* [misc]progress: [Phase 1 of 3] Setting up. * * * [misc]progress: [1/2] Preparing points * * * * [misc]points: Sampling 266 additional inputs, on iter 0 have 0 / 256 * * * * [misc]points: Computing exacts on every 17 of 266 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 64 * * * * [misc]points: Setting MPFR precision to 320 * * * * [misc]points: Setting MPFR precision to 576 * * * * [misc]points: Computing exacts on every 8 of 266 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 320 * * * * [misc]points: Setting MPFR precision to 576 * * * * [misc]points: Setting MPFR precision to 832 * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 4 of 266 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 266 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 1 of 266 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 266 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 210 additional inputs, on iter 1 have 56 / 256 * * * * [misc]points: Computing exacts on every 13 of 210 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 7 of 210 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 3 of 210 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 210 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 210 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 158 additional inputs, on iter 2 have 108 / 256 * * * * [misc]points: Computing exacts on every 10 of 158 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 5 of 158 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 158 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 1 of 158 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 158 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 115 additional inputs, on iter 3 have 151 / 256 * * * * [misc]points: Computing exacts on every 7 of 115 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 4 of 115 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 115 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 115 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 87 additional inputs, on iter 4 have 179 / 256 * * * * [misc]points: Computing exacts on every 5 of 87 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 3 of 87 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 1 of 87 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 87 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 72 additional inputs, on iter 5 have 194 / 256 * * * * [misc]points: Computing exacts on every 4 of 72 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 72 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 1 of 72 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 72 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 63 additional inputs, on iter 6 have 203 / 256 * * * * [misc]points: Computing exacts on every 4 of 63 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 63 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 63 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 51 additional inputs, on iter 7 have 215 / 256 * * * * [misc]points: Computing exacts on every 3 of 51 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 51 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 51 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 37 additional inputs, on iter 8 have 229 / 256 * * * * [misc]points: Computing exacts on every 2 of 37 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 1 of 37 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 37 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 27 additional inputs, on iter 9 have 239 / 256 * * * * [misc]points: Computing exacts on every 2 of 27 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 27 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 22 additional inputs, on iter 10 have 244 / 256 * * * * [misc]points: Computing exacts on every 1 of 22 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 22 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 18 additional inputs, on iter 11 have 248 / 256 * * * * [misc]points: Computing exacts on every 1 of 18 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 18 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 14 additional inputs, on iter 12 have 252 / 256 * * * * [misc]points: Computing exacts for 14 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 11 additional inputs, on iter 13 have 255 / 256 * * * * [misc]points: Computing exacts for 11 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [exit]points: Sampled 256 points with exact outputs * * * [misc]progress: [2/2] Setting up program. * [misc]progress: [Phase 2 of 3] Improving. * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (63 enodes) * [exit]simplify: Simplified to (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) * * [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 / 3 ] rewriting at (2 1 1) * * * * [misc]progress: [ 2 / 3 ] rewriting at (2) * * * * [misc]progress: [ 3 / 3 ] rewriting at (2 1) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 3 ] generating series at (2 1 1) * [misc]approximate: Taking taylor expansion of (* n (* PI 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) 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 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) 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 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) 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 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 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 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [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 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) * * * * [misc]progress: [ 2 / 3 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (pow (* n (* PI 2)) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (* PI 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (* PI 2)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* n (* PI 2))) in k * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of (* PI 2) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (pow (* 2 (* n PI)) 1/2) +nan.0) into (* +nan.0 (sqrt (* n (* 2 PI)))) * [misc]taylor: Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (pow (* n (* PI 2)) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (* n (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (sqrt k)) into (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (pow (* n (* PI 2)) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (* n (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (sqrt k)) into (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [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 (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 k) (+ (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1 (+ (log (* 2 PI)) (log n))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (* 0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) (/ 0 (sqrt k))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (+ (* 1 0) (* -1 (+ (log (* 2 PI)) (log n)))) into (- (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n)))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) * [misc]backup-simplify: Simplify (+ (* 0 (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))))) (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 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) (+ (* -1 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))))) (+ (* +nan.0 (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))))) (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 * [misc]backup-simplify: Simplify (+ 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) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/16 (* (pow (log (* 2 PI)) 2) (log n))) (+ (* 1/48 (pow (log (* 2 PI)) 3)) (+ (* 1/48 (pow (log n) 3)) (* 1/16 (* (log (* 2 PI)) (pow (log n) 2)))))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 0 (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/16 (* (pow (log (* 2 PI)) 2) (log n))) (+ (* 1/48 (pow (log (* 2 PI)) 3)) (+ (* 1/48 (pow (log n) 3)) (* 1/16 (* (log (* 2 PI)) (pow (log n) 2))))))))) (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))))) (+ (* +nan.0 (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))))) (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))))))))))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (pow (log n) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) k)) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (pow k 2) (log n)))))))))))))))))))))))) * [misc]approximate: Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [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 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of (* PI 2) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [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 (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt (/ 1 k))) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt (/ 1 k))) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [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 (- (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))))))) * [misc]approximate: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of (* PI 2) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ -1 n) (* 2 PI)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (+ 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [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 (- (log (* -2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k * [misc]taylor: Taking taylor expansion of (* -2 PI) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k * [misc]taylor: Taking taylor expansion of (/ -1 k) in k * [misc]taylor: Taking taylor expansion of -1 in k * [misc]backup-simplify: Simplify -1 into -1 * [misc]taylor: Taking taylor expansion of k in k * [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 (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) 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 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))))))) * * * * [misc]progress: [ 3 / 3 ] generating series at (2 1) * [misc]approximate: Taking taylor expansion of (pow (* n (* PI 2)) (/ (- 1 k) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* n (* PI 2)) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (* PI 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (* PI 2)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* n (* PI 2))) in k * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of (* PI 2) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]taylor: Taking taylor expansion of (pow (* n (* PI 2)) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (* n (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (* n (* PI 2)) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (* n (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 k) (+ (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1 (+ (log (* 2 PI)) (log n))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (+ (* 1 0) (* -1 (+ (log (* 2 PI)) (log n)))) into (- (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n)))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) * [misc]backup-simplify: Simplify (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 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) (+ (* -1 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* k 1)) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (+ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (log n) (pow k 2)))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))))) * [misc]approximate: Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [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 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of (* PI 2) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [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 (- (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) * [misc]approximate: Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of (* PI 2) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ -1 n) (* 2 PI)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (+ 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [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 (- (log (* -2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k * [misc]taylor: Taking taylor expansion of (* -2 PI) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) 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 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (expm1 (* (* n 2) PI)) * [exit]simplify: Simplified to (expm1 (* (* n 2) PI)) * * * * [misc]progress: [ 2 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (log1p (* (* n 2) PI)) * [exit]simplify: Simplified to (log1p (* (* n 2) PI)) * * * * [misc]progress: [ 3 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 4 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * * [misc]simplify: iters left: 2 (41 enodes) * [exit]simplify: Simplified to (log (* (* PI n) 2)) * [exit]simplify: Simplified to (log (* (* PI n) 2)) * * * * [misc]progress: [ 5 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * * [misc]simplify: iters left: 2 (35 enodes) * * [misc]simplify: iters left: 1 (47 enodes) * [exit]simplify: Simplified to (pow (exp 2) (* PI n)) * [exit]simplify: Simplified to (pow (exp 2) (* PI n)) * * * * [misc]progress: [ 6 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) * * [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 (18 enodes) * [exit]simplify: Simplified to (* (cbrt (* (* PI n) 2)) (cbrt (* (* PI n) 2))) * [exit]simplify: Simplified to (* (cbrt (* (* PI n) 2)) (cbrt (* (* PI n) 2))) * [enter]simplify: Simplifying (cbrt (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (cbrt (* (* n 2) PI)) * [exit]simplify: Simplified to (cbrt (* (* n 2) PI)) * * * * [misc]progress: [ 7 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (203 enodes) * [exit]simplify: Simplified to (pow (* (* PI n) 2) 3) * [exit]simplify: Simplified to (pow (* (* PI n) 2) 3) * * * * [misc]progress: [ 8 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (sqrt (* (* n 2) PI)) * [exit]simplify: Simplified to (sqrt (* (* n 2) PI)) * [enter]simplify: Simplifying (sqrt (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (sqrt (* (* n 2) PI)) * [exit]simplify: Simplified to (sqrt (* (* n 2) PI)) * * * * [misc]progress: [ 9 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 10 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (* n PI) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* PI n) * [exit]simplify: Simplified to (* PI n) * * * * [misc]progress: [ 11 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 12 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (expm1 (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (expm1 (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 13 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (log1p (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (log1p (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 14 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 15 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* n (* PI 2))) (/ (- 1 k) 2)) (log (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (166 enodes) * [exit]simplify: Simplified to (fma (log (* (* n 2) PI)) (/ (- 1 k) 2) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* (* n 2) PI)) (/ (- 1 k) 2) (- (log (sqrt k)))) * * * * [misc]progress: [ 16 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* n (* PI 2))) (/ (- 1 k) 2)) (log (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (166 enodes) * [exit]simplify: Simplified to (fma (log (* (* n 2) PI)) (/ (- 1 k) 2) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* (* n 2) PI)) (/ (- 1 k) 2) (- (log (sqrt k)))) * * * * [misc]progress: [ 17 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (pow (* n (* PI 2)) (/ (- 1 k) 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (302 enodes) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* 2 (* PI n))) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* 2 (* PI n))) (- (log (sqrt k)))) * * * * [misc]progress: [ 18 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (log (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (131 enodes) * * [misc]simplify: iters left: 1 (430 enodes) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* 2 (* PI n))) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* 2 (* PI n))) (- (log (sqrt k)))) * * * * [misc]progress: [ 19 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (exp (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (exp (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 20 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (133 enodes) * * [misc]simplify: iters left: 2 (215 enodes) * * [misc]simplify: iters left: 1 (353 enodes) * [exit]simplify: Simplified to (* (* (pow (* (* PI n) 2) (/ (- 1 k) 2)) (pow (* (* PI n) 2) (/ (- 1 k) 2))) (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (* k (sqrt k)))) * [exit]simplify: Simplified to (* (* (pow (* (* PI n) 2) (/ (- 1 k) 2)) (pow (* (* PI n) 2) (/ (- 1 k) 2))) (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (* k (sqrt k)))) * * * * [misc]progress: [ 21 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) * * [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 (38 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)))) * [enter]simplify: Simplifying (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (cbrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (cbrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 22 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (125 enodes) * * [misc]simplify: iters left: 1 (156 enodes) * [exit]simplify: Simplified to (/ (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (pow (* (* n 2) PI) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (pow (* (* n 2) PI) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 23 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))) * [enter]simplify: Simplifying (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 24 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (- (pow (* n (* PI 2)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (- (pow (* (* n 2) PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (- (pow (* (* n 2) PI) (/ (- 1 k) 2))) * [enter]simplify: Simplifying (- (sqrt k)) * * [misc]simplify: iters left: 3 (3 enodes) * [exit]simplify: Simplified to (- (sqrt k)) * [exit]simplify: Simplified to (- (sqrt k)) * * * * [misc]progress: [ 25 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (pow (* PI 2) (/ (- 1 k) 2)) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k))) * * * * [misc]progress: [ 26 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) * * * * [misc]progress: [ 27 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow n (/ (- 1 k) 2)) 1) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * [enter]simplify: Simplifying (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 28 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (60 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k))) * * [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 (38 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) * * * * [misc]progress: [ 29 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt (sqrt k))) * * [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) * [exit]simplify: Simplified to (* (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) * [exit]simplify: Simplified to (* (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) * [enter]simplify: Simplifying (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [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 (38 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * * * [misc]progress: [ 30 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) 1) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) * [enter]simplify: Simplifying (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (sqrt k)) * [exit]simplify: Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (sqrt k)) * * * * [misc]progress: [ 31 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (15 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 (pow (* PI (* n 2)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k))) * * [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 (38 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) * * * * [misc]progress: [ 32 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [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 (38 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [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 (38 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * * * [misc]progress: [ 33 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) 1) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) * [enter]simplify: Simplifying (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (sqrt k)) * * * * [misc]progress: [ 34 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (cbrt (sqrt k))) * * * * [misc]progress: [ 35 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))) * * * * [misc]progress: [ 36 / 74 ] 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 * [exit]simplify: Simplified to 1 * [enter]simplify: Simplifying (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 37 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 38 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt k)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (6 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * * * * [misc]progress: [ 39 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (pow (* n (* PI 2)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (pow (* PI (* n 2)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (/ (sqrt k) (pow (* PI (* n 2)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 40 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * * * [misc]progress: [ 41 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))) * * * * [misc]progress: [ 42 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) 1) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (pow (* (* n 2) PI) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (* (* n 2) PI) (/ (- 1 k) 2)) * * * * [misc]progress: [ 43 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2))) * * * * [misc]progress: [ 44 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 45 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 46 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (pow (* n (* PI 2)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (pow (* PI (* n 2)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (/ (sqrt k) (pow (* PI (* n 2)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 47 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) * [exit]simplify: Simplified to (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) * * * * [misc]progress: [ 48 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (pow (* n (* PI 2)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (expm1 (pow (* (* n 2) PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (expm1 (pow (* (* n 2) PI) (/ (- 1 k) 2))) * * * * [misc]progress: [ 49 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (pow (* n (* PI 2)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (log1p (pow (* (* n 2) PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (log1p (pow (* (* n 2) PI) (/ (- 1 k) 2))) * * * * [misc]progress: [ 50 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* n (* PI 2))) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2)))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2)))) * * * * [misc]progress: [ 51 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* n (* PI 2))) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2)))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2)))) * * * * [misc]progress: [ 52 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (* 1 (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (81 enodes) * [exit]simplify: Simplified to (/ (- 1 k) 2) * [exit]simplify: Simplified to (/ (- 1 k) 2) * * * * [misc]progress: [ 53 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n (* PI 2)) (/ 1 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * * [misc]simplify: iters left: 2 (22 enodes) * [exit]simplify: Simplified to (pow (* 2 (* PI n)) (/ 1 2)) * [exit]simplify: Simplified to (pow (* 2 (* PI n)) (/ 1 2)) * [enter]simplify: Simplifying (pow (* n (* PI 2)) (/ k 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (18 enodes) * * [misc]simplify: iters left: 2 (20 enodes) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (/ k 2)) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (/ k 2)) * * * * [misc]progress: [ 54 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n (* PI 2)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (pow (* PI (* n 2)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (pow (* PI (* n 2)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * * * [misc]progress: [ 55 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n (* PI 2)) (sqrt (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (pow (* (* n 2) PI) (sqrt (/ (- 1 k) 2))) * [exit]simplify: Simplified to (pow (* (* n 2) PI) (sqrt (/ (- 1 k) 2))) * * * * [misc]progress: [ 56 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n (* PI 2)) 1) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * * [misc]simplify: iters left: 2 (20 enodes) * [exit]simplify: Simplified to (* (* PI n) 2) * [exit]simplify: Simplified to (* (* PI n) 2) * * * * [misc]progress: [ 57 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n (* PI 2)) (- 1 k)) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * * [misc]simplify: iters left: 2 (25 enodes) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- 1 k)) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- 1 k)) * * * * [misc]progress: [ 58 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (pow n (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (17 enodes) * * [misc]simplify: iters left: 2 (19 enodes) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * [enter]simplify: Simplifying (pow (* PI 2) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * * [misc]simplify: iters left: 2 (21 enodes) * [exit]simplify: Simplified to (pow (* 2 PI) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (* 2 PI) (/ (- 1 k) 2)) * * * * [misc]progress: [ 59 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 60 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (log (pow (* n (* PI 2)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (246 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* (* n 2) PI))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* (* n 2) PI))) * * * * [misc]progress: [ 61 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (pow (* n (* PI 2)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (exp (pow (* (* n 2) PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (exp (pow (* (* n 2) PI) (/ (- 1 k) 2))) * * * * [misc]progress: [ 62 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2)))) * [enter]simplify: Simplifying (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) * * * * [misc]progress: [ 63 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (pow (* n (* PI 2)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (pow (pow (* (* n 2) PI) (/ (- 1 k) 2)) 3) * [exit]simplify: Simplified to (pow (pow (* (* n 2) PI) (/ (- 1 k) 2)) 3) * * * * [misc]progress: [ 64 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) * [enter]simplify: Simplifying (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) * * * * [misc]progress: [ 65 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 66 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 67 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 68 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 69 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (pow (log n) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) k)) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (pow k 2) (log n)))))))))))))))))))))))) * * * * [misc]progress: [ 70 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))))))) * * * * [misc]progress: [ 71 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))))))) * * * * [misc]progress: [ 72 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (- (+ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (log n) (pow k 2)))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))))) (sqrt k)) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (113 enodes) * * [misc]simplify: iters left: 4 (377 enodes) * [exit]simplify: Simplified to (/ (+ (* (* (* (pow (* PI 2) 1/2) (pow n 1/2)) (* (* k k) 1/8)) (+ (* (log n) (log n)) (* (log (* PI 2)) (log (* PI 2))))) (- (fma (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/4)) (* (log (* PI 2)) (* (* k k) (log n))) (* (pow (* PI 2) 1/2) (pow n 1/2))) (* (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/2)) (fma k (log (* PI 2)) (* (log n) k))))) (sqrt k)) * * * * [misc]progress: [ 73 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (sqrt k)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (267 enodes) * [exit]simplify: Simplified to (/ (pow (exp (- 1/2 (* 1/2 k))) (+ (log (* PI 2)) (log n))) (sqrt k)) * * * * [misc]progress: [ 74 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt k)) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (277 enodes) * [exit]simplify: Simplified to (/ (pow (exp (- 1/2 (* 1/2 k))) (- (log (* PI -2)) (log (/ -1 n)))) (sqrt k)) * * * [misc]progress: adding candidates to table * * [misc]progress: iteration 2 / 4 * * * [misc]progress: picking best candidate * * * * [misc]pick: Picked # * * * [misc]progress: localizing error * * * [misc]progress: generating rewritten candidates * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 2 1) * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 1) * * * * [misc]progress: [ 3 / 4 ] rewriting at (2) * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 2) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2 1) * [misc]approximate: Taking taylor expansion of (* (* 2 PI) n) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (* 2 PI) n) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* (* 2 PI) n) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 1) (* 0 0)) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 1) (* 0 0))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 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 (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 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 (* (* 2 PI) n) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [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 (* (* 2 PI) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [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 (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) 1) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 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 (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 (* (* 2 PI) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) -1) into (* -2 PI) * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 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 (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 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 (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) * * * * [misc]progress: [ 2 / 4 ] generating series at (2 1) * [misc]approximate: Taking taylor expansion of (/ 1 (sqrt k)) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.0) * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (* (- +nan.0) k) (+ (- +nan.0) (* +nan.0 (/ 1 k)))) into (- (+ +nan.0 (- (+ (* +nan.0 k) (- (* +nan.0 (/ 1 k))))))) * [misc]approximate: Taking taylor expansion of (/ 1 (sqrt (/ 1 k))) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [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 (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [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 (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.0) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 2)) (+ (* (- +nan.0) (/ 1 k)) +nan.0)) into (- (+ +nan.0 (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 2)))))))) * [misc]approximate: Taking taylor expansion of (/ 1 (sqrt (/ 1 (- k)))) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]backup-simplify: Simplify +nan.0 into +nan.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 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.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 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ +nan.0 (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 2)))))))) * * * * [misc]progress: [ 3 / 4 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) in (k n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ 1 (sqrt k)) into (sqrt (/ 1 k)) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) n)) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) n) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) 0) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 1) (* 0 0)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) n)) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) n) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]taylor: Taking taylor expansion of (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) n)) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) n) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]backup-simplify: Simplify (* +nan.0 (pow (* 2 (* n PI)) 1/2)) into (* +nan.0 (sqrt (* n (* 2 PI)))) * [misc]taylor: Taking taylor expansion of (* +nan.0 (sqrt (* n (* 2 PI)))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (sqrt (* n (* 2 PI))) in n * [misc]taylor: Taking taylor expansion of (* n (* 2 PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ (* 2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (* 0 n)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (- (/ -1 2) (+ (* 1/2 (/ 0 2)))) into -1/2 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* n (* 2 PI))) (log (* 2 (* n PI))))) * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (* +nan.0 (* -1/2 (* (sqrt (* n (* 2 PI))) (log (* 2 (* n PI)))))) (* (- +nan.0) (pow (* 2 (* n PI)) 1/2))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))) * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))) in n * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI))))) in n * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n * [misc]taylor: Taking taylor expansion of (sqrt 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (* 2 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (* (sqrt (* n PI)) (sqrt 2)) in n * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) * [misc]taylor: Taking taylor expansion of (sqrt 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log (* 2 PI)) (log n))) into (* (+ (log (* 2 PI)) (log n)) (sqrt 2)) * [misc]backup-simplify: Simplify (* 0 (* (+ (log (* 2 PI)) (log n)) (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify (* 0 (sqrt 2)) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* +nan.0 (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 PI)) * [misc]backup-simplify: Simplify (- (* +nan.0 PI)) into (- (* +nan.0 PI)) * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (* 0 n))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* -1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* n (* 2 PI))) (pow (log (* 2 (* n PI))) 2))) * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (* +nan.0 (* 1/8 (* (sqrt (* n (* 2 PI))) (pow (log (* 2 (* n PI))) 2)))) (+ (* (- +nan.0) (* -1/2 (* (sqrt (* n (* 2 PI))) (log (* 2 (* n PI)))))) (* (- +nan.0) (pow (* 2 (* n PI)) 1/2)))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))))) * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))))) in n * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI))))) in n * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n * [misc]taylor: Taking taylor expansion of (sqrt 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (* 2 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))) in n * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2))) in n * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n * [misc]taylor: Taking taylor expansion of (sqrt 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n * [misc]taylor: Taking taylor expansion of (exp (* 2 (log (log (* 2 (* n PI)))))) in n * [misc]taylor: Taking taylor expansion of (* 2 (log (log (* 2 (* n PI))))) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (log (log (* 2 (* n PI)))) in n * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (* 2 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (log (+ (log (* 2 PI)) (log n))) into (log (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 2 (log (+ (log (* 2 PI)) (log n)))) into (* 2 (log (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 2 (log (+ (log (* 2 PI)) (log n))))) into (pow (+ (log (* 2 PI)) (log n)) 2) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (* (sqrt (* n PI)) (sqrt 2)) in n * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) * [misc]taylor: Taking taylor expansion of (sqrt 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log (* 2 PI)) (log n))) into (* (+ (log (* 2 PI)) (log n)) (sqrt 2)) * [misc]backup-simplify: Simplify (* 0 (* (+ (log (* 2 PI)) (log n)) (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow (+ (log (* 2 PI)) (log n)) 2)) into (* (pow (+ (log (* 2 PI)) (log n)) 2) (sqrt 2)) * [misc]backup-simplify: Simplify (* 0 (* (pow (+ (log (* 2 PI)) (log n)) 2) (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify (* 0 (sqrt 2)) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* (* +nan.0 PI) (* (+ (log (* 2 PI)) (log n)) (sqrt 2)))) into (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2))))))) * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2)))))))) (* 0 0)) into (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2))))))) * [misc]backup-simplify: Simplify (+ (* 0 0) (* (* +nan.0 PI) (sqrt 2))) into (- (* +nan.0 (* PI (sqrt 2)))) * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* PI (sqrt 2))))) (* 0 0)) into (- (* +nan.0 (* PI (sqrt 2)))) * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* PI (sqrt 2))))) into (- (* +nan.0 (* PI (sqrt 2)))) * [misc]backup-simplify: Simplify (+ (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2))))))) (- (* +nan.0 (* PI (sqrt 2))))) into (- (+ (* +nan.0 (* PI (sqrt 2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2))))))))) * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* PI (sqrt 2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2)))))))))) into (- (+ (* +nan.0 (* PI (sqrt 2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2))))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* PI (sqrt 2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2))))))))) into (- (+ (* +nan.0 (* PI (sqrt 2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2))))))))) * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) * [misc]backup-simplify: Simplify (+ (* +nan.0 (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (pow PI 2))) * [misc]backup-simplify: Simplify (- (* +nan.0 (pow PI 2))) into (- (* +nan.0 (pow PI 2))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (pow PI 2))) (* (pow n 2) (/ 1 k))) (+ (* (- (+ (* +nan.0 (* PI (sqrt 2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2))))))))) (* n 1)) (* (- (* +nan.0 PI)) (* n (/ 1 k))))) into (- (+ (* +nan.0 (/ (* (pow n 2) (pow PI 2)) k)) (- (+ (* +nan.0 (* n (* PI (sqrt 2)))) (- (+ (* +nan.0 (/ (* n PI) k)) (- (+ (* +nan.0 (* n (* PI (* (log n) (sqrt 2))))) (- (* +nan.0 (* n (* PI (* (log (* 2 PI)) (sqrt 2)))))))))))))) * [misc]approximate: Taking taylor expansion of (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) in (k n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ 1 (sqrt (/ 1 k))) into (sqrt k) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [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 (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) 1) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [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 (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [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 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [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 (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [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 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) into (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (/ PI n) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ PI 1) into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (* (- (log (* 2 PI)) (log n)) (- 1 (/ 1 k))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* (- +nan.0) (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) into (- (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (/ PI n) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ PI 1) into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (* (- (log (* 2 PI)) (log n)) (- 1 (/ 1 k))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- (log (* 2 PI)) (log n)) 0) (* 0 (- 1 (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 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 (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (+ (* (- +nan.0) 0) (* (- +nan.0) (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))))) into (- (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (/ PI n) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ PI 1) into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (* (- (log (* 2 PI)) (log n)) (- 1 (/ 1 k))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))) (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))))))) * [misc]approximate: Taking taylor expansion of (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) in (k n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (/ 1 (sqrt (/ -1 k))) into (/ 1 (sqrt (/ -1 k))) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) -1) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) (/ -1 n)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) * [misc]taylor: Taking taylor expansion of (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) (/ -1 n)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))) in n * [misc]taylor: Taking taylor expansion of (+ 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n * [misc]taylor: Taking taylor expansion of -2 in n * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of (/ PI n) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ PI 1) into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) into (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) * [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 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* (- +nan.0) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))) in n * [misc]taylor: Taking taylor expansion of (+ 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n * [misc]taylor: Taking taylor expansion of -2 in n * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of (/ PI n) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ PI 1) into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) into (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (+ 1 (/ 1 k)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) 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 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (+ (* (- +nan.0) 0) (* (- +nan.0) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))) in n * [misc]taylor: Taking taylor expansion of (+ 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n * [misc]taylor: Taking taylor expansion of -2 in n * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of (/ PI n) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ PI 1) into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) into (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))))))) * * * * [misc]progress: [ 4 / 4 ] generating series at (2 2) * [misc]approximate: Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) n)) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) n) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) n)) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) n) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) 0) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 1) (* 0 0)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) n)) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) n) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) 0) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 1) (* 0 0)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 k) (+ (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1 (+ (log (* 2 PI)) (log n))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 1) (* 0 0))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (+ (* 1 0) (* -1 (+ (log (* 2 PI)) (log n)))) into (- (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n)))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) * [misc]backup-simplify: Simplify (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 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) (+ (* -1 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* k 1)) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (+ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (log n) (pow k 2)))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))))) * [misc]approximate: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [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 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [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 (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) 1) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [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 (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) 1) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [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 (- (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) * [misc]approximate: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) (/ -1 n)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) -1) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) -1) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (+ 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [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 (- (log (* -2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k * [misc]taylor: Taking taylor expansion of (* -2 PI) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [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 (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (expm1 (* 2 (* n PI))) * [exit]simplify: Simplified to (expm1 (* 2 (* n PI))) * * * * [misc]progress: [ 2 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (log1p (* 2 (* n PI))) * [exit]simplify: Simplified to (log1p (* 2 (* n PI))) * * * * [misc]progress: [ 3 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 4 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * * [misc]simplify: iters left: 2 (40 enodes) * [exit]simplify: Simplified to (log (* (* n PI) 2)) * [exit]simplify: Simplified to (log (* (* n PI) 2)) * * * * [misc]progress: [ 5 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * * [misc]simplify: iters left: 2 (29 enodes) * * [misc]simplify: iters left: 1 (40 enodes) * [exit]simplify: Simplified to (pow (exp PI) (* n 2)) * [exit]simplify: Simplified to (pow (exp PI) (* n 2)) * * * * [misc]progress: [ 6 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* (* 2 PI) n)) (cbrt (* (* 2 PI) n))) * * [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 (18 enodes) * [exit]simplify: Simplified to (* (cbrt (* (* n PI) 2)) (cbrt (* (* n PI) 2))) * [exit]simplify: Simplified to (* (cbrt (* (* n PI) 2)) (cbrt (* (* n PI) 2))) * [enter]simplify: Simplifying (cbrt (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (cbrt (* 2 (* n PI))) * [exit]simplify: Simplified to (cbrt (* 2 (* n PI))) * * * * [misc]progress: [ 7 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (* 2 PI) n) (* (* 2 PI) n)) (* (* 2 PI) n)) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * [exit]simplify: Simplified to (pow (* (* n 2) PI) 3) * [exit]simplify: Simplified to (pow (* (* n 2) PI) 3) * * * * [misc]progress: [ 8 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (sqrt (* 2 (* n PI))) * [exit]simplify: Simplified to (sqrt (* 2 (* n PI))) * [enter]simplify: Simplifying (sqrt (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (sqrt (* 2 (* n PI))) * [exit]simplify: Simplified to (sqrt (* 2 (* n PI))) * * * * [misc]progress: [ 9 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 10 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* PI n) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* n PI) * [exit]simplify: Simplified to (* n PI) * * * * [misc]progress: [ 11 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 12 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (/ 1 (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (expm1 (/ 1 (sqrt k))) * [exit]simplify: Simplified to (expm1 (/ 1 (sqrt k))) * * * * [misc]progress: [ 13 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (/ 1 (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (log1p (/ 1 (sqrt k))) * [exit]simplify: Simplified to (log1p (/ 1 (sqrt k))) * * * * [misc]progress: [ 14 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 15 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- 1/2) * * [misc]simplify: iters left: 2 (2 enodes) * [exit]simplify: Simplified to (- 1/2) * [exit]simplify: Simplified to (- 1/2) * * * * [misc]progress: [ 16 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- 1) * * [misc]simplify: iters left: 2 (2 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (- 1) * [exit]simplify: Simplified to (- 1) * * * * [misc]progress: [ 17 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 18 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (sqrt k))) * * [misc]simplify: iters left: 4 (4 enodes) * [exit]simplify: Simplified to (- (log (sqrt k))) * [exit]simplify: Simplified to (- (log (sqrt k))) * * * * [misc]progress: [ 19 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (log (/ 1 (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (11 enodes) * * [misc]simplify: iters left: 2 (12 enodes) * * [misc]simplify: iters left: 1 (16 enodes) * [exit]simplify: Simplified to (- (log (sqrt k))) * [exit]simplify: Simplified to (- (log (sqrt k))) * * * * [misc]progress: [ 20 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (/ 1 (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (exp (/ 1 (sqrt k))) * [exit]simplify: Simplified to (exp (/ 1 (sqrt k))) * * * * [misc]progress: [ 21 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (8 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) * [enter]simplify: Simplifying (cbrt (/ 1 (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (cbrt (/ 1 (sqrt k))) * [exit]simplify: Simplified to (cbrt (/ 1 (sqrt k))) * * * * [misc]progress: [ 22 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (60 enodes) * * [misc]simplify: iters left: 1 (79 enodes) * [exit]simplify: Simplified to (/ (/ 1 k) (sqrt k)) * [exit]simplify: Simplified to (/ (/ 1 k) (sqrt k)) * * * * [misc]progress: [ 23 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ 1 (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt k))) * [enter]simplify: Simplifying (sqrt (/ 1 (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt k))) * * * * [misc]progress: [ 24 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- 1) * * [misc]simplify: iters left: 2 (2 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (- 1) * [exit]simplify: Simplified to (- 1) * [enter]simplify: Simplifying (- (sqrt k)) * * [misc]simplify: iters left: 3 (3 enodes) * [exit]simplify: Simplified to (- (sqrt k)) * [exit]simplify: Simplified to (- (sqrt k)) * * * * [misc]progress: [ 25 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 26 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt k)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (6 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * * * * [misc]progress: [ 27 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) 1) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (6 enodes) * * [misc]simplify: iters left: 1 (8 enodes) * [exit]simplify: Simplified to (sqrt k) * [exit]simplify: Simplified to (sqrt k) * * * * [misc]progress: [ 28 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * * * [misc]progress: [ 29 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) * * * * [misc]progress: [ 30 / 88 ] 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 * [exit]simplify: Simplified to 1 * * * * [misc]progress: [ 31 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (14 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 (57 enodes) * * [misc]simplify: iters left: 1 (64 enodes) * [exit]simplify: Simplified to (expm1 (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (expm1 (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 32 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (14 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 (57 enodes) * * [misc]simplify: iters left: 1 (64 enodes) * [exit]simplify: Simplified to (log1p (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (log1p (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 33 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 34 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (164 enodes) * [exit]simplify: Simplified to (fma (log (* n (* PI 2))) (/ (- 1 k) 2) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* n (* PI 2))) (/ (- 1 k) 2) (- (log (sqrt k)))) * * * * [misc]progress: [ 35 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (164 enodes) * [exit]simplify: Simplified to (fma (log (* n (* PI 2))) (/ (- 1 k) 2) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* n (* PI 2))) (/ (- 1 k) 2) (- (log (sqrt k)))) * * * * [misc]progress: [ 36 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (302 enodes) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* PI (* n 2))) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* PI (* n 2))) (- (log (sqrt k)))) * * * * [misc]progress: [ 37 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (195 enodes) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* n (* PI 2))) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* n (* PI 2))) (- (log (sqrt k)))) * * * * [misc]progress: [ 38 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (195 enodes) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* n (* PI 2))) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* n (* PI 2))) (- (log (sqrt k)))) * * * * [misc]progress: [ 39 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (/ 1 (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (120 enodes) * * [misc]simplify: iters left: 2 (436 enodes) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* n (* PI 2))) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* n (* PI 2))) (- (log (sqrt k)))) * * * * [misc]progress: [ 40 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (103 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * [exit]simplify: Simplified to (fma (log (* PI (* n 2))) (/ (- 1 k) 2) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* PI (* n 2))) (/ (- 1 k) 2) (- (log (sqrt k)))) * * * * [misc]progress: [ 41 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (pow (exp (/ 1 (sqrt k))) (pow (* n (* PI 2)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (pow (exp (/ 1 (sqrt k))) (pow (* n (* PI 2)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 42 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (179 enodes) * * [misc]simplify: iters left: 2 (347 enodes) * [exit]simplify: Simplified to (* (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (pow (* (* PI 2) n) (/ (- 1 k) 2))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (* k (sqrt k)))) * [exit]simplify: Simplified to (* (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (pow (* (* PI 2) n) (/ (- 1 k) 2))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (* k (sqrt k)))) * * * * [misc]progress: [ 43 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) * * [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 (54 enodes) * * [misc]simplify: iters left: 2 (58 enodes) * * [misc]simplify: iters left: 1 (65 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) * [enter]simplify: Simplifying (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (14 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 (57 enodes) * * [misc]simplify: iters left: 1 (64 enodes) * [exit]simplify: Simplified to (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 44 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (202 enodes) * * [misc]simplify: iters left: 2 (465 enodes) * [exit]simplify: Simplified to (/ (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* n (* PI 2)) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* n (* PI 2)) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 45 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (14 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 (57 enodes) * * [misc]simplify: iters left: 1 (64 enodes) * [exit]simplify: Simplified to (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) * [enter]simplify: Simplifying (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (14 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 (57 enodes) * * [misc]simplify: iters left: 1 (64 enodes) * [exit]simplify: Simplified to (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 46 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* 1 (pow (* (* 2 PI) n) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (/ 1 2)) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (/ 1 2)) * [enter]simplify: Simplifying (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (* (sqrt k) (pow (* 2 (* PI n)) (/ k 2))) * [exit]simplify: Simplified to (* (sqrt k) (pow (* 2 (* PI n)) (/ k 2))) * * * * [misc]progress: [ 47 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 48 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * * [misc]simplify: iters left: 2 (44 enodes) * * [misc]simplify: iters left: 1 (51 enodes) * [exit]simplify: Simplified to (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 49 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (102 enodes) * * [misc]simplify: iters left: 1 (106 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt k)) * [exit]simplify: Simplified to (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt k)) * * * * [misc]progress: [ 50 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (14 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 (57 enodes) * * [misc]simplify: iters left: 1 (64 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)) * * * * [misc]progress: [ 51 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) 1) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * * * * [misc]progress: [ 52 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (14 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 (* (cbrt (/ 1 (sqrt k))) (pow (* n (* PI 2)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt k))) (pow (* n (* PI 2)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 53 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (14 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 (/ 1 (sqrt k))) (pow (* n (* PI 2)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt k))) (pow (* n (* PI 2)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 54 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (63 enodes) * [exit]simplify: Simplified to (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 55 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (63 enodes) * [exit]simplify: Simplified to (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 56 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * * [misc]simplify: iters left: 2 (45 enodes) * * [misc]simplify: iters left: 1 (52 enodes) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)) * * * * [misc]progress: [ 57 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ (- 1 k) 2)) * * * * [misc]progress: [ 58 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 59 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (expm1 (pow (* (* PI 2) n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (expm1 (pow (* (* PI 2) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 60 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (log1p (pow (* (* PI 2) n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (log1p (pow (* (* PI 2) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 61 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2)))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2)))) * * * * [misc]progress: [ 62 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2)))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2)))) * * * * [misc]progress: [ 63 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* 1 (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (81 enodes) * [exit]simplify: Simplified to (/ (- 1 k) 2) * [exit]simplify: Simplified to (/ (- 1 k) 2) * * * * [misc]progress: [ 64 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (/ 1 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * * [misc]simplify: iters left: 2 (22 enodes) * [exit]simplify: Simplified to (pow (* (* PI 2) n) (/ 1 2)) * [exit]simplify: Simplified to (pow (* (* PI 2) n) (/ 1 2)) * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (/ k 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (18 enodes) * * [misc]simplify: iters left: 2 (20 enodes) * [exit]simplify: Simplified to (pow (* 2 (* n PI)) (/ k 2)) * [exit]simplify: Simplified to (pow (* 2 (* n PI)) (/ k 2)) * * * * [misc]progress: [ 65 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (pow (* (* PI 2) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (pow (* (* PI 2) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * * * [misc]progress: [ 66 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (pow (* (* PI 2) n) (sqrt (/ (- 1 k) 2))) * [exit]simplify: Simplified to (pow (* (* PI 2) n) (sqrt (/ (- 1 k) 2))) * * * * [misc]progress: [ 67 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* 2 PI) n) 1) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * * [misc]simplify: iters left: 2 (20 enodes) * [exit]simplify: Simplified to (* (* n PI) 2) * [exit]simplify: Simplified to (* (* n PI) 2) * * * * [misc]progress: [ 68 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (- 1 k)) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * * [misc]simplify: iters left: 2 (25 enodes) * [exit]simplify: Simplified to (pow (* (* PI 2) n) (- 1 k)) * [exit]simplify: Simplified to (pow (* (* PI 2) n) (- 1 k)) * * * * [misc]progress: [ 69 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* 2 PI) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * * [misc]simplify: iters left: 2 (21 enodes) * [exit]simplify: Simplified to (pow (* PI 2) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (* PI 2) (/ (- 1 k) 2)) * [enter]simplify: Simplifying (pow n (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (17 enodes) * * [misc]simplify: iters left: 2 (19 enodes) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * * * * [misc]progress: [ 70 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 71 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (246 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* (* PI 2) n))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* (* PI 2) n))) * * * * [misc]progress: [ 72 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (exp (pow (* (* PI 2) n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (exp (pow (* (* PI 2) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 73 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) * [enter]simplify: Simplifying (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 74 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (pow (pow (* PI (* n 2)) (/ (- 1 k) 2)) 3) * [exit]simplify: Simplified to (pow (pow (* PI (* n 2)) (/ (- 1 k) 2)) 3) * * * * [misc]progress: [ 75 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) * [enter]simplify: Simplifying (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 76 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 77 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (63 enodes) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 78 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (63 enodes) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 79 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (63 enodes) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 80 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (- (+ +nan.0 (- (+ (* +nan.0 k) (- (* +nan.0 (/ 1 k))))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 81 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (- (+ +nan.0 (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 2)))))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 82 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (- (+ +nan.0 (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 2)))))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 83 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (pow n 2) (pow PI 2)) k)) (- (+ (* +nan.0 (* n (* PI (sqrt 2)))) (- (+ (* +nan.0 (/ (* n PI) k)) (- (+ (* +nan.0 (* n (* PI (* (log n) (sqrt 2))))) (- (* +nan.0 (* n (* PI (* (log (* 2 PI)) (sqrt 2)))))))))))))) * * * * [misc]progress: [ 84 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))))))) * * * * [misc]progress: [ 85 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))))))) * * * * [misc]progress: [ 86 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (- (+ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (log n) (pow k 2)))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k)))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (117 enodes) * * [misc]simplify: iters left: 4 (405 enodes) * [exit]simplify: Simplified to (/ (+ (* (* (* k k) (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/8))) (+ (* (log (* PI 2)) (log (* PI 2))) (* (log n) (log n)))) (- (fma (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/4)) (* (* (log n) (* k k)) (log (* PI 2))) (* (pow n 1/2) (pow (* PI 2) 1/2))) (* (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/2)) (fma (log (* PI 2)) k (* (log n) k))))) (sqrt k)) * * * * [misc]progress: [ 87 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (293 enodes) * [exit]simplify: Simplified to (/ (* (pow (* PI 2) (- 1/2 (* k 1/2))) (pow n (- 1/2 (* k 1/2)))) (sqrt k)) * * * * [misc]progress: [ 88 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (307 enodes) * [exit]simplify: Simplified to (/ (pow (pow (exp 1/2) (- 1 k)) (- (log (* PI -2)) (log (/ -1 n)))) (sqrt k)) * * * [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 1) * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 2 2 1) * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 1 1) * * * * [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 (pow (* n (* PI 2)) (/ 1 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (pow (* n (* PI 2)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* n (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* n (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* n (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* n (* PI 2)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* n (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* n (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* n (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* 2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* 2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* 2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 1)))) 24) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* 2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* 2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 1)))) 120) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* 2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* 2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* 2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* 2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* 2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* 2 PI) 1)))) 720) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]approximate: Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* 2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* 2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* 2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 1)))) 24) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) 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 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* 2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* 2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 1)))) 120) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) 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 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* 2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* 2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* 2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* 2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* 2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* 2 PI) 1)))) 720) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) * [misc]approximate: Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) 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 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* -2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* -2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* -2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 1)))) 24) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 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 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* -2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* -2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* -2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* -2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* -2 PI) 1)))) 120) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [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 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* -2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* -2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* -2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* -2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* -2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* -2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* -2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* -2 PI) 1)))) 720) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) * * * * [misc]progress: [ 2 / 4 ] generating series at (2 2 2 1) * [misc]approximate: Taking taylor expansion of (* n (* PI 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) 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 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) 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 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) 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 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 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 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [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 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) * * * * [misc]progress: [ 3 / 4 ] generating series at (2 1 1) * [misc]approximate: Taking taylor expansion of (* n (* PI 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) 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 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) 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 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) 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 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 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 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [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 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) * * * * [misc]progress: [ 4 / 4 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) in k * [misc]taylor: Taking taylor expansion of (pow (* n (* PI 2)) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* n (* PI 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* n (* PI 2)))) in k * [misc]taylor: Taking taylor expansion of (/ 1 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* n (* PI 2))) in k * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of (* PI 2) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) in k * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]taylor: Taking taylor expansion of (pow (* n (* PI 2)) (/ k 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* n (* PI 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* n (* PI 2)))) in k * [misc]taylor: Taking taylor expansion of (/ k 2) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* n (* PI 2))) in k * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of (* PI 2) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp 0) into 1 * [misc]backup-simplify: Simplify (* 0 1) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (* 1/2 (log (* 2 (* n PI)))) 1) 1)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (+ (* 0 (* 1/2 (log (* 2 (* n PI))))) (* +nan.0 1)) into (- +nan.0) * [misc]backup-simplify: Simplify (/ (pow (* 2 (* n PI)) 1/2) (- +nan.0)) into (* +nan.0 (sqrt (* n (* 2 PI)))) * [misc]taylor: Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) in n * [misc]taylor: Taking taylor expansion of (pow (* n (* PI 2)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* n (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* n (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* n (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) in n * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]taylor: Taking taylor expansion of (pow (* n (* PI 2)) (/ k 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* n (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* n (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ k 2) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ k 2) into (* 1/2 k) * [misc]taylor: Taking taylor expansion of (log (* n (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 k) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* k (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (* (sqrt k) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) into (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k)) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k))) into (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) * [misc]taylor: Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) in n * [misc]taylor: Taking taylor expansion of (pow (* n (* PI 2)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* n (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* n (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* n (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) in n * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]taylor: Taking taylor expansion of (pow (* n (* PI 2)) (/ k 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* n (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* n (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ k 2) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ k 2) into (* 1/2 k) * [misc]taylor: Taking taylor expansion of (log (* n (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 k) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* k (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (* (sqrt k) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) into (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k)) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k))) into (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) * [misc]taylor: Taking taylor expansion of (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* k (+ (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* k (+ (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 0 (+ (log (* 2 PI)) (log n))) into 0 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (+ (log (* 2 PI)) (log n)))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 (+ (log (* 2 PI)) (log n))) (* 0 0)) into (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) * [misc]backup-simplify: Simplify (exp 0) into 1 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 1) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [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 (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k))) (+ (* (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1) 1)))) into (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (/ (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1)))) into (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) +nan.0) (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k))) (+ (* (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k)))) (* 0 (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (+ (log (* 2 PI)) (log n))) (* 0 0))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (/ (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))) 1)) (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) (/ (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1)))) into (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) +nan.0) (+ (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) +nan.0) (* (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) 0))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k))) (+ (* (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k)))) (* 0 (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k)))) (* 0 (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (+ (log (* 2 PI)) (log n))) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 3) 6)) (* (/ (pow (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (+ (* 1/16 (* (pow (log (* 2 PI)) 2) (log n))) (+ (* 1/48 (pow (log (* 2 PI)) 3)) (+ (* 1/48 (pow (log n) 3)) (* 1/16 (* (log (* 2 PI)) (pow (log n) 2)))))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (/ (+ (* 1/16 (* (pow (log (* 2 PI)) 2) (log n))) (+ (* 1/48 (pow (log (* 2 PI)) 3)) (+ (* 1/48 (pow (log n) 3)) (* 1/16 (* (log (* 2 PI)) (pow (log n) 2)))))) 1)) (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) (/ (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))) 1)) (* (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) (/ (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1)))) into (- (+ (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (log n)))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 3))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 3))) (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow (log n) 2)))))))) * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) +nan.0) (+ (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) +nan.0) (+ (* (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) +nan.0) (* (- (+ (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (log n)))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 3))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 3))) (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow (log n) 2)))))))) 0)))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))))))))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (pow (log n) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) k)) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (pow k 2) (log n)))))))))))))))))))))))) * [misc]approximate: Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) (* (sqrt (/ 1 k)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) (* (sqrt (/ 1 k)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2)))) in k * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (* PI 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (* PI 2)))) in k * [misc]taylor: Taking taylor expansion of (/ 1 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of (* PI 2) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) 1/2) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [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 (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (* PI 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) (* PI 2)))) in k * [misc]taylor: Taking taylor expansion of (/ (/ 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [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 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of (* PI 2) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (* PI 2))))) into (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) * [misc]backup-simplify: Simplify (* 0 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* +nan.0 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) into (- (* +nan.0 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) * [misc]backup-simplify: Simplify (/ (pow (* 2 (/ PI n)) 1/2) (- (* +nan.0 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) into (* +nan.0 (* (sqrt (/ (* 2 PI) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) (* (sqrt (/ 1 k)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2)))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (/ 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ (/ 1 k) 2) into (/ 1/2 k) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) (* (sqrt (/ 1 k)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2)))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (/ 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ (/ 1 k) 2) into (/ 1/2 k) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (- (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (- (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (+ (* (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (+ (* (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) (* 0 (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (+ (* (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) (* 0 (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) (* 0 (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* k (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 2) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 3) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n)))))))))))))) * [misc]approximate: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) (* (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) (* (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2)))) in k * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2)))) in k * [misc]taylor: Taking taylor expansion of (/ 1 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of (* PI 2) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ -1 n) (* 2 PI)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* -2 (/ PI n))))) into (pow (* -2 (/ PI n)) 1/2) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (* PI 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (* PI 2)))) in k * [misc]taylor: Taking taylor expansion of (/ (/ 1 (- k)) 2) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of (* PI 2) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ -1 n) (* 2 PI)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* -1/2 (log (* -2 (/ PI n)))) into (* -1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (* PI 2))))) into (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) * [misc]backup-simplify: Simplify (* 0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* +nan.0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) into (- (* +nan.0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) * [misc]backup-simplify: Simplify (/ (pow (* -2 (/ PI n)) 1/2) (- (* +nan.0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) into (* +nan.0 (* (sqrt (/ (* PI -2) n)) (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) (* (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2)))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2))) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (/ 1 (- k)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ (/ -1 k) 2) into (/ -1/2 k) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) (* (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2)))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2))) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (/ 1 (- k)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ (/ -1 k) 2) into (/ -1/2 k) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (- (log (* -2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (- (log (* -2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k * [misc]taylor: Taking taylor expansion of (* -2 PI) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) in k * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k * [misc]taylor: Taking taylor expansion of -1/2 in k * [misc]backup-simplify: Simplify -1/2 into -1/2 * [misc]taylor: Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k * [misc]taylor: Taking taylor expansion of (* -2 PI) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) 1) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* -1/2 (- (log (* -2 PI)) (log n))) into (* -1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k * [misc]taylor: Taking taylor expansion of (/ -1 k) in k * [misc]taylor: Taking taylor expansion of -1 in k * [misc]backup-simplify: Simplify -1 into -1 * [misc]taylor: Taking taylor expansion of k in k * [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 (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 0) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) 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 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) 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 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ -1 k)) 0) (* 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) (/ 0 (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (- (/ 0 (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (+ (* (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ -1 k)) 0) (+ (* 0 0) (* 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) (/ 0 (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))))) (* 0 (/ 0 (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (- (/ 0 (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (+ (* (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))))))))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (pow (* n (* PI 2)) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (expm1 (pow (* (* PI n) 2) (/ 1 2))) * [exit]simplify: Simplified to (expm1 (pow (* (* PI n) 2) (/ 1 2))) * * * * [misc]progress: [ 2 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (pow (* n (* PI 2)) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (log1p (pow (* (* PI n) 2) (/ 1 2))) * [exit]simplify: Simplified to (log1p (pow (* (* PI n) 2) (/ 1 2))) * * * * [misc]progress: [ 3 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* n (* PI 2))) (/ 1 2)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (180 enodes) * * [misc]simplify: iters left: 1 (391 enodes) * [exit]simplify: Simplified to (fma (log (* 2 PI)) (/ 1 2) (/ (log n) 2)) * [exit]simplify: Simplified to (fma (log (* 2 PI)) (/ 1 2) (/ (log n) 2)) * * * * [misc]progress: [ 4 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* n (* PI 2))) (/ 1 2)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (180 enodes) * * [misc]simplify: iters left: 1 (391 enodes) * [exit]simplify: Simplified to (fma (log (* 2 PI)) (/ 1 2) (/ (log n) 2)) * [exit]simplify: Simplified to (fma (log (* 2 PI)) (/ 1 2) (/ (log n) 2)) * * * * [misc]progress: [ 5 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (* 1 (/ 1 2)) * * [misc]simplify: iters left: 4 (4 enodes) * * [misc]simplify: iters left: 3 (9 enodes) * [exit]simplify: Simplified to (/ 1 2) * [exit]simplify: Simplified to (/ 1 2) * * * * [misc]progress: [ 6 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n (* PI 2)) (* (cbrt (/ 1 2)) (cbrt (/ 1 2)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (pow (* (* n 2) PI) (* (cbrt (/ 1 2)) (cbrt (/ 1 2)))) * [exit]simplify: Simplified to (pow (* (* n 2) PI) (* (cbrt (/ 1 2)) (cbrt (/ 1 2)))) * * * * [misc]progress: [ 7 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n (* PI 2)) (sqrt (/ 1 2))) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (22 enodes) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (sqrt (/ 1 2))) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (sqrt (/ 1 2))) * * * * [misc]progress: [ 8 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n (* PI 2)) 1) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * * [misc]simplify: iters left: 2 (20 enodes) * [exit]simplify: Simplified to (* (* PI n) 2) * [exit]simplify: Simplified to (* (* PI n) 2) * * * * [misc]progress: [ 9 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n (* PI 2)) 1) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * * [misc]simplify: iters left: 2 (20 enodes) * [exit]simplify: Simplified to (* (* PI n) 2) * [exit]simplify: Simplified to (* (* PI n) 2) * * * * [misc]progress: [ 10 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (pow n (/ 1 2)) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * [exit]simplify: Simplified to (pow n (/ 1 2)) * [exit]simplify: Simplified to (pow n (/ 1 2)) * [enter]simplify: Simplifying (pow (* PI 2) (/ 1 2)) * * [misc]simplify: iters left: 3 (6 enodes) * * [misc]simplify: iters left: 2 (9 enodes) * [exit]simplify: Simplified to (pow (* 2 PI) (/ 1 2)) * [exit]simplify: Simplified to (pow (* 2 PI) (/ 1 2)) * * * * [misc]progress: [ 11 / 86 ] simplifiying candidate # * * * * [misc]progress: [ 12 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (log (pow (* n (* PI 2)) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (72 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (429 enodes) * [exit]simplify: Simplified to (fma (log (* PI n)) (/ 1 2) (/ (log 2) 2)) * [exit]simplify: Simplified to (fma (log (* PI n)) (/ 1 2) (/ (log 2) 2)) * * * * [misc]progress: [ 13 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (pow (* n (* PI 2)) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (exp (pow (* (* PI n) 2) (/ 1 2))) * [exit]simplify: Simplified to (exp (pow (* (* PI n) 2) (/ 1 2))) * * * * [misc]progress: [ 14 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) * [enter]simplify: Simplifying (cbrt (pow (* n (* PI 2)) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (cbrt (pow (* (* PI n) 2) (/ 1 2))) * [exit]simplify: Simplified to (cbrt (pow (* (* PI n) 2) (/ 1 2))) * * * * [misc]progress: [ 15 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ 1 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (pow (pow (* (* n 2) PI) (/ 1 2)) 3) * [exit]simplify: Simplified to (pow (pow (* (* n 2) PI) (/ 1 2)) 3) * * * * [misc]progress: [ 16 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (pow (* n (* PI 2)) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (/ 1 2))) * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (/ 1 2))) * [enter]simplify: Simplifying (sqrt (pow (* n (* PI 2)) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (/ 1 2))) * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (/ 1 2))) * * * * [misc]progress: [ 17 / 86 ] simplifiying candidate # * * * * [misc]progress: [ 18 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (expm1 (* (* n 2) PI)) * [exit]simplify: Simplified to (expm1 (* (* n 2) PI)) * * * * [misc]progress: [ 19 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (log1p (* (* n 2) PI)) * [exit]simplify: Simplified to (log1p (* (* n 2) PI)) * * * * [misc]progress: [ 20 / 86 ] simplifiying candidate # * * * * [misc]progress: [ 21 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * * [misc]simplify: iters left: 2 (41 enodes) * [exit]simplify: Simplified to (log (* (* PI n) 2)) * [exit]simplify: Simplified to (log (* (* PI n) 2)) * * * * [misc]progress: [ 22 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * * [misc]simplify: iters left: 2 (35 enodes) * * [misc]simplify: iters left: 1 (47 enodes) * [exit]simplify: Simplified to (pow (exp 2) (* PI n)) * [exit]simplify: Simplified to (pow (exp 2) (* PI n)) * * * * [misc]progress: [ 23 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) * * [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 (18 enodes) * [exit]simplify: Simplified to (* (cbrt (* (* PI n) 2)) (cbrt (* (* PI n) 2))) * [exit]simplify: Simplified to (* (cbrt (* (* PI n) 2)) (cbrt (* (* PI n) 2))) * [enter]simplify: Simplifying (cbrt (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (cbrt (* (* n 2) PI)) * [exit]simplify: Simplified to (cbrt (* (* n 2) PI)) * * * * [misc]progress: [ 24 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (203 enodes) * [exit]simplify: Simplified to (pow (* (* PI n) 2) 3) * [exit]simplify: Simplified to (pow (* (* PI n) 2) 3) * * * * [misc]progress: [ 25 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (sqrt (* (* n 2) PI)) * [exit]simplify: Simplified to (sqrt (* (* n 2) PI)) * [enter]simplify: Simplifying (sqrt (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (sqrt (* (* n 2) PI)) * [exit]simplify: Simplified to (sqrt (* (* n 2) PI)) * * * * [misc]progress: [ 26 / 86 ] simplifiying candidate # * * * * [misc]progress: [ 27 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (* n PI) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* PI n) * [exit]simplify: Simplified to (* PI n) * * * * [misc]progress: [ 28 / 86 ] simplifiying candidate # * * * * [misc]progress: [ 29 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (expm1 (* (* n 2) PI)) * [exit]simplify: Simplified to (expm1 (* (* n 2) PI)) * * * * [misc]progress: [ 30 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (log1p (* (* n 2) PI)) * [exit]simplify: Simplified to (log1p (* (* n 2) PI)) * * * * [misc]progress: [ 31 / 86 ] simplifiying candidate # * * * * [misc]progress: [ 32 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * * [misc]simplify: iters left: 2 (41 enodes) * [exit]simplify: Simplified to (log (* (* PI n) 2)) * [exit]simplify: Simplified to (log (* (* PI n) 2)) * * * * [misc]progress: [ 33 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * * [misc]simplify: iters left: 2 (35 enodes) * * [misc]simplify: iters left: 1 (47 enodes) * [exit]simplify: Simplified to (pow (exp 2) (* PI n)) * [exit]simplify: Simplified to (pow (exp 2) (* PI n)) * * * * [misc]progress: [ 34 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) * * [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 (18 enodes) * [exit]simplify: Simplified to (* (cbrt (* (* PI n) 2)) (cbrt (* (* PI n) 2))) * [exit]simplify: Simplified to (* (cbrt (* (* PI n) 2)) (cbrt (* (* PI n) 2))) * [enter]simplify: Simplifying (cbrt (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (cbrt (* (* n 2) PI)) * [exit]simplify: Simplified to (cbrt (* (* n 2) PI)) * * * * [misc]progress: [ 35 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (203 enodes) * [exit]simplify: Simplified to (pow (* (* PI n) 2) 3) * [exit]simplify: Simplified to (pow (* (* PI n) 2) 3) * * * * [misc]progress: [ 36 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (sqrt (* (* n 2) PI)) * [exit]simplify: Simplified to (sqrt (* (* n 2) PI)) * [enter]simplify: Simplifying (sqrt (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (sqrt (* (* n 2) PI)) * [exit]simplify: Simplified to (sqrt (* (* n 2) PI)) * * * * [misc]progress: [ 37 / 86 ] simplifiying candidate # * * * * [misc]progress: [ 38 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (* n PI) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* PI n) * [exit]simplify: Simplified to (* PI n) * * * * [misc]progress: [ 39 / 86 ] simplifiying candidate # * * * * [misc]progress: [ 40 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * [exit]simplify: Simplified to (expm1 (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))) * [exit]simplify: Simplified to (expm1 (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))) * * * * [misc]progress: [ 41 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * [exit]simplify: Simplified to (log1p (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))) * [exit]simplify: Simplified to (log1p (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))) * * * * [misc]progress: [ 42 / 86 ] simplifiying candidate # * * * * [misc]progress: [ 43 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* n (* PI 2))) (/ 1 2)) (+ (log (sqrt k)) (* (log (* n (* PI 2))) (/ k 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (237 enodes) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 44 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* n (* PI 2))) (/ 1 2)) (+ (log (sqrt k)) (* (log (* n (* PI 2))) (/ k 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (237 enodes) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 45 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* n (* PI 2))) (/ 1 2)) (+ (log (sqrt k)) (log (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (234 enodes) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 46 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* n (* PI 2))) (/ 1 2)) (log (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (161 enodes) * [exit]simplify: Simplified to (fma (log (* PI (* n 2))) (/ 1 2) (fma (- (/ k 2)) (log (* PI (* n 2))) (- (log (sqrt k))))) * [exit]simplify: Simplified to (fma (log (* PI (* n 2))) (/ 1 2) (fma (- (/ k 2)) (log (* PI (* n 2))) (- (log (sqrt k))))) * * * * [misc]progress: [ 47 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* n (* PI 2))) (/ 1 2)) (+ (log (sqrt k)) (* (log (* n (* PI 2))) (/ k 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (237 enodes) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 48 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* n (* PI 2))) (/ 1 2)) (+ (log (sqrt k)) (* (log (* n (* PI 2))) (/ k 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (237 enodes) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 49 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* n (* PI 2))) (/ 1 2)) (+ (log (sqrt k)) (log (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (234 enodes) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 50 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* n (* PI 2))) (/ 1 2)) (log (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (161 enodes) * [exit]simplify: Simplified to (fma (log (* PI (* n 2))) (/ 1 2) (fma (- (/ k 2)) (log (* PI (* n 2))) (- (log (sqrt k))))) * [exit]simplify: Simplified to (fma (log (* PI (* n 2))) (/ 1 2) (fma (- (/ k 2)) (log (* PI (* n 2))) (- (log (sqrt k))))) * * * * [misc]progress: [ 51 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (pow (* n (* PI 2)) (/ 1 2))) (+ (log (sqrt k)) (* (log (* n (* PI 2))) (/ k 2)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (77 enodes) * * [misc]simplify: iters left: 3 (219 enodes) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 52 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (pow (* n (* PI 2)) (/ 1 2))) (+ (log (sqrt k)) (* (log (* n (* PI 2))) (/ k 2)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (77 enodes) * * [misc]simplify: iters left: 3 (219 enodes) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 53 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (pow (* n (* PI 2)) (/ 1 2))) (+ (log (sqrt k)) (log (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (156 enodes) * [exit]simplify: Simplified to (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 54 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (pow (* n (* PI 2)) (/ 1 2))) (log (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (128 enodes) * [exit]simplify: Simplified to (- (* (log (* PI (* n 2))) (- (/ 1 2) (/ k 2))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (log (* PI (* n 2))) (- (/ 1 2) (/ k 2))) (log (sqrt k))) * * * * [misc]progress: [ 55 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (log (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))) * * [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 (71 enodes) * * [misc]simplify: iters left: 2 (185 enodes) * [exit]simplify: Simplified to (fma (log (* (* 2 PI) n)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* (* 2 PI) n)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 56 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * [exit]simplify: Simplified to (exp (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))) * [exit]simplify: Simplified to (exp (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))) * * * * [misc]progress: [ 57 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ 1 2))) (* (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* n (* PI 2)) (/ k 2)) (pow (* n (* PI 2)) (/ k 2))) (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (134 enodes) * [exit]simplify: Simplified to (* (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (* (pow (* (* PI n) 2) (/ k 2)) (pow (* (* PI n) 2) (/ k 2)))) (/ (pow (* (* PI n) 2) (/ 1 2)) (/ (* (sqrt k) k) (pow (* (* PI n) 2) (/ 1 2))))) * [exit]simplify: Simplified to (* (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (* (pow (* (* PI n) 2) (/ k 2)) (pow (* (* PI n) 2) (/ k 2)))) (/ (pow (* (* PI n) 2) (/ 1 2)) (/ (* (sqrt k) k) (pow (* (* PI n) 2) (/ 1 2))))) * * * * [misc]progress: [ 58 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ 1 2))) (* (* (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (121 enodes) * * [misc]simplify: iters left: 3 (448 enodes) * [exit]simplify: Simplified to (* (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (* (pow (* (* PI n) 2) (/ k 2)) k)) (* (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (* (pow (* (* PI n) 2) (/ k 2)) k)) (* (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)))) * * * * [misc]progress: [ 59 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))) (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))) * * [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 (33 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* (* n 2) PI) (/ k 2)) (sqrt k)))) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* (* n 2) PI) (/ k 2)) (sqrt k))))) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* (* n 2) PI) (/ k 2)) (sqrt k)))) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* (* n 2) PI) (/ k 2)) (sqrt k))))) * [enter]simplify: Simplifying (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * [exit]simplify: Simplified to (cbrt (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))) * [exit]simplify: Simplified to (cbrt (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))) * * * * [misc]progress: [ 60 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (299 enodes) * [exit]simplify: Simplified to (/ (* (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2))) (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2)))) (* (/ (sqrt k) (pow (* (* 2 PI) n) (/ 1 2))) (* k (pow (* (* 2 PI) n) (/ k 2))))) * [exit]simplify: Simplified to (/ (* (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2))) (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2)))) (* (/ (sqrt k) (pow (* (* 2 PI) n) (/ 1 2))) (* k (pow (* (* 2 PI) n) (/ k 2))))) * * * * [misc]progress: [ 61 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * [exit]simplify: Simplified to (sqrt (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))) * [exit]simplify: Simplified to (sqrt (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))) * [enter]simplify: Simplifying (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * [exit]simplify: Simplified to (sqrt (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))) * [exit]simplify: Simplified to (sqrt (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))) * * * * [misc]progress: [ 62 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (- (pow (* n (* PI 2)) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (- (pow (* (* PI n) 2) (/ 1 2))) * [exit]simplify: Simplified to (- (pow (* (* PI n) 2) (/ 1 2))) * [enter]simplify: Simplifying (- (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * [exit]simplify: Simplified to (* (pow (* (* n PI) 2) (/ k 2)) (- (sqrt k))) * [exit]simplify: Simplified to (* (pow (* (* n PI) 2) (/ k 2)) (- (sqrt k))) * * * * [misc]progress: [ 63 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow n (/ 1 2)) (sqrt k)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (sqrt k)) * [enter]simplify: Simplifying (/ (pow (* PI 2) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) * * [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 (/ (pow (* 2 PI) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2))) * * * * [misc]progress: [ 64 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (sqrt k)) * * [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 (32 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2)))) (sqrt k)) * [exit]simplify: Simplified to (/ (* (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2)))) (sqrt k)) * [enter]simplify: Simplifying (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (pow (* (* PI n) 2) (/ k 2))) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (pow (* (* PI n) 2) (/ k 2))) * * * * [misc]progress: [ 65 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt k)) * * [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 (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt k)) * [enter]simplify: Simplifying (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (pow (* (* PI n) 2) (/ k 2))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (pow (* (* PI n) 2) (/ k 2))) * * * * [misc]progress: [ 66 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt k)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (6 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * [enter]simplify: Simplifying (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) * * [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 (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) * * * * [misc]progress: [ 67 / 86 ] simplifiying candidate # * * * * [misc]progress: [ 68 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt k)) (pow (* PI (* n 2)) (/ k 2))) * [exit]simplify: Simplified to (/ (/ 1 (sqrt k)) (pow (* PI (* n 2)) (/ k 2))) * * * * [misc]progress: [ 69 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) (pow (* n (* PI 2)) (/ 1 2))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (38 enodes) * * [misc]simplify: iters left: 1 (39 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))) * [exit]simplify: Simplified to (/ (sqrt k) (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))) * * * * [misc]progress: [ 70 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt k)) * * [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 (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)) * * * * [misc]progress: [ 71 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) (pow (* PI 2) (/ 1 2))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (38 enodes) * * [misc]simplify: iters left: 1 (39 enodes) * [exit]simplify: Simplified to (* (/ (sqrt k) (pow (* PI 2) (/ 1 2))) (pow (* PI (* n 2)) (/ k 2))) * [exit]simplify: Simplified to (* (/ (sqrt k) (pow (* PI 2) (/ 1 2))) (pow (* PI (* n 2)) (/ k 2))) * * * * [misc]progress: [ 72 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (39 enodes) * * [misc]simplify: iters left: 1 (40 enodes) * [exit]simplify: Simplified to (/ (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2))) (cbrt (pow (* 2 (* n PI)) (/ 1 2)))) * [exit]simplify: Simplified to (/ (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2))) (cbrt (pow (* 2 (* n PI)) (/ 1 2)))) * * * * [misc]progress: [ 73 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) (sqrt (pow (* n (* PI 2)) (/ 1 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (39 enodes) * * [misc]simplify: iters left: 1 (40 enodes) * [exit]simplify: Simplified to (/ (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2))) (sqrt (pow (* 2 (* n PI)) (/ 1 2)))) * [exit]simplify: Simplified to (/ (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2))) (sqrt (pow (* 2 (* n PI)) (/ 1 2)))) * * * * [misc]progress: [ 74 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) (pow (* n (* PI 2)) (/ 1 2))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (38 enodes) * * [misc]simplify: iters left: 1 (39 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))) * [exit]simplify: Simplified to (/ (sqrt k) (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))) * * * * [misc]progress: [ 75 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) * * [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 (115 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (305 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (* n 2)) (/ (sqrt PI) (sqrt k))) (pow (* (* n 2) PI) (/ k 2))) * * * * [misc]progress: [ 76 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (236 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (* PI 2)) (/ (sqrt n) (sqrt k))) (pow (* (* PI n) 2) (/ k 2))) * * * * [misc]progress: [ 77 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (112 enodes) * * [misc]simplify: iters left: 2 (271 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (* PI -2)) (pow (/ -1 n) 1/2)) (pow (* PI (* 2 n)) (/ k 2))) (sqrt k)) * * * * [misc]progress: [ 78 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* 2 (* PI n)) (/ 1 2)) (sqrt k)) (pow (* 2 (* PI n)) (/ k 2))) * * * * [misc]progress: [ 79 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* 2 (* PI n)) (/ 1 2)) (sqrt k)) (pow (* 2 (* PI n)) (/ k 2))) * * * * [misc]progress: [ 80 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* 2 (* PI n)) (/ 1 2)) (sqrt k)) (pow (* 2 (* PI n)) (/ k 2))) * * * * [misc]progress: [ 81 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* (* 2 PI) n) (/ 1 2)) (sqrt k)) (pow (* (* 2 PI) n) (/ k 2))) * * * * [misc]progress: [ 82 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* (* 2 PI) n) (/ 1 2)) (sqrt k)) (pow (* (* 2 PI) n) (/ k 2))) * * * * [misc]progress: [ 83 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* (* 2 PI) n) (/ 1 2)) (sqrt k)) (pow (* (* 2 PI) n) (/ k 2))) * * * * [misc]progress: [ 84 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (pow (log n) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) k)) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (pow k 2) (log n)))))))))))))))))))))))) * * * * [misc]progress: [ 85 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* k (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 2) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 3) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n)))))))))))))) * * * * [misc]progress: [ 86 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))))))))) * * * [misc]progress: adding candidates to table * * [misc]progress: iteration 4 / 4 * * * [misc]progress: picking best candidate * * * * [misc]pick: Picked # * * * [misc]progress: localizing error * * * [misc]progress: generating rewritten candidates * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 1 1 1) * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 2 1 1 1) * * * * [misc]progress: [ 3 / 4 ] rewriting at (2) * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 2 1 1) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 4 ] generating series at (2 1 1 1) * [misc]approximate: Taking taylor expansion of (* PI (* n 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* PI (* n 2)) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* n 2) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* PI (* n 2)) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* n 2) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* 0 2) into 0 * [misc]backup-simplify: Simplify (* PI 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 2)) into 2 * [misc]backup-simplify: Simplify (+ (* PI 2) (* 0 0)) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 2) (* 0 0))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 2) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 0 0)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 0 0))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 0 0)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* PI (* (/ 1 n) 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 n) 2)) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* (/ 1 n) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [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 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 n) 2)) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* (/ 1 n) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [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 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* 