* [misc]progress: [Phase 1 of 3] Setting up. * * * [misc]progress: [1/2] Preparing points * * * * [misc]points: Sampling 256 additional inputs, on iter 0 have 0 / 256 * * * * [misc]points: Computing exacts on every 16 of 256 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 64 * * * * [misc]points: Setting MPFR precision to 320 * * * * [misc]points: Computing exacts on every 8 of 256 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 64 * * * * [misc]points: Setting MPFR precision to 320 * * * * [misc]points: Setting MPFR precision to 576 * * * * [misc]points: Setting MPFR precision to 832 * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Computing exacts on every 4 of 256 points to ramp up precision * * * * [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 2 of 256 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 256 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 207 additional inputs, on iter 1 have 49 / 256 * * * * [misc]points: Computing exacts on every 12 of 207 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 207 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 207 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 207 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 170 additional inputs, on iter 2 have 86 / 256 * * * * [misc]points: Computing exacts on every 10 of 170 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 170 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 170 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 170 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 136 additional inputs, on iter 3 have 120 / 256 * * * * [misc]points: Computing exacts on every 8 of 136 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 136 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 136 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 136 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 111 additional inputs, on iter 4 have 145 / 256 * * * * [misc]points: Computing exacts on every 6 of 111 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 111 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 111 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 93 additional inputs, on iter 5 have 163 / 256 * * * * [misc]points: Computing exacts on every 5 of 93 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 93 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 93 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 78 additional inputs, on iter 6 have 178 / 256 * * * * [misc]points: Computing exacts on every 4 of 78 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 78 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 78 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 67 additional inputs, on iter 7 have 189 / 256 * * * * [misc]points: Computing exacts on every 4 of 67 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 67 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 67 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 58 additional inputs, on iter 8 have 198 / 256 * * * * [misc]points: Computing exacts on every 3 of 58 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 58 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 9 have 207 / 256 * * * * [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 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 10 have 217 / 256 * * * * [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 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 11 have 226 / 256 * * * * [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 22 additional inputs, on iter 12 have 234 / 256 * * * * [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 15 additional inputs, on iter 13 have 241 / 256 * * * * [misc]points: Computing exacts for 15 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 12 additional inputs, on iter 14 have 244 / 256 * * * * [misc]points: Computing exacts for 12 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 10 additional inputs, on iter 15 have 246 / 256 * * * * [misc]points: Computing exacts for 10 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 6 additional inputs, on iter 16 have 250 / 256 * * * * [misc]points: Computing exacts for 6 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 6 additional inputs, on iter 17 have 250 / 256 * * * * [misc]points: Computing exacts for 6 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 6 additional inputs, on iter 18 have 250 / 256 * * * * [misc]points: Computing exacts for 6 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 4 additional inputs, on iter 19 have 253 / 256 * * * * [misc]points: Computing exacts for 4 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 4 additional inputs, on iter 20 have 254 / 256 * * * * [misc]points: Computing exacts for 4 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 4 additional inputs, on iter 21 have 255 / 256 * * * * [misc]points: Computing exacts for 4 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 4 additional inputs, on iter 22 have 255 / 256 * * * * [misc]points: Computing exacts for 4 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) * * * * [misc]progress: [ 2 / 3 ] rewriting at (2 1 1) * * * * [misc]progress: [ 3 / 3 ] rewriting at (2) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 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: [ 2 / 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: [ 3 / 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: simplifying candidates * * * * [misc]progress: [ 1 / 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: [ 2 / 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: [ 3 / 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: [ 4 / 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: [ 5 / 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: [ 6 / 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: [ 7 / 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: [ 8 / 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: [ 9 / 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: [ 10 / 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: [ 11 / 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: [ 12 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 13 / 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: [ 14 / 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: [ 15 / 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: [ 16 / 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: [ 17 / 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: [ 18 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 19 / 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: [ 20 / 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: [ 21 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 22 / 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: [ 23 / 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: [ 24 / 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: [ 25 / 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: [ 26 / 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: [ 27 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 28 / 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: [ 29 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 30 / 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: [ 31 / 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: [ 32 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 33 / 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: [ 34 / 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: [ 35 / 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: [ 36 / 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: [ 37 / 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: [ 38 / 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: [ 39 / 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: [ 40 / 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: [ 41 / 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: [ 42 / 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: [ 43 / 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: [ 44 / 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: [ 45 / 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: [ 46 / 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: [ 47 / 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: [ 48 / 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: [ 49 / 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: [ 50 / 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: [ 51 / 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: [ 52 / 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: [ 53 / 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: [ 54 / 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: [ 55 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 56 / 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: [ 57 / 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: [ 58 / 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: [ 59 / 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: [ 60 / 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: [ 61 / 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: [ 62 / 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: [ 63 / 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: [ 64 / 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: [ 65 / 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: [ 66 / 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: [ 67 / 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: [ 68 / 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: [ 69 / 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: [ 70 / 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: [ 71 / 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: [ 72 / 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: [ 73 / 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: [ 74 / 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: adding candidates to table * * [misc]progress: iteration 2 / 4 * * * [misc]progress: picking best candidate * * * * [misc]pick: Picked # * * * [misc]progress: localizing error * * * [misc]progress: generating rewritten candidates * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 1 2 1) * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 1 1 1) * * * * [misc]progress: [ 3 / 4 ] rewriting at (2) * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 1 1) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 4 ] generating series at (2 1 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: [ 2 / 4 ] generating series at (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 (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ 1 2)) (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 (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 (/ (pow (* 2 (* n PI)) 1/2) 1) into (sqrt (* n (* 2 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 (/ (sqrt (* n (* 2 PI))) +nan.0) into (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))) * [misc]taylor: Taking taylor expansion of (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ 1 2)) (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 (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 (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) into (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* 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 (+ (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)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ 1 2)) (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 (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 (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) into (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* 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 (+ (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 (- (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (+ (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) (/ 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 (+ (* 1/2 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 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (+ (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (* 0 (/ 0 (exp (* 1/2 (* 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)) (+ (* (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) (/ 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 (- (+ (* 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 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (+ (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (* 0 (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (* 0 (/ 0 (exp (* 1/2 (* 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)) (+ (* (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) (/ 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 (- (+ (* 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)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (/ (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) (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 (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 (/ (pow (* 2 (/ PI n)) 1/2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) into (* (sqrt (/ (* 2 PI) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI 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 