) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) PI) (sqrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1038 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (198 enodes) * * [misc]simplify: iters left: 1 (312 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (284 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 1039 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 1))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (114 enodes) * * [misc]simplify: iters left: 1 (129 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (121 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) PI) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) PI) (sqrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1040 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) 1)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (78 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (/ (/ (* 4/3 (sqrt (+ 1 (* v v)))) (* (sqrt (- 1 (* v v))) PI)) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (* 4/3 (sqrt (+ 1 (* v v)))) (* (sqrt (- 1 (* v v))) PI)) (sqrt (sqrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 1041 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (135 enodes) * * [misc]simplify: iters left: 2 (188 enodes) * * [misc]simplify: iters left: 1 (303 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (72 enodes) * * [misc]simplify: iters left: 2 (122 enodes) * * [misc]simplify: iters left: 1 (171 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1042 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (104 enodes) * * [misc]simplify: iters left: 3 (227 enodes) * * [misc]simplify: iters left: 2 (464 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (* PI (sqrt (- 1 (pow v 6))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (* PI (sqrt (- 1 (pow v 6))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (131 enodes) * * [misc]simplify: iters left: 2 (211 enodes) * * [misc]simplify: iters left: 1 (248 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ (+ (* v v) 1) (pow v 4))) (sqrt (+ (* v v) 1))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (* PI (sqrt (- 1 (pow v 6))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (* (sqrt (+ (+ (* v v) 1) (pow v 4))) (sqrt (+ (* v v) 1))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 1043 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (79 enodes) * * [misc]simplify: iters left: 3 (167 enodes) * * [misc]simplify: iters left: 2 (371 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (pow v 4))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (- 1 (pow v 4))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* 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) * * [misc]simplify: iters left: 2 (29 enodes) * [exit]simplify: Simplified to (/ (+ 1 (* v v)) (sqrt (sqrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (- 1 (pow v 4))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (+ 1 (* v v)) (sqrt (sqrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 1044 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt 1) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (74 enodes) * * [misc]simplify: iters left: 3 (132 enodes) * * [misc]simplify: iters left: 2 (226 enodes) * * [misc]simplify: iters left: 1 (337 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (sqrt (- 1 (pow v 4))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (sqrt (- 1 (pow v 4))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (sqrt (- 1 (pow v 4))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 1045 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt 1) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (103 enodes) * * [misc]simplify: iters left: 2 (148 enodes) * * [misc]simplify: iters left: 1 (156 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 4)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 4)))) (* (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 1046 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (100 enodes) * * [misc]simplify: iters left: 3 (198 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (* (/ (sqrt (+ 1 (* v v))) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1047 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * * [misc]simplify: iters left: 2 (354 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (cbrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (cbrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1048 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (193 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1049 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (177 enodes) * * [misc]simplify: iters left: 1 (226 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1050 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (193 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1051 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (305 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1052 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (161 enodes) * * [misc]simplify: iters left: 2 (341 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (cbrt (sqrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (* (/ (sqrt (+ 1 (* v v))) (cbrt (sqrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1053 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (131 enodes) * * [misc]simplify: iters left: 2 (229 enodes) * * [misc]simplify: iters left: 1 (400 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (cbrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (cbrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1054 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (143 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1055 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (95 enodes) * * [misc]simplify: iters left: 2 (128 enodes) * * [misc]simplify: iters left: 1 (140 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1056 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (143 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1057 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (93 enodes) * * [misc]simplify: iters left: 2 (111 enodes) * * [misc]simplify: iters left: 1 (118 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1058 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt 1) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (242 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (- 1 (pow v 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (- 1 (pow v 4))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (262 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (cbrt (sqrt (- 1 (* v v))))) (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (- 1 (pow v 4))))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1059 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt 1) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (131 enodes) * * [misc]simplify: iters left: 1 (138 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (262 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1060 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt 1) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (127 enodes) * * [misc]simplify: iters left: 1 (134 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (262 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1061 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt 1) (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (61 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (- 1 (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (- 1 (pow v 4)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (180 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (/ (/ 4/3 PI) (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (- 1 (pow v 4)))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (/ (/ 4/3 PI) (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1062 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt 1) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (127 enodes) * * [misc]simplify: iters left: 1 (134 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (262 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1063 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt 1) (/ 1 1))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (58 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (- 1 (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (- 1 (pow v 4)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (180 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (/ (/ 4/3 PI) (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (- 1 (pow v 4)))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (/ (/ 4/3 PI) (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1064 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt 1) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (179 enodes) * * [misc]simplify: iters left: 2 (368 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (121 enodes) * * [misc]simplify: iters left: 2 (288 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (cbrt (sqrt (- 1 (* v v))))) (sqrt (+ 2 (* v (* -6 v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (cbrt (sqrt (- 1 (* v v))))) (sqrt (+ 2 (* v (* -6 v))))))) * * * * [misc]progress: [ 1065 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt 1) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (124 enodes) * * [misc]simplify: iters left: 2 (190 enodes) * * [misc]simplify: iters left: 1 (275 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (121 enodes) * * [misc]simplify: iters left: 2 (288 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (cbrt (- 1 (* v v))))) (sqrt (+ 2 (* v (* -6 v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (cbrt (- 1 (* v v))))) (sqrt (+ 2 (* v (* -6 v))))))) * * * * [misc]progress: [ 1066 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt 1) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (250 enodes) * * [misc]simplify: iters left: 1 (396 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (121 enodes) * * [misc]simplify: iters left: 2 (288 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (+ 2 (* v (* -6 v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (+ 2 (* v (* -6 v))))))) * * * * [misc]progress: [ 1067 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt 1) (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (73 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (81 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (- 1 (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (sqrt (- 1 (pow v 4)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (120 enodes) * * [misc]simplify: iters left: 2 (289 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* -6 v) v)))) PI) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (sqrt (- 1 (pow v 4)))) (/ (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* -6 v) v)))) PI))) * * * * [misc]progress: [ 1068 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt 1) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (250 enodes) * * [misc]simplify: iters left: 1 (396 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (121 enodes) * * [misc]simplify: iters left: 2 (288 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (+ 2 (* v (* -6 v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (+ 2 (* v (* -6 v))))))) * * * * [misc]progress: [ 1069 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt 1) (/ 4/3 1))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (75 enodes) * * [misc]simplify: iters left: 2 (90 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (- 1 (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (sqrt (- 1 (pow v 4)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (120 enodes) * * [misc]simplify: iters left: 2 (289 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* -6 v) v)))) PI) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (sqrt (- 1 (pow v 4)))) (/ (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* -6 v) v)))) PI))) * * * * [misc]progress: [ 1070 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt 1) 1)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (58 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (- 1 (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (- 1 (pow v 4)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (180 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (/ (/ 4/3 PI) (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (- 1 (pow v 4)))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (/ (/ 4/3 PI) (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1071 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt 1) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (120 enodes) * * [misc]simplify: iters left: 2 (188 enodes) * * [misc]simplify: iters left: 1 (259 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (71 enodes) * * [misc]simplify: iters left: 2 (108 enodes) * * [misc]simplify: iters left: 1 (157 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* -6 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* -6 (* v v))))))) * * * * [misc]progress: [ 1072 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt 1) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (98 enodes) * * [misc]simplify: iters left: 3 (232 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (- 1 (pow (* v v) 3)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (- 1 (pow (* v v) 3)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (179 enodes) * * [misc]simplify: iters left: 2 (308 enodes) * * [misc]simplify: iters left: 1 (443 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (pow v 4) (+ (* v v) 1))) (/ (sqrt (+ (* v v) 1)) (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (- 1 (pow (* v v) 3)))) (* (sqrt (+ (pow v 4) (+ (* v v) 1))) (/ (sqrt (+ (* v v) 1)) (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1073 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt 1) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (180 enodes) * * [misc]simplify: iters left: 2 (445 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (- 1 (pow v 4))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (- 1 (pow v 4))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 1 (* v v))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (27 enodes) * * [misc]simplify: iters left: 2 (28 enodes) * [exit]simplify: Simplified to (/ (+ 1 (* v v)) (sqrt (+ 2 (* v (* -6 v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (- 1 (pow v 4))) (/ (+ 1 (* v v)) (sqrt (+ 2 (* v (* -6 v))))))) * * * * [misc]progress: [ 1074 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (126 enodes) * * [misc]simplify: iters left: 2 (234 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 4)))) (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 4)))) (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (* v v))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 4)))) (/ (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) (/ (* (sqrt (+ 1 (* v v))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1075 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (118 enodes) * * [misc]simplify: iters left: 1 (172 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (- 1 (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (- 1 (pow v 4)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (* v v))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (- 1 (pow v 4)))) (/ (* (sqrt (+ 1 (* v v))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1076 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (108 enodes) * * [misc]simplify: iters left: 3 (275 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (* (sqrt (sqrt (+ (* (* v v) -6) 2))) (sqrt (- 1 (pow v 4))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (* (sqrt (sqrt (+ (* (* v v) -6) 2))) (sqrt (- 1 (pow v 4))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (* (sqrt (sqrt (+ (* (* v v) -6) 2))) (sqrt (- 1 (pow v 4))))) (/ (/ (* (cbrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 1077 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (190 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (* (/ (cbrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (* (/ (cbrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (/ (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) (/ (/ (* (cbrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 1078 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (190 enodes) * [exit]simplify: Simplified to (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (* (cbrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 1079 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (393 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (* v v))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (* (sqrt (+ 1 (* v v))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1080 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (190 enodes) * [exit]simplify: Simplified to (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (* (cbrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 1081 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (183 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (* v v))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (* (sqrt (+ 1 (* v v))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1082 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (183 enodes) * * [misc]simplify: iters left: 2 (422 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (* (sqrt (sqrt (+ (* (* v v) -6) 2))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (* (sqrt (sqrt (+ (* (* v v) -6) 2))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (/ (* (sqrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (* (sqrt (sqrt (+ (* (* v v) -6) 2))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))))) (/ (/ (* (sqrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 1083 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (257 enodes) * * [misc]simplify: iters left: 1 (491 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (/ (* (sqrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (* (sqrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 1084 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (79 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (247 enodes) * * [misc]simplify: iters left: 1 (479 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (/ (* (sqrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (* (sqrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 1085 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (114 enodes) * * [misc]simplify: iters left: 2 (152 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (* v v))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (* (sqrt (+ 1 (* v v))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1086 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (79 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (247 enodes) * * [misc]simplify: iters left: 1 (479 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (/ (* (sqrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (* (sqrt (/ 4/3 PI)) (sqrt (+ 1 (* v v)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 1087 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (125 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (310 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ 1 (* v v))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (* (sqrt (+ 1 (* v v))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1088 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (181 enodes) * * [misc]simplify: iters left: 2 (347 enodes) * [exit]simplify: Simplified to (/ (* (/ 1 (cbrt (sqrt (- 1 (* v v))))) (/ 1 (cbrt (sqrt (- 1 (* v v)))))) (* (sqrt (- 1 (pow v 4))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (/ 1 (cbrt (sqrt (- 1 (* v v))))) (/ 1 (cbrt (sqrt (- 1 (* v v)))))) (* (sqrt (- 1 (pow v 4))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (* (sqrt (+ 1 (* v v))) (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (/ 1 (cbrt (sqrt (- 1 (* v v))))) (/ 1 (cbrt (sqrt (- 1 (* v v)))))) (* (sqrt (- 1 (pow v 4))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) (/ (/ (* (sqrt (+ 1 (* v v))) (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1089 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (79 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (233 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (* (sqrt (+ 1 (* v v))) (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (* (sqrt (+ 1 (* v v))) (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1090 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (77 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (233 enodes) * * [misc]simplify: iters left: 1 (381 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (* (sqrt (+ 1 (* v v))) (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (* (sqrt (+ 1 (* v v))) (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1091 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (82 enodes) * * [misc]simplify: iters left: 2 (94 enodes) * * [misc]simplify: iters left: 1 (116 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (/ (/ (* 4/3 (sqrt (+ 1 (* v v)))) (* (sqrt (- 1 (* v v))) PI)) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (* 4/3 (sqrt (+ 1 (* v v)))) (* (sqrt (- 1 (* v v))) PI)) (sqrt (sqrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 1092 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (77 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * * [misc]simplify: iters left: 2 (233 enodes) * * [misc]simplify: iters left: 1 (381 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (183 enodes) * * [misc]simplify: iters left: 1 (263 enodes) * [exit]simplify: Simplified to (/ (/ (* (sqrt (+ 1 (* v v))) (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (* (sqrt (+ 1 (* v v))) (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1093 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 1))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (96 enodes) * * [misc]simplify: iters left: 1 (103 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (/ (/ (* 4/3 (sqrt (+ 1 (* v v)))) (* (sqrt (- 1 (* v v))) PI)) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (* 4/3 (sqrt (+ 1 (* v v)))) (* (sqrt (- 1 (* v v))) PI)) (sqrt (sqrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 1094 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (178 enodes) * * [misc]simplify: iters left: 2 (327 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (cbrt (sqrt (- 1 (* v v))))) (* (* (sqrt (- 1 (pow v 4))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (cbrt (sqrt (- 1 (* v v))))) (* (* (sqrt (- 1 (pow v 4))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (284 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (cbrt (sqrt (- 1 (* v v))))) (* (* (sqrt (- 1 (pow v 4))) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2))))) (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (cbrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 1095 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (284 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (cbrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 1096 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (198 enodes) * * [misc]simplify: iters left: 1 (312 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (284 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 1097 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (122 enodes) * * [misc]simplify: iters left: 1 (176 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (121 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) PI) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) PI) (sqrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1098 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (198 enodes) * * [misc]simplify: iters left: 1 (312 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (284 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 1099 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 1))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (114 enodes) * * [misc]simplify: iters left: 1 (129 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (121 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) PI) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) PI) (sqrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1100 