1 2) into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* PI (* (/ 1 (- n)) 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- n)) 2)) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- n)) 2)) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* -1 2) into -2 * [misc]backup-simplify: Simplify (* PI -2) into (* -2 PI) * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 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 (+ (* -1 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 -2)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 -2))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 -2)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -2))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -2)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -2))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) * * * * [misc]progress: [ 2 / 4 ] generating series at (2 2 1 1 1) * [misc]approximate: Taking taylor expansion of (* n (* PI 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) 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 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) 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 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) 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 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 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 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [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 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) * * * * [misc]progress: [ 3 / 4 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))) in k * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI (* n 2)) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* PI (* n 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* PI (* n 2)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* PI (* n 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* n 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* n 2) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* n 2) into (* 2 n) * [misc]backup-simplify: Simplify (* PI (* 2 n)) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]backup-simplify: Simplify (sqrt (pow (* 2 (* n PI)) 1/2)) into (pow (* n (* 2 PI)) 1/4) * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 (* 2 n))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (- (/ -1 2) (+ (* 1/2 (/ 0 2)))) into -1/2 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* n (* 2 PI))) (log (* 2 (* n PI))))) * [misc]backup-simplify: Simplify (/ (* -1/2 (* (sqrt (* n (* 2 PI))) (log (* 2 (* n PI))))) (* 2 (sqrt (pow (* 2 (* n PI)) 1/2)))) into (* -1/4 (* (pow (/ (* n PI) 2) 1/4) (* (sqrt 2) (log (* 2 (* n PI)))))) * [misc]taylor: Taking taylor expansion of (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* n (* PI 2)) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (* PI 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (* PI 2)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* n (* PI 2))) in k * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of (* PI 2) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]backup-simplify: Simplify (sqrt (pow (* 2 (* n PI)) 1/2)) into (pow (* n (* 2 PI)) 1/4) * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (- (/ -1 2) (+ (* 1/2 (/ 0 2)))) into -1/2 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* n (* 2 PI))) (log (* 2 (* n PI))))) * [misc]backup-simplify: Simplify (/ (* -1/2 (* (sqrt (* n (* 2 PI))) (log (* 2 (* n PI))))) (* 2 (sqrt (pow (* 2 (* n PI)) 1/2)))) into (* -1/4 (* (pow (/ (* n PI) 2) 1/4) (* (sqrt 2) (log (* 2 (* n PI)))))) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (pow (* n (* 2 PI)) 1/4) +nan.0) into (* +nan.0 (pow (* n (* 2 PI)) 1/4)) * [misc]taylor: Taking taylor expansion of (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))) in n * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* PI (* n 2)) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* PI (* n 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* PI (* n 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (* PI (* n 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* n 2)) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* n 2) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* 0 2) into 0 * [misc]backup-simplify: Simplify (* PI 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 2)) into 2 * [misc]backup-simplify: Simplify (+ (* PI 2) (* 0 0)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) into (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 2) (* 0 0))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))))) into 0 * [misc]taylor: Taking taylor expansion of (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* n (* PI 2)) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (* n (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) into (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))))) into 0 * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) (sqrt k)) into (sqrt (/ (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) k)) * [misc]taylor: Taking taylor expansion of (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))) in n * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* PI (* n 2)) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* PI (* n 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* PI (* n 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (* PI (* n 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* n 2)) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* n 2) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* 0 2) into 0 * [misc]backup-simplify: Simplify (* PI 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 2)) into 2 * [misc]backup-simplify: Simplify (+ (* PI 2) (* 0 0)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) into (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 2) (* 0 0))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))))) into 0 * [misc]taylor: Taking taylor expansion of (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* n (* PI 2)) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (* n (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) into (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))))) into 0 * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) (sqrt k)) into (sqrt (/ (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) k)) * [misc]backup-simplify: Simplify (* (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) (sqrt (/ (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) k))) into (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [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 (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 k) (+ (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1 (+ (log (* 2 PI)) (log n))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (* 0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (sqrt (/ (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) k)) (/ 0 (sqrt k))))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) 0) (* 0 (sqrt (/ (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) k)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (+ (* 1 0) (* -1 (+ (log (* 2 PI)) (log n)))) into (- (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n)))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) * [misc]backup-simplify: Simplify (+ (* 0 (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))))) (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (sqrt (/ (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) k)) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 2) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) 0) (+ (* 0 0) (* 0 (sqrt (/ (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) k))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 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) (+ (* -1 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))))) (+ (* +nan.0 (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))))) (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (sqrt (/ (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) k)) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 * [misc]backup-simplify: Simplify (+ 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) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/16 (* (pow (log (* 2 PI)) 2) (log n))) (+ (* 1/48 (pow (log (* 2 PI)) 3)) (+ (* 1/48 (pow (log n) 3)) (* 1/16 (* (log (* 2 PI)) (pow (log n) 2)))))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 0 (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/16 (* (pow (log (* 2 PI)) 2) (log n))) (+ (* 1/48 (pow (log (* 2 PI)) 3)) (+ (* 1/48 (pow (log n) 3)) (* 1/16 (* (log (* 2 PI)) (pow (log n) 2))))))))) (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))))) (+ (* +nan.0 (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))))) (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))))))))))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (pow (log n) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) k)) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (pow k 2) (log n)))))))))))))))))))))))) * [misc]approximate: Taking taylor expansion of (* (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (- 1 (/ 1 k)) 2))) (/ (sqrt (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (* (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (- 1 (/ 1 k)) 2))) (/ (sqrt (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (- 1 (/ 1 k)) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* PI (* (/ 1 n) 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* PI (* (/ 1 n) 2)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [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 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (* PI (* (/ 1 n) 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 n) 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* (/ 1 n) 2) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* (/ 1 n) 2) into (/ 2 n) * [misc]backup-simplify: Simplify (* PI (/ 2 n)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* PI (* (/ 1 n) 2))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) * [misc]backup-simplify: Simplify (sqrt (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) into (sqrt (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))))) into 0 * [misc]taylor: Taking taylor expansion of (/ (sqrt (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (sqrt (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [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 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of (* PI 2) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) * [misc]backup-simplify: Simplify (sqrt (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) into (sqrt (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))))) into 0 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [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 (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (sqrt (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) +nan.0) into (* +nan.0 (sqrt (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) * [misc]taylor: Taking taylor expansion of (* (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (- 1 (/ 1 k)) 2))) (/ (sqrt (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k)))) in n * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (- 1 (/ 1 k)) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* PI (* (/ 1 n) 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* PI (* (/ 1 n) 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* PI (* (/ 1 n) 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 n) 2)) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* (/ 1 n) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [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 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* 1 2) into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))) into 0 * [misc]taylor: Taking taylor expansion of (/ (sqrt (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (sqrt (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))) into 0 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) into (sqrt (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) k)) * [misc]taylor: Taking taylor expansion of (* (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (- 1 (/ 1 k)) 2))) (/ (sqrt (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k)))) in n * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (- 1 (/ 1 k)) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* PI (* (/ 1 n) 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* PI (* (/ 1 n) 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* PI (* (/ 1 n) 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 n) 2)) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* (/ 1 n) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [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 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* 1 2) into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))) into 0 * [misc]taylor: Taking taylor expansion of (/ (sqrt (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (sqrt (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))) into 0 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) into (sqrt (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) k)) * [misc]backup-simplify: Simplify (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (sqrt (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) k))) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [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 (- (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (sqrt (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) k)) (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 0) (* 0 (sqrt (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) k)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (sqrt (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) k)) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 0) (+ (* 0 0) (* 0 (sqrt (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) k))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (sqrt (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) k)) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) 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 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))))))) * [misc]approximate: Taking taylor expansion of (* (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (- 1 (/ 1 (- k))) 2))) (/ (sqrt (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k))))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (* (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (- 1 (/ 1 (- k))) 2))) (/ (sqrt (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k))))) in k * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (- 1 (/ 1 (- k))) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* PI (* (/ 1 (- n)) 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* PI (* (/ 1 (- n)) 2)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* PI (* (/ 1 (- n)) 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- n)) 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) 2) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* (/ -1 n) 2) into (/ -2 n) * [misc]backup-simplify: Simplify (* PI (/ -2 n)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* PI (* (/ 1 (- n)) 2))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) * [misc]backup-simplify: Simplify (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) into (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))))) into 0 * [misc]taylor: Taking taylor expansion of (/ (sqrt (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of (* PI 2) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ -1 n) (* 2 PI)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) * [misc]backup-simplify: Simplify (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) into (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))))) into 0 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) +nan.0) into (* +nan.0 (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) * [misc]taylor: Taking taylor expansion of (* (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (- 1 (/ 1 (- k))) 2))) (/ (sqrt (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k))))) in n * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (- 1 (/ 1 (- k))) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* PI (* (/ 1 (- n)) 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* PI (* (/ 1 (- n)) 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* PI (* (/ 1 (- n)) 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- n)) 2)) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* -1 2) into -2 * [misc]backup-simplify: Simplify (* PI -2) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) * [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 2)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 -2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))))) into 0 * [misc]taylor: Taking taylor expansion of (/ (sqrt (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (sqrt (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) 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 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))))) into 0 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) (sqrt (/ -1 k))) into (* (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) (/ 1 (sqrt (/ -1 k)))) * [misc]taylor: Taking taylor expansion of (* (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (- 1 (/ 1 (- k))) 2))) (/ (sqrt (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k))))) in n * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (- 1 (/ 1 (- k))) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* PI (* (/ 1 (- n)) 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* PI (* (/ 1 (- n)) 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* PI (* (/ 1 (- n)) 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- n)) 2)) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* -1 2) into -2 * [misc]backup-simplify: Simplify (* PI -2) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) * [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 2)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 -2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))))) into 0 * [misc]taylor: Taking taylor expansion of (/ (sqrt (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (sqrt (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) 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 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))))) into 0 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) (sqrt (/ -1 k))) into (* (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) (/ 1 (sqrt (/ -1 k)))) * [misc]backup-simplify: Simplify (* (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) (* (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) (/ 1 (sqrt (/ -1 k))))) into (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (+ 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [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 (- (log (* -2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k * [misc]taylor: Taking taylor expansion of (* -2 PI) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k * [misc]taylor: Taking taylor expansion of (/ -1 k) in k * [misc]taylor: Taking taylor expansion of -1 in k * [misc]backup-simplify: Simplify -1 into -1 * [misc]taylor: Taking taylor expansion of k in k * [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 (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (* (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) (/ 1 (sqrt (/ -1 k)))) (/ 0 (sqrt (/ -1 k)))))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) 0) (* 0 (* (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) (/ 1 (sqrt (/ -1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (* (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) (/ 1 (sqrt (/ -1 k)))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) 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 2))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 -2))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) 0) (+ (* 0 0) (* 0 (* (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) (/ 1 (sqrt (/ -1 k))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))))))) * * * * [misc]progress: [ 4 / 4 ] generating series at (2 2 1 1) * [misc]approximate: Taking taylor expansion of (pow (* n (* PI 2)) (/ (- 1 k) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* n (* PI 2)) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (* PI 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (* PI 2)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* n (* PI 2))) in k * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of (* PI 2) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]taylor: Taking taylor expansion of (pow (* n (* PI 2)) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (* n (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (* n (* PI 2)) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (* n (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 k) (+ (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1 (+ (log (* 2 PI)) (log n))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (+ (* 1 0) (* -1 (+ (log (* 2 PI)) (log n)))) into (- (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n)))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) * [misc]backup-simplify: Simplify (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 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) (+ (* -1 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* k 1)) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (+ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (log n) (pow k 2)))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))))) * [misc]approximate: Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [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 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of (* PI 2) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [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 (- (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) * [misc]approximate: Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of (* PI 2) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ -1 n) (* 2 PI)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-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 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (+ 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [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 (- (log (* -2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k * [misc]taylor: Taking taylor expansion of (* -2 PI) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) 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 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (* PI (* n 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (expm1 (* (* PI 2) n)) * [exit]simplify: Simplified to (expm1 (* (* PI 2) n)) * * * * [misc]progress: [ 2 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (* PI (* n 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (log1p (* (* PI 2) n)) * [exit]simplify: Simplified to (log1p (* (* PI 2) n)) * * * * [misc]progress: [ 3 / 103 ] simplifiying candidate # * * * * [misc]progress: [ 4 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* PI (* n 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * * [misc]simplify: iters left: 2 (41 enodes) * [exit]simplify: Simplified to (log (* (* n PI) 2)) * [exit]simplify: Simplified to (log (* (* n PI) 2)) * * * * [misc]progress: [ 5 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* PI (* n 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * * [misc]simplify: iters left: 2 (35 enodes) * * [misc]simplify: iters left: 1 (47 enodes) * [exit]simplify: Simplified to (pow (exp 2) (* n PI)) * [exit]simplify: Simplified to (pow (exp 2) (* n PI)) * * * * [misc]progress: [ 6 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* PI (* n 2))) (cbrt (* PI (* n 2)))) * * [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 (18 enodes) * [exit]simplify: Simplified to (* (cbrt (* (* n PI) 2)) (cbrt (* (* n PI) 2))) * [exit]simplify: Simplified to (* (cbrt (* (* n PI) 2)) (cbrt (* (* n PI) 2))) * [enter]simplify: Simplifying (cbrt (* PI (* n 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (cbrt (* (* PI 2) n)) * [exit]simplify: Simplified to (cbrt (* (* PI 2) n)) * * * * [misc]progress: [ 7 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* PI (* n 2)) (* PI (* n 2))) (* PI (* n 2))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (203 enodes) * [exit]simplify: Simplified to (pow (* (* n PI) 2) 3) * [exit]simplify: Simplified to (pow (* (* n PI) 2) 3) * * * * [misc]progress: [ 8 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* PI (* n 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) * [enter]simplify: Simplifying (sqrt (* PI (* n 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) * * * * [misc]progress: [ 9 / 103 ] simplifiying candidate # * * * * [misc]progress: [ 10 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* PI n) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* n PI) * [exit]simplify: Simplified to (* n PI) * * * * [misc]progress: [ 11 / 103 ] simplifiying candidate # * * * * [misc]progress: [ 12 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (expm1 (* (* n 2) PI)) * [exit]simplify: Simplified to (expm1 (* (* n 2) PI)) * * * * [misc]progress: [ 13 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (log1p (* (* n 2) PI)) * [exit]simplify: Simplified to (log1p (* (* n 2) PI)) * * * * [misc]progress: [ 14 / 103 ] simplifiying candidate # * * * * [misc]progress: [ 15 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * * [misc]simplify: iters left: 2 (41 enodes) * [exit]simplify: Simplified to (log (* (* PI n) 2)) * [exit]simplify: Simplified to (log (* (* PI n) 2)) * * * * [misc]progress: [ 16 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * * [misc]simplify: iters left: 2 (35 enodes) * * [misc]simplify: iters left: 1 (47 enodes) * [exit]simplify: Simplified to (pow (exp 2) (* PI n)) * [exit]simplify: Simplified to (pow (exp 2) (* PI n)) * * * * [misc]progress: [ 17 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) * * [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 (18 enodes) * [exit]simplify: Simplified to (* (cbrt (* (* PI n) 2)) (cbrt (* (* PI n) 2))) * [exit]simplify: Simplified to (* (cbrt (* (* PI n) 2)) (cbrt (* (* PI n) 2))) * [enter]simplify: Simplifying (cbrt (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (cbrt (* (* n 2) PI)) * [exit]simplify: Simplified to (cbrt (* (* n 2) PI)) * * * * [misc]progress: [ 18 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (203 enodes) * [exit]simplify: Simplified to (pow (* (* PI n) 2) 3) * [exit]simplify: Simplified to (pow (* (* PI n) 2) 3) * * * * [misc]progress: [ 19 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (sqrt (* (* n 2) PI)) * [exit]simplify: Simplified to (sqrt (* (* n 2) PI)) * [enter]simplify: Simplifying (sqrt (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (sqrt (* (* n 2) PI)) * [exit]simplify: Simplified to (sqrt (* (* n 2) PI)) * * * * [misc]progress: [ 20 / 103 ] simplifiying candidate # * * * * [misc]progress: [ 21 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* n PI) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* PI n) * [exit]simplify: Simplified to (* PI n) * * * * [misc]progress: [ 22 / 103 ] simplifiying candidate # * * * * [misc]progress: [ 23 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (58 enodes) * * [misc]simplify: iters left: 1 (60 enodes) * [exit]simplify: Simplified to (expm1 (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (expm1 (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 24 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (58 enodes) * * [misc]simplify: iters left: 1 (60 enodes) * [exit]simplify: Simplified to (log1p (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (log1p (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 25 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (57 enodes) * * [misc]simplify: iters left: 1 (59 enodes) * [exit]simplify: Simplified to (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 26 / 103 ] simplifiying candidate # * * * * [misc]progress: [ 27 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2)))) (- (log (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (log (sqrt k)))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (- (log (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (- (log (sqrt k)) (log (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))))) * [exit]simplify: Simplified to (- (log (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (- (log (sqrt k)) (log (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))))) * * * * [misc]progress: [ 28 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2)))) (log (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (68 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (- (log (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (- (log (sqrt k)) (log (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))))) * [exit]simplify: Simplified to (- (log (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (- (log (sqrt k)) (log (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))))) * * * * [misc]progress: [ 29 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (82 enodes) * * [misc]simplify: iters left: 2 (112 enodes) * * [misc]simplify: iters left: 1 (158 enodes) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* (* n PI) 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* (* n PI) 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 30 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (60 enodes) * * [misc]simplify: iters left: 1 (62 enodes) * [exit]simplify: Simplified to (exp (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (exp (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 31 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2)))) (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2)))) (/ (* (* (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (54 enodes) * * [misc]simplify: iters left: 4 (138 enodes) * * [misc]simplify: iters left: 3 (443 enodes) * [exit]simplify: Simplified to (/ (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (pow (* (* PI 2) n) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* (* PI 2) n) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (pow (* (* PI 2) n) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* (* PI 2) n) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 32 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2)))) (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2)))) (* (* (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (120 enodes) * * [misc]simplify: iters left: 3 (311 enodes) * [exit]simplify: Simplified to (pow (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)) 3) * [exit]simplify: Simplified to (pow (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)) 3) * * * * [misc]progress: [ 33 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)))) (cbrt (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (56 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (61 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)))) * [enter]simplify: Simplifying (cbrt (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (58 enodes) * * [misc]simplify: iters left: 1 (60 enodes) * [exit]simplify: Simplified to (cbrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (cbrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 34 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))) (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)))) (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (197 enodes) * * [misc]simplify: iters left: 2 (440 enodes) * [exit]simplify: Simplified to (/ (* (pow (* (* n PI) 2) (/ (- 1 k) 2)) (pow (* (* n PI) 2) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* (* n PI) 2) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (* (pow (* (* n PI) 2) (/ (- 1 k) 2)) (pow (* (* n PI) 2) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* (* n PI) 2) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 35 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (* PI (* n 2)) (/ (- 1 k) 2)) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (52 enodes) * [exit]simplify: Simplified to (* (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) k) (pow (* (* PI 2) n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (* (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) k) (pow (* (* PI 2) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 36 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (58 enodes) * * [misc]simplify: iters left: 1 (60 enodes) * [exit]simplify: Simplified to (sqrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) * [enter]simplify: Simplifying (sqrt (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (58 enodes) * * [misc]simplify: iters left: 1 (60 enodes) * [exit]simplify: Simplified to (sqrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 37 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* (* PI 2) n) (/ 1 2))) (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (sqrt (pow (* (* PI 2) n) (/ 1 2))) (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* (* n PI) 2) (/ k 2))) (sqrt k)) * [exit]simplify: Simplified to (* (sqrt (pow (* (* n PI) 2) (/ k 2))) (sqrt k)) * * * * [misc]progress: [ 38 / 103 ] simplifiying candidate # * * * * [misc]progress: [ 39 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (* (cbrt (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))) (cbrt (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (* (cbrt (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt k))) (cbrt (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt k))))) * [exit]simplify: Simplified to (* (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (* (cbrt (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt k))) (cbrt (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt k))))) * * * * [misc]progress: [ 40 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (sqrt (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k))) (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (sqrt (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k))) (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 41 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (* (cbrt (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (124 enodes) * * [misc]simplify: iters left: 2 (165 enodes) * * [misc]simplify: iters left: 1 (192 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (/ (cbrt (sqrt k)) (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))) (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (/ (cbrt (sqrt k)) (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))) (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (cbrt (sqrt k)))) * * * * [misc]progress: [ 42 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (* (cbrt (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (71 enodes) * * [misc]simplify: iters left: 2 (85 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))))) (/ (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))))) * [exit]simplify: Simplified to (/ (* (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))))) (/ (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))))) * * * * [misc]progress: [ 43 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (* (cbrt (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))) 1)) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (76 enodes) * * [misc]simplify: iters left: 2 (128 enodes) * * [misc]simplify: iters left: 1 (147 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))) (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))) (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 44 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (pow n (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (68 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (84 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (pow n (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (* (/ (sqrt (pow n (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (sqrt k)))) * * * * [misc]progress: [ 45 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (pow n (/ (- 1 k) 2))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (51 enodes) * * [misc]simplify: iters left: 1 (52 enodes) * [exit]simplify: Simplified to (* (sqrt (pow n (/ (- 1 k) 2))) (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))) * [exit]simplify: Simplified to (* (sqrt (pow n (/ (- 1 k) 2))) (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))) * * * * [misc]progress: [ 46 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (pow n (/ (- 1 k) 2))) 1)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (58 enodes) * * [misc]simplify: iters left: 1 (64 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (sqrt (pow n (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (sqrt (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (sqrt (pow n (/ (- 1 k) 2)))) * * * * [misc]progress: [ 47 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (72 enodes) * * [misc]simplify: iters left: 2 (80 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (fabs (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))))) * [exit]simplify: Simplified to (* (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (fabs (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))))) * * * * [misc]progress: [ 48 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (56 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt (sqrt k))) (fabs (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))))) * [exit]simplify: Simplified to (* (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt (sqrt k))) (fabs (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))))) * * * * [misc]progress: [ 49 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))) 1)) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (63 enodes) * * [misc]simplify: iters left: 1 (83 enodes) * [exit]simplify: Simplified to (* (fabs (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (fabs (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 50 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (86 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))))) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))))) * * * * [misc]progress: [ 51 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (53 enodes) * * [misc]simplify: iters left: 1 (54 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))) * [exit]simplify: Simplified to (* (sqrt (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))) * * * * [misc]progress: [ 52 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) 1)) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (60 enodes) * * [misc]simplify: iters left: 1 (63 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))) * [exit]simplify: Simplified to (* (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))) * * * * [misc]progress: [ 53 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (68 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (84 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt 1))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt 1))) * * * * [misc]progress: [ 54 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt 1) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * * [misc]simplify: iters left: 2 (50 enodes) * * [misc]simplify: iters left: 1 (51 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (/ (sqrt 1) (sqrt (sqrt k)))) * [exit]simplify: Simplified to (* (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (/ (sqrt 1) (sqrt (sqrt k)))) * * * * [misc]progress: [ 55 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt 1) 1)) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (57 enodes) * * [misc]simplify: iters left: 1 (63 enodes) * [exit]simplify: Simplified to (* (sqrt 1) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (sqrt 1) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 56 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (86 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))))) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))))) * * * * [misc]progress: [ 57 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (53 enodes) * * [misc]simplify: iters left: 1 (54 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))) * [exit]simplify: Simplified to (* (sqrt (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))) * * * * [misc]progress: [ 58 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) 1)) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (60 enodes) * * [misc]simplify: iters left: 1 (63 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))) * [exit]simplify: Simplified to (* (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))) * * * * [misc]progress: [ 59 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [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 (81 enodes) * * [misc]simplify: iters left: 2 (120 enodes) * * [misc]simplify: iters left: 1 (169 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * * * [misc]progress: [ 60 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ 1 (sqrt (sqrt k)))) * * [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 (55 enodes) * * [misc]simplify: iters left: 2 (71 enodes) * * [misc]simplify: iters left: 1 (72 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * * * [misc]progress: [ 61 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ 1 1)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 62 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) 1) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 63 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (40 enodes) * [exit]simplify: Simplified to (pow (* (* PI 2) n) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (* (* PI 2) n) (/ (- 1 k) 2)) * * * * [misc]progress: [ 64 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2)))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (52 enodes) * * [misc]simplify: iters left: 1 (53 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt k))) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt k))) * * * * [misc]progress: [ 65 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* n 2) (/ (- 1 k) 2))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (17 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 (49 enodes) * * [misc]simplify: iters left: 1 (50 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* 2 n) (/ (- 1 k) 2))) (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt k))) * [exit]simplify: Simplified to (* (sqrt (pow (* 2 n) (/ (- 1 k) 2))) (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt k))) * * * * [misc]progress: [ 66 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2)))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (52 enodes) * * [misc]simplify: iters left: 1 (53 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt k))) * [exit]simplify: Simplified to (* (sqrt (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt k))) * * * * [misc]progress: [ 67 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2)))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (52 enodes) * * [misc]simplify: iters left: 1 (53 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt k))) * [exit]simplify: Simplified to (* (sqrt (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt k))) * * * * [misc]progress: [ 68 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (57 enodes) * * [misc]simplify: iters left: 1 (59 enodes) * [exit]simplify: Simplified to (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 69 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2)))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (52 enodes) * * [misc]simplify: iters left: 1 (53 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt k))) * [exit]simplify: Simplified to (* (sqrt (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt k))) * * * * [misc]progress: [ 70 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (57 enodes) * * [misc]simplify: iters left: 1 (59 enodes) * [exit]simplify: Simplified to (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 71 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (40 enodes) * [exit]simplify: Simplified to (pow (* (* PI 2) n) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (* (* PI 2) n) (/ (- 1 k) 2)) * * * * [misc]progress: [ 72 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ 1 2))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (51 enodes) * * [misc]simplify: iters left: 1 (52 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (/ (sqrt k) (sqrt (pow (* (* PI 2) n) (/ 1 2))))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (/ (sqrt k) (sqrt (pow (* (* PI 2) n) (/ 1 2))))) * * * * [misc]progress: [ 73 / 103 ] simplifiying candidate # * * * * [misc]progress: [ 74 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (pow (* n (* PI 2)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (expm1 (pow (* (* n 2) PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (expm1 (pow (* (* n 2) PI) (/ (- 1 k) 2))) * * * * [misc]progress: [ 75 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (pow (* n (* PI 2)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (log1p (pow (* (* n 2) PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (log1p (pow (* (* n 2) PI) (/ (- 1 k) 2))) * * * * [misc]progress: [ 76 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* n (* PI 2))) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2)))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2)))) * * * * [misc]progress: [ 77 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* n (* PI 2))) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2)))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2)))) * * * * [misc]progress: [ 78 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* 1 (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (81 enodes) * [exit]simplify: Simplified to (/ (- 1 k) 2) * [exit]simplify: Simplified to (/ (- 1 k) 2) * * * * [misc]progress: [ 79 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n (* PI 2)) (/ 1 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * * [misc]simplify: iters left: 2 (22 enodes) * [exit]simplify: Simplified to (pow (* 2 (* PI n)) (/ 1 2)) * [exit]simplify: Simplified to (pow (* 2 (* PI n)) (/ 1 2)) * [enter]simplify: Simplifying (pow (* n (* PI 2)) (/ k 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (18 enodes) * * [misc]simplify: iters left: 2 (20 enodes) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (/ k 2)) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (/ k 2)) * * * * [misc]progress: [ 80 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n (* PI 2)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (pow (* PI (* n 2)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (pow (* PI (* n 2)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * * * [misc]progress: [ 81 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n (* PI 2)) (sqrt (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (pow (* (* n 2) PI) (sqrt (/ (- 1 k) 2))) * [exit]simplify: Simplified to (pow (* (* n 2) PI) (sqrt (/ (- 1 k) 2))) * * * * [misc]progress: [ 82 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n (* PI 2)) 1) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * * [misc]simplify: iters left: 2 (20 enodes) * [exit]simplify: Simplified to (* (* PI n) 2) * [exit]simplify: Simplified to (* (* PI n) 2) * * * * [misc]progress: [ 83 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n (* PI 2)) (- 1 k)) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * * [misc]simplify: iters left: 2 (25 enodes) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- 1 k)) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- 1 k)) * * * * [misc]progress: [ 84 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (pow n (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (17 enodes) * * [misc]simplify: iters left: 2 (19 enodes) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * [enter]simplify: Simplifying (pow (* PI 2) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * * [misc]simplify: iters left: 2 (21 enodes) * [exit]simplify: Simplified to (pow (* 2 PI) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (* 2 PI) (/ (- 1 k) 2)) * * * * [misc]progress: [ 85 / 103 ] simplifiying candidate # * * * * [misc]progress: [ 86 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (log (pow (* n (* PI 2)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (246 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* (* n 2) PI))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* (* n 2) PI))) * * * * [misc]progress: [ 87 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (pow (* n (* PI 2)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (exp (pow (* (* n 2) PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (exp (pow (* (* n 2) PI) (/ (- 1 k) 2))) * * * * [misc]progress: [ 88 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2)))) * [enter]simplify: Simplifying (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) * * * * [misc]progress: [ 89 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (pow (* n (* PI 2)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (pow (pow (* (* n 2) PI) (/ (- 1 k) 2)) 3) * [exit]simplify: Simplified to (pow (pow (* (* n 2) PI) (/ (- 1 k) 2)) 3) * * * * [misc]progress: [ 90 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) * [enter]simplify: Simplifying (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) * * * * [misc]progress: [ 91 / 103 ] simplifiying candidate # * * * * [misc]progress: [ 92 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (58 enodes) * [exit]simplify: Simplified to (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 93 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (58 enodes) * [exit]simplify: Simplified to (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 94 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (58 enodes) * [exit]simplify: Simplified to (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 95 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * [exit]simplify: Simplified to (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 96 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * [exit]simplify: Simplified to (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 97 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * [exit]simplify: Simplified to (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 98 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (pow (log n) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) k)) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (pow k 2) (log n)))))))))))))))))))))))) * * * * [misc]progress: [ 99 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))))))) * * * * [misc]progress: [ 100 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))))))) * * * * [misc]progress: [ 101 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (- (+ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (log n) (pow k 2)))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k)))))) (sqrt k))) * * [misc]simplify: iters left: 6 (48 enodes) * * [misc]simplify: iters left: 5 (133 enodes) * * [misc]simplify: iters left: 4 (404 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (sqrt k)) (sqrt (+ (* (* (* k k) (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/8))) (+ (* (log (* PI 2)) (log (* PI 2))) (* (log n) (log n)))) (- (fma (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/4)) (* (* (log n) (* k k)) (log (* PI 2))) (* (pow n 1/2) (pow (* PI 2) 1/2))) (* (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/2)) (fma (log (* PI 2)) k (* (log n) k))))))) * * * * [misc]progress: [ 102 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))) (sqrt k))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (54 enodes) * * [misc]simplify: iters left: 4 (105 enodes) * * [misc]simplify: iters left: 3 (304 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (exp (- 1/2 (* 1/2 k))) (+ (log n) (log (* PI 2))))) (/ (sqrt k) (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))) * * * * [misc]progress: [ 103 / 103 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (sqrt (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) (sqrt k))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (55 enodes) * * [misc]simplify: iters left: 4 (108 enodes) * * [misc]simplify: iters left: 3 (317 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (sqrt k)) (sqrt (pow (exp (- 1/2 (* 1/2 k))) (- (log (* PI -2)) (log (/ -1 n)))))) * * * [misc]progress: adding candidates to table * [misc]progress: [Phase 3 of 3] Extracting. * * [misc]regime-changes: Finding splitpoints for: (# # # # # # # # # # # #) * [misc]regimes: Found splitpoints: (#s(sp 0 k +nan.0)) , with alts (#) * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * [exit]simplify: Simplified to (* (/ 1 (sqrt k)) (pow (* n (* PI 2)) (/ (- 1 k) 2))) * * * * [misc]points: Sampling 8010 additional inputs, on iter 0 have 0 / 8000 * * * * [misc]points: Computing exacts on every 501 of 8010 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 250 of 8010 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 125 of 8010 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 63 of 8010 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 31 of 8010 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 16 of 8010 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 8 of 8010 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 4 of 8010 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 8010 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 8010 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 6439 additional inputs, on iter 1 have 1571 / 8000 * * * * [misc]points: Computing exacts on every 402 of 6439 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 201 of 6439 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 101 of 6439 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 50 of 6439 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 25 of 6439 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 13 of 6439 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 6 of 6439 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 3 of 6439 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 6439 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 6439 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 5189 additional inputs, on iter 2 have 2821 / 8000 * * * * [misc]points: Computing exacts on every 324 of 5189 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 162 of 5189 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 81 of 5189 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 41 of 5189 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 20 of 5189 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 10 of 5189 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 5 of 5189 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 3 of 5189 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 1 of 5189 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 5189 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 4189 additional inputs, on iter 3 have 3821 / 8000 * * * * [misc]points: Computing exacts on every 262 of 4189 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 131 of 4189 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 65 of 4189 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 33 of 4189 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 16 of 4189 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 8 of 4189 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 4 of 4189 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 4189 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 1 of 4189 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 4189 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 3397 additional inputs, on iter 4 have 4613 / 8000 * * * * [misc]points: Computing exacts on every 212 of 3397 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 106 of 3397 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 53 of 3397 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 27 of 3397 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 13 of 3397 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 7 of 3397 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 3 of 3397 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 3397 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 3397 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 2761 additional inputs, on iter 5 have 5249 / 8000 * * * * [misc]points: Computing exacts on every 173 of 2761 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 86 of 2761 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 43 of 2761 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 22 of 2761 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 11 of 2761 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 5 of 2761 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 3 of 2761 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 1 of 2761 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 2761 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 2245 additional inputs, on iter 6 have 5765 / 8000 * * * * [misc]points: Computing exacts on every 140 of 2245 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 70 of 2245 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 35 of 2245 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 18 of 2245 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 9 of 2245 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 4 of 2245 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 2245 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 1 of 2245 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 2245 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 1798 additional inputs, on iter 7 have 6212 / 8000 * * * * [misc]points: Computing exacts on every 112 of 1798 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 56 of 1798 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 28 of 1798 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 14 of 1798 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 7 of 1798 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 4 of 1798 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 1798 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 1798 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 1436 additional inputs, on iter 8 have 6574 / 8000 * * * * [misc]points: Computing exacts on every 90 of 1436 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 45 of 1436 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 22 of 1436 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 11 of 1436 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 6 of 1436 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 3 of 1436 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 1 of 1436 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 1436 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 1158 additional inputs, on iter 9 have 6852 / 8000 * * * * [misc]points: Computing exacts on every 72 of 1158 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 36 of 1158 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 18 of 1158 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 9 of 1158 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 5 of 1158 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 1158 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 1 of 1158 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 1158 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 917 additional inputs, on iter 10 have 7093 / 8000 * * * * [misc]points: Computing exacts on every 57 of 917 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 29 of 917 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 14 of 917 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 7 of 917 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 4 of 917 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 917 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 917 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 755 additional inputs, on iter 11 have 7255 / 8000 * * * * [misc]points: Computing exacts on every 47 of 755 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 24 of 755 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 12 of 755 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 6 of 755 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 3 of 755 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 1 of 755 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 755 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 600 additional inputs, on iter 12 have 7410 / 8000 * * * * [misc]points: Computing exacts on every 38 of 600 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 19 of 600 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 9 of 600 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 5 of 600 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 600 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 1 of 600 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 600 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 481 additional inputs, on iter 13 have 7529 / 8000 * * * * [misc]points: Computing exacts on every 30 of 481 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 15 of 481 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 8 of 481 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 4 of 481 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 481 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 481 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 375 additional inputs, on iter 14 have 7635 / 8000 * * * * [misc]points: Computing exacts on every 23 of 375 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 12 of 375 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 6 of 375 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 3 of 375 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 1 of 375 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 375 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 312 additional inputs, on iter 15 have 7698 / 8000 * * * * [misc]points: Computing exacts on every 20 of 312 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 10 of 312 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 5 of 312 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 312 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 1 of 312 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 312 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 268 additional inputs, on iter 16 have 7742 / 8000 * * * * [misc]points: Computing exacts on every 17 of 268 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 8 of 268 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 4 of 268 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 268 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 1 of 268 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 268 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 213 additional inputs, on iter 17 have 7797 / 8000 * * * * [misc]points: Computing exacts on every 13 of 213 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 7 of 213 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 3 of 213 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 213 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 213 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 166 additional inputs, on iter 18 have 7844 / 8000 * * * * [misc]points: Computing exacts on every 10 of 166 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 5 of 166 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 3 of 166 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 1 of 166 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 166 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 126 additional inputs, on iter 19 have 7884 / 8000 * * * * [misc]points: Computing exacts on every 8 of 126 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 4 of 126 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 126 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 126 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 100 additional inputs, on iter 20 have 7910 / 8000 * * * * [misc]points: Computing exacts on every 6 of 100 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 3 of 100 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 100 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 100 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 82 additional inputs, on iter 21 have 7928 / 8000 * * * * [misc]points: Computing exacts on every 5 of 82 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 3 of 82 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 1 of 82 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 82 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 63 additional inputs, on iter 22 have 7947 / 8000 * * * * [misc]points: Computing exacts on every 4 of 63 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 63 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 63 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 49 additional inputs, on iter 23 have 7961 / 8000 * * * * [misc]points: Computing exacts on every 3 of 49 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 49 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 49 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 39 additional inputs, on iter 24 have 7971 / 8000 * * * * [misc]points: Computing exacts on every 2 of 39 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 1 of 39 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 39 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 30 additional inputs, on iter 25 have 7980 / 8000 * * * * [misc]points: Computing exacts on every 2 of 30 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 30 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 24 additional inputs, on iter 26 have 7986 / 8000 * * * * [misc]points: Computing exacts on every 2 of 24 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 24 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 19 additional inputs, on iter 27 have 7991 / 8000 * * * * [misc]points: Computing exacts on every 1 of 19 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 19 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 17 additional inputs, on iter 28 have 7993 / 8000 * * * * [misc]points: Computing exacts on every 1 of 17 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 17 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 14 additional inputs, on iter 29 have 7996 / 8000 * * * * [misc]points: Computing exacts for 14 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 14 additional inputs, on iter 30 have 7996 / 8000 * * * * [misc]points: Computing exacts for 14 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 11 additional inputs, on iter 31 have 7999 / 8000 * * * * [misc]points: Computing exacts for 11 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [exit]points: Sampled 8005 points with exact outputs