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 (/ (* 2 PI) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) +nan.0) into (* +nan.0 (* (sqrt (/ PI n)) (/ (sqrt 2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) * [misc]taylor: Taking taylor expansion of (/ (/ (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) (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 (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 (/ (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 (/ 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 (- (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 k)) * [misc]taylor: Taking taylor expansion of (/ (/ (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) (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 (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 (/ (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 (/ 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 (- (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 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 (- (/ 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 (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (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 (+ (* 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 (- (/ 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 (- (+ (* (/ 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 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (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 (+ (* 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 (- (/ 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 (- (+ (* (/ 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 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (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 (+ (* 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)) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) (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 (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 (/ (pow (* -2 (/ PI n)) 1/2) (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) into (* (sqrt (/ (* PI -2) n)) (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI 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 (- 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 (/ (* PI -2) n)) (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) +nan.0) into (* +nan.0 (/ (sqrt (* -2 (/ PI n))) (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) * [misc]taylor: Taking taylor expansion of (/ (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) (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 (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 (/ (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 (/ 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 (- (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)) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) (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 (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 (/ (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 (/ 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 (- (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 (- (/ 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 (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (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 (+ (* -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 (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 (- 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 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (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 (+ (* -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: [ 4 / 4 ] generating series at (2 1 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: simplifying candidates * * * * [misc]progress: [ 1 / 159 ] 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 / 159 ] 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 / 159 ] simplifiying candidate # * * * * [misc]progress: [ 4 / 159 ] 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 / 159 ] 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 / 159 ] 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 / 159 ] 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 / 159 ] 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 / 159 ] simplifiying candidate # * * * * [misc]progress: [ 10 / 159 ] 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 / 159 ] simplifiying candidate # * * * * [misc]progress: [ 12 / 159 ] 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 / 159 ] 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 / 159 ] simplifiying candidate # * * * * [misc]progress: [ 15 / 159 ] 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 / 159 ] 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 / 159 ] 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 / 159 ] 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 / 159 ] 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 / 159 ] simplifiying candidate # * * * * [misc]progress: [ 21 / 159 ] 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 / 159 ] simplifiying candidate # * * * * [misc]progress: [ 23 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 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: [ 24 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 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: [ 25 / 159 ] simplifiying candidate # * * * * [misc]progress: [ 26 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (* (log (* n (* PI 2))) (/ 1 2)) (* (log (* n (* PI 2))) (/ k 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (307 enodes) * [exit]simplify: Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 27 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (* (log (* n (* PI 2))) (/ 1 2)) (* (log (* n (* PI 2))) (/ k 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (307 enodes) * [exit]simplify: Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 28 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (* (log (* n (* PI 2))) (/ 1 2)) (log (pow (* n (* PI 2)) (/ k 2)))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (284 enodes) * [exit]simplify: Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 29 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (* (log (* n (* PI 2))) (/ 1 2)) (* (log (* n (* PI 2))) (/ k 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (307 enodes) * [exit]simplify: Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 30 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (* (log (* n (* PI 2))) (/ 1 2)) (* (log (* n (* PI 2))) (/ k 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (307 