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) 1)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (78 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (/ (/ (* 4/3 (sqrt (+ 1 (* v v)))) (* (sqrt (- 1 (* v v))) PI)) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (* 4/3 (sqrt (+ 1 (* v v)))) (* (sqrt (- 1 (* v v))) PI)) (sqrt (sqrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 1101 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (135 enodes) * * [misc]simplify: iters left: 2 (188 enodes) * * [misc]simplify: iters left: 1 (303 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (72 enodes) * * [misc]simplify: iters left: 2 (122 enodes) * * [misc]simplify: iters left: 1 (171 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1102 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (104 enodes) * * [misc]simplify: iters left: 3 (227 enodes) * * [misc]simplify: iters left: 2 (464 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (* PI (sqrt (- 1 (pow v 6))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (* PI (sqrt (- 1 (pow v 6))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (131 enodes) * * [misc]simplify: iters left: 2 (211 enodes) * * [misc]simplify: iters left: 1 (248 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ (+ (* v v) 1) (pow v 4))) (sqrt (+ (* v v) 1))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (* PI (sqrt (- 1 (pow v 6))))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (* (sqrt (+ (+ (* v v) 1) (pow v 4))) (sqrt (+ (* v v) 1))) (sqrt (sqrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 1103 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (79 enodes) * * [misc]simplify: iters left: 3 (167 enodes) * * [misc]simplify: iters left: 2 (371 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (- 1 (pow v 4))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (- 1 (pow v 4))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* 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) * * [misc]simplify: iters left: 2 (29 enodes) * [exit]simplify: Simplified to (/ (+ 1 (* v v)) (sqrt (sqrt (+ 2 (* -6 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (- 1 (pow v 4))) (sqrt (sqrt (+ (* (* v v) -6) 2)))) (/ (+ 1 (* v v)) (sqrt (sqrt (+ 2 (* -6 (* v v)))))))) * * * * [misc]progress: [ 1104 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ 1 (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (118 enodes) * * [misc]simplify: iters left: 2 (220 enodes) * * [misc]simplify: iters left: 1 (286 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (- 1 (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (- 1 (pow v 4)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (sqrt (- 1 (pow v 4)))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 1105 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ 1 (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (100 enodes) * * [misc]simplify: iters left: 2 (148 enodes) * * [misc]simplify: iters left: 1 (156 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 4)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (- 1 (pow v 4)))) (* (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v))))))) * * * * [misc]progress: [ 1106 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (98 enodes) * * [misc]simplify: iters left: 3 (231 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4))))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (* (/ (sqrt (+ 1 (* v v))) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1107 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (170 enodes) * * [misc]simplify: iters left: 2 (454 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (cbrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (cbrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1108 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (178 enodes) * * [misc]simplify: iters left: 2 (495 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1109 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (203 enodes) * * [misc]simplify: iters left: 1 (413 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1110 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (178 enodes) * * [misc]simplify: iters left: 2 (495 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1111 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (279 enodes) * * [misc]simplify: iters left: 1 (483 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (- 1 (pow v 4)))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1112 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ 1 (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (164 enodes) * * [misc]simplify: iters left: 2 (380 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (cbrt (sqrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (* (/ (sqrt (+ 1 (* v v))) (cbrt (sqrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1113 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ 1 (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (130 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (328 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (cbrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (cbrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1114 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ 1 (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (278 enodes) * * [misc]simplify: iters left: 1 (380 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1115 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ 1 (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (147 enodes) * * [misc]simplify: iters left: 1 (160 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1116 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ 1 (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (278 enodes) * * [misc]simplify: iters left: 1 (380 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1117 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ 1 (/ (sqrt (/ 4/3 PI)) 1))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (84 enodes) * * [misc]simplify: iters left: 2 (122 enodes) * * [misc]simplify: iters left: 1 (135 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (pow v 4)))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1118 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ 1 (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (124 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (251 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 4)))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (262 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1119 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ 1 (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (131 enodes) * * [misc]simplify: iters left: 1 (135 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (262 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1120 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ 1 (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (96 enodes) * * [misc]simplify: iters left: 2 (124 enodes) * * [misc]simplify: iters left: 1 (128 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (262 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1121 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ 1 (/ 1 (sqrt 1)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (61 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (- 1 (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (- 1 (pow v 4)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (180 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (/ (/ 4/3 PI) (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (- 1 (pow v 4)))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (/ (/ 4/3 PI) (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1122 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ 1 (/ 1 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (96 enodes) * * [misc]simplify: iters left: 2 (124 enodes) * * [misc]simplify: iters left: 1 (128 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (262 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (+ 2 (* (* -6 v) v)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1123 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ 1 (/ 1 1))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (54 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (- 1 (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (- 1 (pow v 4)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (180 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (/ (/ 4/3 PI) (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (- 1 (pow v 4)))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (/ (/ 4/3 PI) (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1124 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ 1 (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (154 enodes) * * [misc]simplify: iters left: 2 (334 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (121 enodes) * * [misc]simplify: iters left: 2 (288 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (cbrt (sqrt (- 1 (* v v))))) (sqrt (+ 2 (* v (* -6 v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (cbrt (sqrt (- 1 (* v v))))) (sqrt (+ 2 (* v (* -6 v))))))) * * * * [misc]progress: [ 1125 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ 1 (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (119 enodes) * * [misc]simplify: iters left: 2 (186 enodes) * * [misc]simplify: iters left: 1 (247 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (121 enodes) * * [misc]simplify: iters left: 2 (288 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (cbrt (- 1 (* v v))))) (sqrt (+ 2 (* v (* -6 v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (fabs (cbrt (- 1 (* v v))))) (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (cbrt (- 1 (* v v))))) (sqrt (+ 2 (* v (* -6 v))))))) * * * * [misc]progress: [ 1126 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ 1 (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (115 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (253 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (121 enodes) * * [misc]simplify: iters left: 2 (288 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (+ 2 (* v (* -6 v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (+ 2 (* v (* -6 v))))))) * * * * [misc]progress: [ 1127 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ 1 (/ 4/3 (sqrt 1)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (75 enodes) * * [misc]simplify: iters left: 2 (79 enodes) * * [misc]simplify: iters left: 1 (83 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (- 1 (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (sqrt (- 1 (pow v 4)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (120 enodes) * * [misc]simplify: iters left: 2 (289 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* -6 v) v)))) PI) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (sqrt (- 1 (pow v 4)))) (/ (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* -6 v) v)))) PI))) * * * * [misc]progress: [ 1128 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ 1 (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (115 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (253 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (121 enodes) * * [misc]simplify: iters left: 2 (288 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (+ 2 (* v (* -6 v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 (sqrt (- 1 (pow v 4)))) (sqrt (sqrt (- 1 (* v v))))) (/ (/ (/ (sqrt (+ 1 (* v v))) PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (+ 2 (* v (* -6 v))))))) * * * * [misc]progress: [ 1129 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ 1 (/ 4/3 1))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (72 enodes) * * [misc]simplify: iters left: 2 (79 enodes) * * [misc]simplify: iters left: 1 (81 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (- 1 (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 4/3 (sqrt (- 1 (pow v 4)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (120 enodes) * * [misc]simplify: iters left: 2 (289 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* -6 v) v)))) PI) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 4/3 (sqrt (- 1 (pow v 4)))) (/ (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* -6 v) v)))) PI))) * * * * [misc]progress: [ 1130 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ 1 1)) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (53 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (- 1 (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (- 1 (pow v 4)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (180 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (/ (/ 4/3 PI) (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (- 1 (pow v 4)))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (/ (/ 4/3 PI) (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1131 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ 1 (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (113 enodes) * * [misc]simplify: iters left: 2 (166 enodes) * * [misc]simplify: iters left: 1 (253 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ 1 (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (71 enodes) * * [misc]simplify: iters left: 2 (108 enodes) * * [misc]simplify: iters left: 1 (157 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* -6 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (/ (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* -6 (* v v))))))) * * * * [misc]progress: [ 1132 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ 1 (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (221 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (- 1 (* (pow v 3) (pow v 3))))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (- 1 (* (pow v 3) (pow v 3))))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (179 enodes) * * [misc]simplify: iters left: 2 (308 enodes) * * [misc]simplify: iters left: 1 (443 enodes) * [exit]simplify: Simplified to (* (sqrt (+ (pow v 4) (+ (* v v) 1))) (/ (sqrt (+ (* v v) 1)) (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (- 1 (* (pow v 3) (pow v 3))))) (* (sqrt (+ (pow v 4) (+ (* v v) 1))) (/ (sqrt (+ (* v v) 1)) (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1133 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ 1 (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (174 enodes) * * [misc]simplify: iters left: 2 (436 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (- 1 (pow v 4))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 4/3 PI) (- 1 (pow v 4))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 1 (* v v))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 1 (* v v))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (27 enodes) * * [misc]simplify: iters left: 2 (28 enodes) * [exit]simplify: Simplified to (/ (+ 1 (* v v)) (sqrt (+ 2 (* v (* -6 v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 4/3 PI) (- 1 (pow v 4))) (/ (+ 1 (* v v)) (sqrt (+ 2 (* v (* -6 v))))))) * * * * [misc]progress: [ 1134 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) 1) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (53 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (- 1 (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ 1 (sqrt (- 1 (pow v 4)))) (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (180 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (/ (/ 4/3 PI) (sqrt (+ 2 (* v (* -6 v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ 1 (sqrt (- 1 (pow v 4)))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (/ (/ 4/3 PI) (sqrt (+ 2 (* v (* -6 v)))))))) * * * * [misc]progress: [ 1135 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (sqrt (+ 2 (* (* v v) -6)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (+ (* (* v v) -6) 2))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (+ (* (* v v) -6) 2))) (/ (sqrt (+ 1 (* v v))) (/ 1 (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (/ 1 (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (211 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (/ 4/3 PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (pow v 4)))) (sqrt (+ (* (* v v) -6) 2))) (* (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) (/ 4/3 PI)))) * * * * [misc]progress: [ 1136 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ 4/3 PI))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (134 enodes) * * [misc]simplify: iters left: 2 (187 enodes) * * [misc]simplify: iters left: 1 (301 enodes) * [exit]simplify: Simplified to (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (+ (* (* v v) -6) 2))) * [misc]simplify: Simplified (2 1) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (+ (* (* v v) -6) 2))) (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))))) * [enter]simplify: Simplifying (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ (/ 4/3 PI) (sqrt (- 1 (pow v 4)))) (sqrt (+ (* (* v v) -6) 2))) (/ (sqrt (+ 1 (* v v))) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 1137 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 1138 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 1139 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 1140 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (80 enodes) * [exit]simplify: Simplified to (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (* (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) (cbrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1141 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (80 enodes) * [exit]simplify: Simplified to (sqrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (sqrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) (sqrt (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1142 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1143 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1144 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1145 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1146 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1147 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1148 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1149 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1150 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1151 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1152 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1153 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1154 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1155 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) 1))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1156 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (56 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (81 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1157 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (56 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (81 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1158 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (56 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (81 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1159 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (80 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt 1)))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI))))) * * * * [misc]progress: [ 1160 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (56 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (81 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1161 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (80 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 1 1))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI))))) * * * * [misc]progress: [ 1162 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (110 enodes) * * [misc]simplify: iters left: 1 (136 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1163 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (110 enodes) * * [misc]simplify: iters left: 1 (136 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (cbrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (cbrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1164 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (110 enodes) * * [misc]simplify: iters left: 1 (136 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1165 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (108 enodes) * * [misc]simplify: iters left: 1 (131 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt 1)))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1166 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (110 enodes) * * [misc]simplify: iters left: 1 (136 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1167 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (108 enodes) * * [misc]simplify: iters left: 1 (131 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 1))) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1168 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (80 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) 1)) (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI))))) * * * * [misc]progress: [ 1169 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (45 enodes) * * [misc]simplify: iters left: 1 (50 enodes) * [exit]simplify: Simplified to (* (sqrt (- 1 (* v v))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ 4/3 PI))) (* (sqrt (- 1 (* v v))) (cbrt (sqrt (+ 2 (* (* v v) -6))))))) * * * * [misc]progress: [ 1170 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (162 enodes) * * [misc]simplify: iters left: 2 (270 enodes) * * [misc]simplify: iters left: 1 (379 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (sqrt (+ (+ (* v v) (pow v 4)) 1))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) (/ (cbrt (sqrt (+ 2 (* (* -6 v) v)))) (sqrt (+ (+ (* v v) (pow v 4)) 1))))) * * * * [misc]progress: [ 1171 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (* (cbrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (sqrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) (/ (cbrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v)))))) * * * * [misc]progress: [ 1172 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1173 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1174 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1175 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1176 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1177 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1178 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1179 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1180 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1181 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1182 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1183 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1184 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1185 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (sqrt (/ 4/3 PI)) 1))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1186 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (56 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (81 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1187 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (56 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (81 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1188 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (56 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (81 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1189 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (80 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt 1)))) (* (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI))))) * * * * [misc]progress: [ 1190 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (56 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (81 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1191 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (80 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 1 1))) (* (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI))))) * * * * [misc]progress: [ 1192 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (110 enodes) * * [misc]simplify: iters left: 1 (136 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (+ 2 (* (* v v) -6)))) (* PI (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (* (sqrt (cbrt (+ 2 (* (* v v) -6)))) (* PI (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1193 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (110 enodes) * * [misc]simplify: iters left: 1 (136 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (cbrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) (* (sqrt (cbrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (cbrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1194 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (110 enodes) * * [misc]simplify: iters left: 1 (136 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) (* (sqrt (cbrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1195 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (108 enodes) * * [misc]simplify: iters left: 1 (131 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt 1)))) (* (sqrt (cbrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1196 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (110 enodes) * * [misc]simplify: iters left: 1 (136 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) (* (sqrt (cbrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1197 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (108 enodes) * * [misc]simplify: iters left: 1 (131 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 1))) (* (sqrt (cbrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1198 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (80 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) 1)) (* (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI))))) * * * * [misc]progress: [ 1199 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (45 enodes) * * [misc]simplify: iters left: 1 (50 enodes) * [exit]simplify: Simplified to (* (sqrt (- 1 (* v v))) (sqrt (cbrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ 4/3 PI))) (* (sqrt (- 1 (* v v))) (sqrt (cbrt (+ 2 (* (* v v) -6))))))) * * * * [misc]progress: [ 1200 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (162 enodes) * * [misc]simplify: iters left: 2 (270 enodes) * * [misc]simplify: iters left: 1 (379 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (+ 2 (* (* -6 v) v)))) (sqrt (+ (+ (* v v) (pow v 4)) 1))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) (/ (sqrt (cbrt (+ 2 (* (* -6 v) v)))) (sqrt (+ (+ (* v v) (pow v 4)) 1))))) * * * * [misc]progress: [ 1201 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (* (cbrt (+ 2 (* (* v v) -6))) (cbrt (+ 2 (* (* v v) -6))))) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) (/ (sqrt (cbrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v)))))) * * * * [misc]progress: [ 1202 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1203 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1204 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1205 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1206 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1207 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1208 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1209 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1210 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1211 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1212 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1213 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1214 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1215 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) 1))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1216 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (56 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (81 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1217 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (56 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (81 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1218 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (56 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (81 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1219 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (80 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt 1)))) (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI))))) * * * * [misc]progress: [ 1220 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (56 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (81 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1221 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (80 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 1))) (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI))))) * * * * [misc]progress: [ 1222 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (110 enodes) * * [misc]simplify: iters left: 1 (136 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1223 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (110 enodes) * * [misc]simplify: iters left: 1 (136 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (cbrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (cbrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1224 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (110 enodes) * * [misc]simplify: iters left: 1 (136 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1225 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (108 enodes) * * [misc]simplify: iters left: 1 (131 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt 1)))) (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1226 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (110 enodes) * * [misc]simplify: iters left: 1 (136 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1227 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (108 enodes) * * [misc]simplify: iters left: 1 (131 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 1))) (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1228 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (80 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) 1)) (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI))))) * * * * [misc]progress: [ 1229 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (45 enodes) * * [misc]simplify: iters left: 1 (50 enodes) * [exit]simplify: Simplified to (* (sqrt (- 1 (* v v))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI))) (* (sqrt (- 1 (* v v))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * * * * [misc]progress: [ 1230 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (162 enodes) * * [misc]simplify: iters left: 2 (270 enodes) * * [misc]simplify: iters left: 1 (379 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* -6 v) v)))) (sqrt (+ (+ (* v v) (pow v 4)) 1))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) (/ (sqrt (sqrt (+ 2 (* (* -6 v) v)))) (sqrt (+ (+ (* v v) (pow v 4)) 1))))) * * * * [misc]progress: [ 1231 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v)))))) * * * * [misc]progress: [ 1232 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 2 (* (* v v) -6))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt 1) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) (/ (sqrt (+ 2 (* (* v v) -6))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1233 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt 1) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1234 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ 4/3 PI))))) * * * * [misc]progress: [ 1235 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) (/ (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ 4/3 PI))))) * * * * [misc]progress: [ 1236 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ 4/3 PI))))) * * * * [misc]progress: [ 1237 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1238 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ 4/3 PI))))) * * * * [misc]progress: [ 1239 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt 1) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1240 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ 4/3 PI))))) * * * * [misc]progress: [ 1241 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) (/ (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ 4/3 PI))))) * * * * [misc]progress: [ 1242 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ 4/3 PI))))) * * * * [misc]progress: [ 1243 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1244 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ 4/3 PI))))) * * * * [misc]progress: [ 1245 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt 1) (/ (sqrt (/ 4/3 PI)) 1))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1246 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (80 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt 1) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI)))) * * * * [misc]progress: [ 1247 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (80 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt 1) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) (/ (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI)))) * * * * [misc]progress: [ 1248 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (80 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt 1) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) (/ (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI)))) * * * * [misc]progress: [ 1249 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (79 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt 1) (/ 1 (sqrt 1)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1250 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (80 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt 1) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) (/ (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI)))) * * * * [misc]progress: [ 1251 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (79 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt 1) (/ 1 1))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1252 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (108 enodes) * * [misc]simplify: iters left: 1 (131 enodes) * [exit]simplify: Simplified to (* (* (sqrt (+ 2 (* (* v v) -6))) PI) (cbrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt 1) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (* (* (sqrt (+ 2 (* (* v v) -6))) PI) (cbrt (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1253 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (108 enodes) * * [misc]simplify: iters left: 1 (131 enodes) * [exit]simplify: Simplified to (* (* (sqrt (+ 2 (* (* v v) -6))) PI) (sqrt (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt 1) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) (* (* (sqrt (+ 2 (* (* v v) -6))) PI) (sqrt (cbrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1254 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (108 enodes) * * [misc]simplify: iters left: 1 (131 enodes) * [exit]simplify: Simplified to (* (* (sqrt (+ 2 (* (* v v) -6))) PI) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt 1) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) (* (* (sqrt (+ 2 (* (* v v) -6))) PI) (sqrt (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1255 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (107 enodes) * * [misc]simplify: iters left: 1 (130 enodes) * [exit]simplify: Simplified to (* (* (sqrt (- 1 (* v v))) PI) (sqrt (+ 2 (* (* -6 v) v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt 1) (/ 4/3 (sqrt 1)))) (* (* (sqrt (- 1 (* v v))) PI) (sqrt (+ 2 (* (* -6 v) v)))))) * * * * [misc]progress: [ 1256 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (108 enodes) * * [misc]simplify: iters left: 1 (131 enodes) * [exit]simplify: Simplified to (* (* (sqrt (+ 2 (* (* v v) -6))) PI) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt 1) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) (* (* (sqrt (+ 2 (* (* v v) -6))) PI) (sqrt (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1257 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (107 enodes) * * [misc]simplify: iters left: 1 (130 enodes) * [exit]simplify: Simplified to (* (* (sqrt (- 1 (* v v))) PI) (sqrt (+ 2 (* (* -6 v) v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt 1) (/ 4/3 1))) (* (* (sqrt (- 1 (* v v))) PI) (sqrt (+ 2 (* (* -6 v) v)))))) * * * * [misc]progress: [ 1258 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (79 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt 1) 1)) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1259 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ 1 (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * * [misc]simplify: iters left: 2 (44 enodes) * * [misc]simplify: iters left: 1 (49 enodes) * [exit]simplify: Simplified to (* (sqrt (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt 1) (/ 4/3 PI))) (* (sqrt (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))))) * * * * [misc]progress: [ 1260 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (181 enodes) * * [misc]simplify: iters left: 2 (320 enodes) * * [misc]simplify: iters left: 1 (488 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ (+ (* v v) 1) (pow v 4)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt 1) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ (+ (* v v) 1) (pow v 4)))))) * * * * [misc]progress: [ 1261 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 1 (* v v)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt 1) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 1 (* v v)))))) * * * * [misc]progress: [ 1262 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1263 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1264 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1265 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1266 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1267 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1268 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1269 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1270 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1271 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1272 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1273 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1274 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1275 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) 1))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1276 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (56 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (81 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1277 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (56 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (81 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1278 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (56 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (81 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1279 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (80 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt 1)))) (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI))))) * * * * [misc]progress: [ 1280 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (56 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (81 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (sqrt (- 1 (* v v))))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1281 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (80 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 1))) (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI))))) * * * * [misc]progress: [ 1282 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (110 enodes) * * [misc]simplify: iters left: 1 (136 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1283 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (110 enodes) * * [misc]simplify: iters left: 1 (136 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (cbrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (cbrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1284 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (110 enodes) * * [misc]simplify: iters left: 1 (136 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1285 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (108 enodes) * * [misc]simplify: iters left: 1 (131 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt 1)))) (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1286 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (110 enodes) * * [misc]simplify: iters left: 1 (136 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1287 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 1 PI) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (108 enodes) * * [misc]simplify: iters left: 1 (131 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 1))) (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (* PI (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1288 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (80 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) 1)) (* (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (sqrt (- 1 (* v v))) (/ 4/3 PI))))) * * * * [misc]progress: [ 1289 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 1 (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (45 enodes) * * [misc]simplify: iters left: 1 (50 enodes) * [exit]simplify: Simplified to (* (sqrt (- 1 (* v v))) (sqrt (sqrt (+ 2 (* (* v v) -6))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI))) (* (sqrt (- 1 (* v v))) (sqrt (sqrt (+ 2 (* (* v v) -6))))))) * * * * [misc]progress: [ 1290 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (162 enodes) * * [misc]simplify: iters left: 2 (270 enodes) * * [misc]simplify: iters left: 1 (379 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* -6 v) v)))) (sqrt (+ (+ (* v v) (pow v 4)) 1))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) (/ (sqrt (sqrt (+ 2 (* (* -6 v) v)))) (sqrt (+ (+ (* v v) (pow v 4)) 1))))) * * * * [misc]progress: [ 1291 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) (/ (sqrt (sqrt (+ 2 (* (* v v) -6)))) (sqrt (+ 1 (* v v)))))) * * * * [misc]progress: [ 1292 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 2 (* (* v v) -6))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (* (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) (/ (sqrt (+ 2 (* (* v v) -6))) (cbrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1293 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1294 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ 4/3 PI))))) * * * * [misc]progress: [ 1295 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) (/ (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ 4/3 PI))))) * * * * [misc]progress: [ 1296 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ 4/3 PI))))) * * * * [misc]progress: [ 1297 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1298 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (cbrt (/ 4/3 PI))))) * * * * [misc]progress: [ 1299 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1300 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ 4/3 PI))))) * * * * [misc]progress: [ 1301 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) (/ (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ 4/3 PI))))) * * * * [misc]progress: [ 1302 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ 4/3 PI))))) * * * * [misc]progress: [ 1303 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (/ (sqrt (/ 4/3 PI)) (sqrt 1)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1304 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))) (/ (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (sqrt (/ 4/3 PI))))) * * * * [misc]progress: [ 1305 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (/ (sqrt (/ 4/3 PI)) 1))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1306 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (80 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (/ (* (cbrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI)))) * * * * [misc]progress: [ 1307 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (80 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) (/ (* (sqrt (cbrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI)))) * * * * [misc]progress: [ 1308 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (80 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (/ 1 (sqrt (sqrt (- 1 (* v v))))))) (/ (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI)))) * * * * [misc]progress: [ 1309 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (79 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (/ 1 (sqrt 1)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1310 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (80 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI)) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (/ 1 (sqrt (sqrt (- 1 (* v v))))))) (/ (* (sqrt (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (/ 4/3 PI)))) * * * * [misc]progress: [ 1311 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (79 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (/ 1 1))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1312 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (108 enodes) * * [misc]simplify: iters left: 1 (131 enodes) * [exit]simplify: Simplified to (* (* (sqrt (+ 2 (* (* v v) -6))) PI) (cbrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))))) (* (* (sqrt (+ 2 (* (* v v) -6))) PI) (cbrt (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1313 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (108 enodes) * * [misc]simplify: iters left: 1 (131 enodes) * [exit]simplify: Simplified to (* (* (sqrt (+ 2 (* (* v v) -6))) PI) (sqrt (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))))) (* (* (sqrt (+ 2 (* (* v v) -6))) PI) (sqrt (cbrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1314 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (108 enodes) * * [misc]simplify: iters left: 1 (131 enodes) * [exit]simplify: Simplified to (* (* (sqrt (+ 2 (* (* v v) -6))) PI) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) (* (* (sqrt (+ 2 (* (* v v) -6))) PI) (sqrt (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1315 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (107 enodes) * * [misc]simplify: iters left: 1 (130 enodes) * [exit]simplify: Simplified to (* (* (sqrt (- 1 (* v v))) PI) (sqrt (+ 2 (* (* -6 v) v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (/ 4/3 (sqrt 1)))) (* (* (sqrt (- 1 (* v v))) PI) (sqrt (+ 2 (* (* -6 v) v)))))) * * * * [misc]progress: [ 1316 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (108 enodes) * * [misc]simplify: iters left: 1 (131 enodes) * [exit]simplify: Simplified to (* (* (sqrt (+ 2 (* (* v v) -6))) PI) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (/ 4/3 (sqrt (sqrt (- 1 (* v v))))))) (* (* (sqrt (+ 2 (* (* v v) -6))) PI) (sqrt (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1317 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 1 PI) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (107 enodes) * * [misc]simplify: iters left: 1 (130 enodes) * [exit]simplify: Simplified to (* (* (sqrt (- 1 (* v v))) PI) (sqrt (+ 2 (* (* -6 v) v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (/ 4/3 1))) (* (* (sqrt (- 1 (* v v))) PI) (sqrt (+ 2 (* (* -6 v) v)))))) * * * * [misc]progress: [ 1318 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (79 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 1)) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1319 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ 1 (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * * [misc]simplify: iters left: 2 (44 enodes) * * [misc]simplify: iters left: 1 (49 enodes) * [exit]simplify: Simplified to (* (sqrt (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (/ 4/3 PI))) (* (sqrt (- 1 (* v v))) (sqrt (+ 2 (* (* v v) -6)))))) * * * * [misc]progress: [ 1320 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (181 enodes) * * [misc]simplify: iters left: 2 (320 enodes) * * [misc]simplify: iters left: 1 (488 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ (+ (* v v) 1) (pow v 4)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ (+ (* v v) 1) (pow v 4)))))) * * * * [misc]progress: [ 1321 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 1 (* v v)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ 1 (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))))) (/ (sqrt (+ 2 (* (* v v) -6))) (sqrt (+ 1 (* v v)))))) * * * * [misc]progress: [ 1322 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (79 enodes) * [exit]simplify: Simplified to (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) 1) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1323 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (83 enodes) * * [misc]simplify: iters left: 1 (127 enodes) * [exit]simplify: Simplified to (* (* PI 3/4) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (* (* PI 3/4) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 1324 / 1400 ] 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) (/ (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ 4/3 PI))) (sqrt (- 1 (* v v))))) * * * * [misc]progress: [ 1325 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (* (cbrt (/ 1 (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))) (/ (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (cbrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1326 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ 1 (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (sqrt (/ 1 (sqrt (- 1 (* v v))))) (/ (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (/ 1 (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1327 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 1328 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 1329 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (- (pow 1 3) (pow (* v v) 3)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (71 enodes) * * [misc]simplify: iters left: 2 (80 enodes) * * [misc]simplify: iters left: 1 (85 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (- 1 (pow v 6)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (/ 1 (sqrt (- 1 (pow v 6)))) (/ (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v)))))))) * * * * [misc]progress: [ 1330 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (- (* 1 1) (* (* v v) (* v v))))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (- 1 (pow v 4)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (/ 1 (sqrt (- 1 (pow v 4)))) (/ (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (+ 1 (* v v)))))) * * * * [misc]progress: [ 1331 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2) to (λ (v) (* (/ (/ 1 (sqrt (- 1 (* v v)))) (sqrt (+ 2 (* (* v v) -6)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))) * * * * [misc]progress: [ 1332 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 1333 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 1334 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 1335 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 1336 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 1337 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 1338 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 1339 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 1340 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 1341 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 1342 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 1343 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (/ 4/3 PI)) (log (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * * [misc]simplify: iters left: 2 (68 enodes) * * [misc]simplify: iters left: 1 (86 enodes) * [exit]simplify: Simplified to (- (log (/ 4/3 PI)) (log (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2 2 1) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (exp (- (log (/ 4/3 PI)) (log (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 1344 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 1345 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 1346 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (/ 4/3 PI) (/ 4/3 PI)) (/ 4/3 PI)) (* (* (sqrt (- 1 (* v v))) (sqrt (- 1 (* v v)))) (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (285 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ 64/27 PI) (* PI PI)) (- 1 (* v v))) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2 2 1) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (cbrt (/ (/ (/ (/ 64/27 PI) (* PI PI)) (- 1 (* v v))) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1347 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 1348 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 1349 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 1350 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 1351 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (42 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2 2 1) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (* (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (cbrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 1352 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (13 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 (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2 2 1) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (fabs (cbrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 1353 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2 2 1) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 1354 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt 1)) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2 2 1) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1355 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2 2 1) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (sqrt (sqrt (- 1 (* v v))))) (/ (cbrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 1356 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) 1) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * * [misc]simplify: iters left: 2 (57 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2 2 1) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (/ (cbrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1357 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2 2 1) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (/ (sqrt (/ 4/3 PI)) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (sqrt (/ 4/3 PI)) (cbrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 1358 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 4/3 PI)) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2 2 1) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (/ (sqrt (/ 4/3 PI)) (fabs (cbrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (cbrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 1359 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2 2 1) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 1360 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 4/3 PI)) (sqrt 1)) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (9 enodes) * [exit]simplify: Simplified to (sqrt (/ 4/3 PI)) * [misc]simplify: Simplified (2 2 2 1) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (sqrt (/ 4/3 PI)) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (sqrt (/ 4/3 PI)) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1361 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2 2 1) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))) (/ (sqrt (/ 4/3 PI)) (sqrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 1362 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 4/3 PI)) 1) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * * [misc]simplify: iters left: 3 (10 enodes) * [exit]simplify: Simplified to (sqrt (/ 4/3 PI)) * [misc]simplify: Simplified (2 2 2 1) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (sqrt (/ 4/3 PI)) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (sqrt (/ 4/3 PI)) (/ (sqrt (/ 4/3 PI)) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1363 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * [exit]simplify: Simplified to (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * [misc]simplify: Simplified (2 2 2 1) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (/ 1 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 4/3 PI) (cbrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 1364 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * [exit]simplify: Simplified to (/ 1 (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2 2 1) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (/ 1 (fabs (cbrt (- 1 (* v v))))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (/ 1 (fabs (cbrt (- 1 (* v v))))) (/ (/ 4/3 PI) (sqrt (cbrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 1365 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2 2 1) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (/ 1 (sqrt (sqrt (- 1 (* v v))))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (/ 1 (sqrt (sqrt (- 1 (* v v))))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 1366 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt 1)) * * [misc]simplify: iters left: 3 (3 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 2 2 1) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* 1 (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* 1 (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1367 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2 2 1) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (/ 1 (sqrt (sqrt (- 1 (* v v))))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (/ 1 (sqrt (sqrt (- 1 (* v v))))) (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 1368 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 1) * * [misc]simplify: iters left: 2 (2 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 2 2 1) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* 1 (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* 1 (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1369 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * [exit]simplify: Simplified to (/ (/ 4/3 (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2 2 1) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (/ (/ 4/3 (cbrt (sqrt (- 1 (* v v))))) (cbrt (sqrt (- 1 (* v v))))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * [exit]simplify: Simplified to (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (/ 4/3 (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (/ (/ 1 PI) (cbrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 1370 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 4/3 (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * [exit]simplify: Simplified to (/ 4/3 (fabs (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2 2 1) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * [exit]simplify: Simplified to (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (/ 4/3 (fabs (cbrt (- 1 (* v v))))) (/ (/ 1 PI) (sqrt (cbrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 1371 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2 2 1) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * [exit]simplify: Simplified to (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 1372 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 4/3 (sqrt 1)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (6 enodes) * [exit]simplify: Simplified to 4/3 * [misc]simplify: Simplified (2 2 2 1) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* 4/3 (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 PI) (sqrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * [exit]simplify: Simplified to (/ (/ 1 PI) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* 4/3 (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1373 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2 2 1) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * [enter]simplify: Simplifying (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * [exit]simplify: Simplified to (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))) * [misc]simplify: Simplified (2 2 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (/ 4/3 (sqrt (sqrt (- 1 (* v v))))) (/ (/ 1 PI) (sqrt (sqrt (- 1 (* v v))))))))) * * * * [misc]progress: [ 1374 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 4/3 1) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (5 enodes) * [exit]simplify: Simplified to 4/3 * [misc]simplify: Simplified (2 2 2 1) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* 4/3 (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * [enter]simplify: Simplifying (/ (/ 1 PI) (sqrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * [exit]simplify: Simplified to (/ (/ 1 PI) (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* 4/3 (/ (/ 1 PI) (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1375 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 1376 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 1377 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 1378 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (cbrt (sqrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * [exit]simplify: Simplified to (cbrt (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ (/ 4/3 PI) (* (cbrt (sqrt (- 1 (* v v)))) (cbrt (sqrt (- 1 (* v v)))))) (cbrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1379 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (cbrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * [exit]simplify: Simplified to (sqrt (cbrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ (/ 4/3 PI) (sqrt (* (cbrt (- 1 (* v v))) (cbrt (- 1 (* v v)))))) (sqrt (cbrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1380 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (sqrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * [exit]simplify: Simplified to (sqrt (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1381 / 1400 ] 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 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ (/ 4/3 PI) (sqrt 1)) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1382 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (sqrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * [exit]simplify: Simplified to (sqrt (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 2 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ (/ 4/3 PI) (sqrt (sqrt (- 1 (* v v))))) (sqrt (sqrt (- 1 (* v v)))))))) * * * * [misc]progress: [ 1383 / 1400 ] 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 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ (/ 4/3 PI) 1) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1384 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) * * [misc]simplify: iters left: 5 (5 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) * [misc]simplify: Simplified (2 2 2 1) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (* (cbrt (/ 4/3 PI)) (cbrt (/ 4/3 PI))) (/ (sqrt (- 1 (* v v))) (cbrt (/ 4/3 PI))))))) * * * * [misc]progress: [ 1385 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ 4/3 PI)) * * [misc]simplify: iters left: 3 (4 enodes) * [exit]simplify: Simplified to (sqrt (/ 4/3 PI)) * [misc]simplify: Simplified (2 2 2 1) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (sqrt (/ 4/3 PI)) (/ (sqrt (- 1 (* v v))) (sqrt (/ 4/3 PI))))))) * * * * [misc]progress: [ 1386 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 1387 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 1388 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (+ (* 1 1) (+ (* (* v v) (* v v)) (* 1 (* v v))))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (87 enodes) * * [misc]simplify: iters left: 2 (125 enodes) * * [misc]simplify: iters left: 1 (142 enodes) * [exit]simplify: Simplified to (sqrt (+ 1 (+ (* v v) (pow v 4)))) * [misc]simplify: Simplified (2 2 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (/ (/ 4/3 PI) (sqrt (- (pow 1 3) (pow (* v v) 3)))) (sqrt (+ 1 (+ (* v v) (pow v 4)))))))) * * * * [misc]progress: [ 1389 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (+ 1 (* v v))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * [exit]simplify: Simplified to (sqrt (+ 1 (* v v))) * [misc]simplify: Simplified (2 2 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (* (/ (/ 4/3 PI) (sqrt (- (* 1 1) (* (* v v) (* v v))))) (sqrt (+ 1 (* v v))))))) * * * * [misc]progress: [ 1390 / 1400 ] simplifiying candidate # * * * * [misc]progress: [ 1391 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (- 1 (* v v)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (- 1 (* v v)))) * [misc]simplify: Simplified (2 1) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1392 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* 4/3 (/ (pow v 4) (* (sqrt 2) PI))) (+ (* 4/3 (/ 1 (* (sqrt 2) PI))) (+ (* 4 (/ (pow v 4) (* (pow (sqrt 2) 3) PI))) (+ (* 18 (/ (pow v 4) (* (pow (sqrt 2) 5) PI))) (+ (* 4 (/ (pow v 2) (* (pow (sqrt 2) 3) PI))) (* 4/3 (/ (pow v 2) (* (sqrt 2) PI)))))))) * * [misc]simplify: iters left: 6 (34 enodes) * * [misc]simplify: iters left: 5 (86 enodes) * * [misc]simplify: iters left: 4 (261 enodes) * [exit]simplify: Simplified to (+ (+ (* (/ (pow v 4) PI) (/ 2 (sqrt 2))) (+ (/ (/ 4/3 (sqrt 2)) PI) (/ (* (/ 4/3 PI) (pow v 4)) (sqrt 2)))) (+ (* (/ v (/ PI v)) (+ (/ 4/3 (sqrt 2)) (/ 2 (sqrt 2)))) (/ (* (/ 18 PI) (pow v 4)) (pow (sqrt 2) 5)))) * [misc]simplify: Simplified (2) to (λ (v) (+ (+ (* (/ (pow v 4) PI) (/ 2 (sqrt 2))) (+ (/ (/ 4/3 (sqrt 2)) PI) (/ (* (/ 4/3 PI) (pow v 4)) (sqrt 2)))) (+ (* (/ v (/ PI v)) (+ (/ 4/3 (sqrt 2)) (/ 2 (sqrt 2)))) (/ (* (/ 18 PI) (pow v 4)) (pow (sqrt 2) 5))))) * * * * [misc]progress: [ 1393 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 4/3 (/ 1 (* (sqrt -6) (* (pow v 3) (* (pow (sqrt -1) 2) PI))))) (+ (* 2/3 (/ 1 (* (pow (sqrt -1) 2) (* (pow v 5) (* (sqrt -6) PI))))) (+ (/ 1 (* (pow v 7) (* (sqrt -6) (* (pow (sqrt -1) 2) PI)))) (+ (* 2/3 (/ 1 (* (pow v 7) (* (pow (sqrt -6) 5) (* (pow (sqrt -1) 2) PI))))) (+ (* 2/3 (/ 1 (* (sqrt -6) (* (pow v 5) (* (pow (sqrt -1) 2) PI))))) (+ (* 4/3 (/ 1 (* (pow (sqrt -1) 2) (* (pow v 7) (* (pow (sqrt -6) 5) PI))))) (+ (* 1/6 (/ 1 (* (pow (sqrt -1) 6) (* (pow v 7) (* (sqrt -6) PI))))) (* 1/6 (/ 1 (* (pow v 7) (* (sqrt -6) (* (pow (sqrt -1) 6) PI)))))))))))) (+ (* 4/3 (/ 1 (* (pow (sqrt -6) 3) (* (pow v 5) (* (pow (sqrt -1) 2) PI))))) (* 4/3 (/ 1 (* (pow (sqrt -1) 2) (* (pow v 7) (* (pow (sqrt -6) 3) PI))))))) * * [misc]simplify: iters left: 6 (74 enodes) * * [misc]simplify: iters left: 5 (207 enodes) * [exit]simplify: Simplified to (- (+ (+ (+ (/ 2/3 (* (* (* -1 PI) (sqrt -6)) (pow v 5))) (/ 4/3 (* (* (* v v) (* v -1)) (* (sqrt -6) PI)))) (+ (/ (/ 1 (pow v 7)) (* (* -1 PI) (sqrt -6))) (/ 2/3 (* (pow (sqrt -6) 5) (* (* -1 PI) (pow v 7)))))) (+ (+ (/ (* (/ 1 (pow v 7)) 1/6) (* (pow (sqrt -1) 6) (* (sqrt -6) PI))) (/ (* 4/3 -1) (* (pow (sqrt -6) 5) (* PI (pow v 7))))) (+ (/ (* (/ 1 (pow v 7)) 1/6) (* (pow (sqrt -1) 6) (* (sqrt -6) PI))) (/ 2/3 (* (* (* -1 PI) (sqrt -6)) (pow v 5)))))) (+ (/ 4/3 (* (* -6 (sqrt -6)) (* (* -1 PI) (pow v 5)))) (/ (* 4/3 -1) (* (pow v 7) (* (sqrt -6) (* -6 PI)))))) * [misc]simplify: Simplified (2) to (λ (v) (- (+ (+ (+ (/ 2/3 (* (* (* -1 PI) (sqrt -6)) (pow v 5))) (/ 4/3 (* (* (* v v) (* v -1)) (* (sqrt -6) PI)))) (+ (/ (/ 1 (pow v 7)) (* (* -1 PI) (sqrt -6))) (/ 2/3 (* (pow (sqrt -6) 5) (* (* -1 PI) (pow v 7)))))) (+ (+ (/ (* (/ 1 (pow v 7)) 1/6) (* (pow (sqrt -1) 6) (* (sqrt -6) PI))) (/ (* 4/3 -1) (* (pow (sqrt -6) 5) (* PI (pow v 7))))) (+ (/ (* (/ 1 (pow v 7)) 1/6) (* (pow (sqrt -1) 6) (* (sqrt -6) PI))) (/ 2/3 (* (* (* -1 PI) (sqrt -6)) (pow v 5)))))) (+ (/ 4/3 (* (* -6 (sqrt -6)) (* (* -1 PI) (pow v 5)))) (/ (* 4/3 -1) (* (pow v 7) (* (sqrt -6) (* -6 PI))))))) * * * * [misc]progress: [ 1394 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 4/3 (/ 1 (* (pow (sqrt -6) 3) (* (pow v 7) (* (pow (sqrt -1) 2) PI))))) (* 4/3 (/ 1 (* (pow (sqrt -1) 2) (* (pow v 5) (* (pow (sqrt -6) 3) PI)))))) (+ (* 4/3 (/ 1 (* (sqrt -6) (* (pow v 3) (* (pow (sqrt -1) 2) PI))))) (+ (* 2/3 (/ 1 (* (sqrt -6) (* (pow v 5) (* (pow (sqrt -1) 2) PI))))) (+ (/ 1 (* (pow (sqrt -1) 2) (* (pow v 7) (* (sqrt -6) PI)))) (+ (* 1/6 (/ 1 (* (sqrt -6) (* (pow v 7) (* (pow (sqrt -1) 6) PI))))) (+ (* 4/3 (/ 1 (* (pow (sqrt -6) 5) (* (pow v 7) (* (pow (sqrt -1) 2) PI))))) (+ (* 2/3 (/ 1 (* (pow (sqrt -1) 2) (* (pow v 7) (* (pow (sqrt -6) 5) PI))))) (+ (* 2/3 (/ 1 (* (pow (sqrt -1) 2) (* (pow v 5) (* (sqrt -6) PI))))) (* 1/6 (/ 1 (* (pow (sqrt -1) 6) (* (pow v 7) (* (sqrt -6) PI))))))))))))) * * [misc]simplify: iters left: 6 (73 enodes) * * [misc]simplify: iters left: 5 (203 enodes) * [exit]simplify: Simplified to (- (- (- (+ (/ 4/3 (* (* (* PI -1) (pow v 7)) (* -6 (sqrt -6)))) (/ -4/3 (* (* (pow v 5) PI) (* -6 (sqrt -6))))) (/ 4/3 (* (* (* v v) (* v -1)) (* (sqrt -6) PI)))) (/ (* 2/3 -1) (* (* (pow v 5) PI) (sqrt -6)))) (+ (+ (/ -1 (* (sqrt -6) (* PI (pow v 7)))) (+ (/ (* (/ 1 (sqrt -6)) 1/6) (* (pow (sqrt -1) 6) (* PI (pow v 7)))) (/ 4/3 (* (* (* PI -1) (pow v 7)) (pow (sqrt -6) 5))))) (+ (/ (* 2/3 -1) (* (* (pow v 7) PI) (pow (sqrt -6) 5))) (+ (/ (* 2/3 -1) (* (* (pow v 5) PI) (sqrt -6))) (/ (* (/ 1 (sqrt -6)) 1/6) (* (pow (sqrt -1) 6) (* PI (pow v 7)))))))) * [misc]simplify: Simplified (2) to (λ (v) (- (- (- (+ (/ 4/3 (* (* (* PI -1) (pow v 7)) (* -6 (sqrt -6)))) (/ -4/3 (* (* (pow v 5) PI) (* -6 (sqrt -6))))) (/ 4/3 (* (* (* v v) (* v -1)) (* (sqrt -6) PI)))) (/ (* 2/3 -1) (* (* (pow v 5) PI) (sqrt -6)))) (+ (+ (/ -1 (* (sqrt -6) (* PI (pow v 7)))) (+ (/ (* (/ 1 (sqrt -6)) 1/6) (* (pow (sqrt -1) 6) (* PI (pow v 7)))) (/ 4/3 (* (* (* PI -1) (pow v 7)) (pow (sqrt -6) 5))))) (+ (/ (* 2/3 -1) (* (* (pow v 7) PI) (pow (sqrt -6) 5))) (+ (/ (* 2/3 -1) (* (* (pow v 5) PI) (sqrt -6))) (/ (* (/ 1 (sqrt -6)) 1/6) (* (pow (sqrt -1) 6) (* PI (pow v 7))))))))) * * * * [misc]progress: [ 1395 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (* -6 (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) -6) * [misc]simplify: Simplified (2 2 1 1 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1396 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (* -6 (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) -6) * [misc]simplify: Simplified (2 2 1 1 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1397 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (* -6 (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) -6) * [misc]simplify: Simplified (2 2 1 1 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))))) * * * * [misc]progress: [ 1398 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* 2/3 (/ (pow v 2) PI)) (+ (* 4/3 (/ 1 PI)) (* 1/2 (/ (pow v 4) PI)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (101 enodes) * [exit]simplify: Simplified to (+ (+ (* (/ v PI) (* 2/3 v)) (* (pow v 4) (/ 1/2 PI))) (/ 4/3 PI)) * [misc]simplify: Simplified (2 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (+ (+ (* (/ v PI) (* 2/3 v)) (* (pow v 4) (/ 1/2 PI))) (/ 4/3 PI))))) * * * * [misc]progress: [ 1399 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* 4/3 (/ 1 (* v (* (sqrt -1) PI)))) (+ (* 1/3 (/ 1 (* (pow v 5) (* (sqrt -1) PI)))) (+ (* 2/3 (/ 1 (* (pow v 3) (* (sqrt -1) PI)))) (* 1/6 (/ 1 (* (pow v 5) (* (pow (sqrt -1) 5) PI))))))) * * [misc]simplify: iters left: 6 (31 enodes) * * [misc]simplify: iters left: 5 (76 enodes) * * [misc]simplify: iters left: 4 (154 enodes) * * [misc]simplify: iters left: 3 (286 enodes) * * [misc]simplify: iters left: 2 (482 enodes) * [exit]simplify: Simplified to (+ (+ (/ (/ (/ 4/3 v) (sqrt -1)) PI) (/ (/ 2/3 (* v PI)) (* (sqrt -1) (* v v)))) (* (+ (/ 1/6 (pow (sqrt -1) 5)) (/ 1/3 (sqrt -1))) (/ (/ 1 PI) (pow v 5)))) * [misc]simplify: Simplified (2 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (+ (+ (/ (/ (/ 4/3 v) (sqrt -1)) PI) (/ (/ 2/3 (* v PI)) (* (sqrt -1) (* v v)))) (* (+ (/ 1/6 (pow (sqrt -1) 5)) (/ 1/3 (sqrt -1))) (/ (/ 1 PI) (pow v 5))))))) * * * * [misc]progress: [ 1400 / 1400 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 4/3 (/ 1 (* v (* (sqrt -1) PI)))) (+ (* 1/3 (/ 1 (* (pow v 5) (* (sqrt -1) PI)))) (+ (* 2/3 (/ 1 (* (pow v 3) (* (sqrt -1) PI)))) (* 1/6 (/ 1 (* (pow v 5) (* (pow (sqrt -1) 5) PI)))))))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (80 enodes) * * [misc]simplify: iters left: 4 (176 enodes) * * [misc]simplify: iters left: 3 (392 enodes) * [exit]simplify: Simplified to (+ (+ (- (/ (/ -1/3 (pow v 5)) (* (sqrt -1) PI)) (/ (/ (/ 2/3 v) (* v v)) (* (sqrt -1) PI))) (/ (/ -1/6 (pow v 5)) (* (pow (sqrt -1) 5) PI))) (/ -4/3 (* (* v PI) (sqrt -1)))) * [misc]simplify: Simplified (2 2 2) to (λ (v) (/ (/ 1 (sqrt (- 1 (* v v)))) (/ (sqrt (+ 2 (* (* v v) -6))) (+ (+ (- (/ (/ -1/3 (pow v 5)) (* (sqrt -1) PI)) (/ (/ (/ 2/3 v) (* v v)) (* (sqrt -1) PI))) (/ (/ -1/6 (pow v 5)) (* (pow (sqrt -1) 5) PI))) (/ -4/3 (* (* v PI) (sqrt -1))))))) * * * [misc]progress: adding candidates to table