enodes) * [exit]simplify: Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 31 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (* (log (* n (* PI 2))) (/ 1 2)) (log (pow (* n (* PI 2)) (/ k 2)))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (284 enodes) * [exit]simplify: Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 32 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (log (pow (* n (* PI 2)) (/ 1 2))) (* (log (* n (* PI 2))) (/ k 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (263 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: [ 33 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (log (pow (* n (* PI 2)) (/ 1 2))) (* (log (* n (* PI 2))) (/ k 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (263 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: [ 34 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (log (pow (* n (* PI 2)) (/ 1 2))) (log (pow (* n (* PI 2)) (/ k 2)))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (206 enodes) * [exit]simplify: Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* n 2) PI)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* n 2) PI)) (- (log (sqrt k)))) * * * * [misc]progress: [ 35 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (283 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: [ 36 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (log (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (103 enodes) * * [misc]simplify: iters left: 1 (295 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: [ 37 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 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: [ 38 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (* (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ 1 2))) (* (* (pow (* n (* PI 2)) (/ k 2)) (pow (* n (* PI 2)) (/ k 2))) (pow (* n (* PI 2)) (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (113 enodes) * * [misc]simplify: iters left: 3 (390 enodes) * [exit]simplify: Simplified to (/ (* (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (* (pow (* (* PI n) 2) (/ k 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) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (* (pow (* (* PI n) 2) (/ k 2)) (/ (* (sqrt k) k) (pow (* (* PI n) 2) (/ 1 2))))) * * * * [misc]progress: [ 39 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (96 enodes) * * [misc]simplify: iters left: 3 (266 enodes) * [exit]simplify: Simplified to (* (/ (pow (* PI (* n 2)) (/ 1 2)) (* (pow (* PI (* n 2)) (/ k 2)) (* (sqrt k) k))) (* (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (/ (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)) (* (sqrt k) k))) (* (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))))) * * * * [misc]progress: [ 40 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))) (cbrt (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))) (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)))) (cbrt (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2))))) * [enter]simplify: Simplifying (cbrt (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 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: [ 41 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (196 enodes) * [exit]simplify: Simplified to (/ (/ (* (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ 1 2))) (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))) (/ (* k (pow (* (* 2 PI) n) (/ k 2))) (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2))))) * [exit]simplify: Simplified to (/ (/ (* (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ 1 2))) (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))) (/ (* k (pow (* (* 2 PI) n) (/ k 2))) (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2))))) * * * * [misc]progress: [ 42 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 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)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 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: [ 43 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (- (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (29 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)))) * [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: [ 44 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (52 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (* (/ (cbrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k))) * * * * [misc]progress: [ 45 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))) * [enter]simplify: Simplifying (/ (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 46 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))) 1) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * * [misc]simplify: iters left: 2 (52 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))) (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)))) (cbrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))))) * [enter]simplify: Simplifying (/ (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 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 (/ (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt k)) * [exit]simplify: Simplified to (/ (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt k)) * * * * [misc]progress: [ 47 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (17 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 (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k))) * * * * [misc]progress: [ 48 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 49 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) 1) * * [misc]simplify: iters left: 6 (14 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 (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)))) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 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 (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt k)) * * * * [misc]progress: [ 50 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow n (/ 1 2)) (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [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 (30 enodes) * * [misc]simplify: iters left: 2 (31 enodes) * [exit]simplify: Simplified to (/ (/ (pow n (/ 1 2)) (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (/ (pow n (/ 1 2)) (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (pow (* PI 2) (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (cbrt (sqrt k))) (pow (* 2 PI) (/ k 2))) * [exit]simplify: Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (cbrt (sqrt k))) (pow (* 2 PI) (/ k 2))) * * * * [misc]progress: [ 51 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow n (/ 1 2)) (pow n (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * [exit]simplify: Simplified to (/ (/ (pow n (/ 1 2)) (sqrt (sqrt k))) (pow n (/ k 2))) * [exit]simplify: Simplified to (/ (/ (pow n (/ 1 2)) (sqrt (sqrt k))) (pow n (/ k 2))) * [enter]simplify: Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (pow (* PI 2) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt (sqrt k))) (pow (* 2 PI) (/ k 2))) * [exit]simplify: Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt (sqrt k))) (pow (* 2 PI) (/ k 2))) * * * * [misc]progress: [ 52 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow n (/ 1 2)) (pow n (/ k 2))) 1) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (22 enodes) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (pow n (/ k 2))) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (pow n (/ k 2))) * [enter]simplify: Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (pow (* PI 2) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt k)) (pow (* 2 PI) (/ k 2))) * [exit]simplify: Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt k)) (pow (* 2 PI) (/ k 2))) * * * * [misc]progress: [ 53 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (72 enodes) * * [misc]simplify: iters left: 1 (75 enodes) * [exit]simplify: Simplified to (/ (/ (pow n (/ 1 2)) (cbrt (pow (* n (* 2 PI)) (/ k 2)))) (* (cbrt (pow (* n (* 2 PI)) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * [exit]simplify: Simplified to (/ (/ (pow n (/ 1 2)) (cbrt (pow (* n (* 2 PI)) (/ k 2)))) (* (cbrt (pow (* n (* 2 PI)) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (cbrt (sqrt k))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (cbrt (sqrt k))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) * * * * [misc]progress: [ 54 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * [exit]simplify: Simplified to (/ (/ (/ (pow n (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (/ (pow n (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) * * * * [misc]progress: [ 55 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) 1) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * [exit]simplify: Simplified to (/ (/ (pow n (/ 1 2)) (cbrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow n (/ 1 2)) (cbrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ k 2)))) * * * * [misc]progress: [ 56 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow n (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (46 enodes) * [exit]simplify: Simplified to (/ (/ (pow n (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* n (* 2 PI)) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow n (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* n (* 2 PI)) (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (cbrt (sqrt k))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (cbrt (sqrt k))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) * * * * [misc]progress: [ 57 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow n (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (/ (pow n (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow n (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) * * * * [misc]progress: [ 58 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow n (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) 1) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (37 enodes) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (sqrt (pow (* n (* 2 PI)) (/ k 2)))) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (sqrt (pow (* n (* 2 PI)) (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * * * * [misc]progress: [ 59 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow n (/ 1 2)) 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (/ (pow n (/ 1 2)) (cbrt (sqrt k))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (pow n (/ 1 2)) (cbrt (sqrt k))) (cbrt (sqrt k))) * [enter]simplify: Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (cbrt (sqrt k))) (pow (* PI (* n 2)) (/ k 2))) * [exit]simplify: Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (cbrt (sqrt k))) (pow (* PI (* n 2)) (/ k 2))) * * * * [misc]progress: [ 60 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow n (/ 1 2)) 1) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt (sqrt k))) (pow (* PI (* n 2)) (/ k 2))) * [exit]simplify: Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt (sqrt k))) (pow (* PI (* n 2)) (/ k 2))) * * * * [misc]progress: [ 61 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow n (/ 1 2)) 1) 1) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (11 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)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt k)) (pow (* (* 2 PI) n) (/ k 2))) * [exit]simplify: Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt k)) (pow (* (* 2 PI) n) (/ k 2))) * * * * [misc]progress: [ 62 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (86 enodes) * * [misc]simplify: iters left: 2 (124 enodes) * * [misc]simplify: iters left: 1 (143 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* (* 2 PI) n) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow n (/ k 2)) (cbrt (pow (* (* 2 PI) n) (/ 1 2))))) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* (* 2 PI) n) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow n (/ k 2)) (cbrt (pow (* (* 2 PI) n) (/ 1 2))))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* 2 PI) (/ k 2)))) * [exit]simplify: Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* 2 PI) (/ k 2)))) * * * * [misc]progress: [ 63 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (pow n (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (56 enodes) * * [misc]simplify: iters left: 2 (64 enodes) * * [misc]simplify: iters left: 1 (67 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (pow n (/ k 2))) (/ (sqrt (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ 1 2))))) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (pow n (/ k 2))) (/ (sqrt (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ 1 2))))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* 2 PI) (/ k 2)))) * [exit]simplify: Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* 2 PI) (/ k 2)))) * * * * [misc]progress: [ 64 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (pow n (/ k 2))) 1) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (152 enodes) * * [misc]simplify: iters left: 1 (253 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* PI (* n 2)) (/ 1 2))) (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (pow n (/ k 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* PI (* n 2)) (/ 1 2))) (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (pow n (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (pow (* 2 PI) (/ k 2)) (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (pow (* 2 PI) (/ k 2)) (sqrt k))) * * * * [misc]progress: [ 65 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (248 enodes) * * [misc]simplify: iters left: 1 (309 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k))) (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (* (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k))) (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k))) * * * * [misc]progress: [ 66 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (127 enodes) * * [misc]simplify: iters left: 1 (145 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt k)))) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 67 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) 1) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (95 enodes) * * [misc]simplify: iters left: 2 (301 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2))))) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2))))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ k 2)))) * * * * [misc]progress: [ 68 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (87 enodes) * * [misc]simplify: iters left: 2 (127 enodes) * * [misc]simplify: iters left: 1 (146 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (pow (* 2 (* PI n)) (/ 1 2))))) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (pow (* 2 (* PI n)) (/ 1 2))))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k))) * * * * [misc]progress: [ 69 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (65 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* n 2) PI) (/ 1 2))))) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* n 2) PI) (/ 1 2))))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 70 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) 1) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (157 enodes) * * [misc]simplify: iters left: 1 (277 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 PI) n) (/ 1 2))) (/ (sqrt (pow (* (* 2 PI) n) (/ k 2))) (cbrt (pow (* (* 2 PI) n) (/ 1 2))))) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 PI) n) (/ 1 2))) (/ (sqrt (pow (* (* 2 PI) n) (/ k 2))) (cbrt (pow (* (* 2 PI) n) (/ 1 2))))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * * * * [misc]progress: [ 71 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (102 enodes) * * [misc]simplify: iters left: 2 (238 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (* 2 PI) n) (/ 1 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* 2 PI) n) (/ 1 2))) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (* 2 PI) n) (/ 1 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* 2 PI) n) (/ 1 2))) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))) * [exit]simplify: Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))) * * * * [misc]progress: [ 72 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) 1) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (133 enodes) * * [misc]simplify: iters left: 1 (138 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* PI (* n 2)) (/ 1 2))) (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt (sqrt k)))) * [exit]simplify: Simplified to (* (cbrt (pow (* PI (* n 2)) (/ 1 2))) (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))) * [exit]simplify: Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))) * * * * [misc]progress: [ 73 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) 1) 1) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (49 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2)))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (pow (* PI (* n 2)) (/ k 2)) (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (pow (* PI (* n 2)) (/ k 2)) (sqrt k))) * * * * [misc]progress: [ 74 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (46 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 PI) n) (/ 1 2))) (* (pow n (/ k 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 PI) n) (/ 1 2))) (* (pow n (/ k 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* 2 PI) (/ k 2)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* 2 PI) (/ k 2)))) * * * * [misc]progress: [ 75 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow n (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (sqrt (sqrt k)) (pow n (/ k 2)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (sqrt (sqrt k)) (pow n (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* 2 PI) (/ k 2)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* 2 PI) (/ k 2)))) * * * * [misc]progress: [ 76 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow n (/ k 2))) 1) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow n (/ k 2))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow n (/ k 2))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (pow (* 2 PI) (/ k 2)) (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (pow (* 2 PI) (/ k 2)) (sqrt k))) * * * * [misc]progress: [ 77 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (76 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2)))) (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (pow (* 2 (* PI n)) (/ k 2))))) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2)))) (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (pow (* 2 (* PI n)) (/ k 2))))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k))) * * * * [misc]progress: [ 78 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (49 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 79 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) 1) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))) * [exit]simplify: Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ k 2)))) * * * * [misc]progress: [ 80 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k))) * * * * [misc]progress: [ 81 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 82 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) 1) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (38 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * * * * [misc]progress: [ 83 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))) * * * * [misc]progress: [ 84 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) 1) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))) * * * * [misc]progress: [ 85 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) 1) 1) * * [misc]simplify: iters left: 6 (11 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 (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))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (pow (* PI (* n 2)) (/ k 2)) (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (pow (* PI (* n 2)) (/ k 2)) (sqrt k))) * * * * [misc]progress: [ 86 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (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 (28 enodes) * * [misc]simplify: iters left: 2 (29 enodes) * [exit]simplify: Simplified to (/ (/ 1 (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (/ 1 (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* PI 2) (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (pow (* PI (* n 2)) (/ 1 2)) (* (cbrt (sqrt k)) (pow (* 2 PI) (/ k 2)))) * [exit]simplify: Simplified to (/ (pow (* PI (* n 2)) (/ 1 2)) (* (cbrt (sqrt k)) (pow (* 2 PI) (/ k 2)))) * * * * [misc]progress: [ 87 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (pow n (/ k 2))) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (pow n (/ k 2))) * [enter]simplify: Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* PI 2) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (pow (* PI (* n 2)) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* 2 PI) (/ k 2)))) * [exit]simplify: Simplified to (/ (pow (* PI (* n 2)) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* 2 PI) (/ k 2)))) * * * * [misc]progress: [ 88 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n (/ k 2))) 1) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * * [misc]simplify: iters left: 3 (18 enodes) * [exit]simplify: Simplified to (/ 1 (pow n (/ k 2))) * [exit]simplify: Simplified to (/ 1 (pow n (/ k 2))) * [enter]simplify: Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* PI 2) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (pow (* (* n 2) PI) (/ 1 2)) (* (sqrt k) (pow (* 2 PI) (/ k 2)))) * [exit]simplify: Simplified to (/ (pow (* (* n 2) PI) (/ 1 2)) (* (sqrt k) (pow (* 2 PI) (/ k 2)))) * * * * [misc]progress: [ 89 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (70 enodes) * * [misc]simplify: iters left: 1 (73 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (* (cbrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (pow (* (* 2 n) PI) (/ k 2))))) * [exit]simplify: Simplified to (/ (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (* (cbrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (pow (* (* 2 n) PI) (/ k 2))))) * [enter]simplify: Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (cbrt (sqrt k))) (cbrt (pow (* PI (* n 2)) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (cbrt (sqrt k))) (cbrt (pow (* PI (* n 2)) (/ k 2)))) * * * * [misc]progress: [ 90 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * * [misc]simplify: iters left: 2 (46 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (* (sqrt (sqrt k)) (cbrt (pow (* (* 2 n) PI) (/ k 2))))) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (* (sqrt (sqrt k)) (cbrt (pow (* (* 2 n) PI) (/ k 2))))) * [enter]simplify: Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* PI (* n 2)) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* PI (* n 2)) (/ k 2)))) * * * * [misc]progress: [ 91 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) 1) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (40 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ k 2)))) * * * * [misc]progress: [ 92 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (pow (* n (* PI 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (44 enodes) * [exit]simplify: Simplified to (/ (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* (* 2 n) PI) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* (* 2 n) PI) (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (cbrt (sqrt k))) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (cbrt (sqrt k))) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * * * * [misc]progress: [ 93 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (sqrt (pow (* 2 (* PI n)) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (sqrt (pow (* 2 (* PI n)) (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * * * * [misc]progress: [ 94 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (pow (* n (* PI 2)) (/ k 2)))) 1) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (pow (* n (* PI 2)) (/ k 2)))) * [exit]simplify: Simplified to (/ 1 (sqrt (pow (* n (* PI 2)) (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * * * * [misc]progress: [ 95 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 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 2)) (pow (* n (* PI 2)) (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (cbrt (sqrt k))) * * * * [misc]progress: [ 96 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (sqrt (sqrt k))) * * [misc]simplify: iters left: 4 (6 enodes) * * [misc]simplify: iters left: 3 (8 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 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k))) * * * * [misc]progress: [ 97 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) 1) * * [misc]simplify: iters left: 4 (3 enodes) * * [misc]simplify: iters left: 3 (5 enodes) * [exit]simplify: Simplified to 1 * [exit]simplify: Simplified to 1 * [enter]simplify: Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (pow (* (* n 2) PI) (/ 1 2)) (* (sqrt k) (pow (* (* n 2) PI) (/ k 2)))) * [exit]simplify: Simplified to (/ (pow (* (* n 2) PI) (/ 1 2)) (* (sqrt k) (pow (* (* n 2) PI) (/ k 2)))) * * * * [misc]progress: [ 98 / 159 ] 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 2)) (pow (* n (* PI 2)) (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (cbrt (sqrt k))) * * * * [misc]progress: [ 99 / 159 ] 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 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k))) * * * * [misc]progress: [ 100 / 159 ] 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 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (pow (* (* n 2) PI) (/ 1 2)) (* (sqrt k) (pow (* (* n 2) PI) (/ k 2)))) * [exit]simplify: Simplified to (/ (pow (* (* n 2) PI) (/ 1 2)) (* (sqrt k) (pow (* (* n 2) PI) (/ k 2)))) * * * * [misc]progress: [ 101 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n (* PI 2)) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ 1 (pow (* n (* PI 2)) (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (pow (* n (* PI 2)) (/ k 2))) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (pow (* n (* PI 2)) (/ k 2))) * * * * [misc]progress: [ 102 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt (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 (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (/ 1 (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (pow (* n (* PI 2)) (/ k 2))) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (pow (* n (* PI 2)) (/ k 2))) * * * * [misc]progress: [ 103 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n (* PI 2)) (/ 1 2)) 1) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 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)) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (/ 1 2)) * [enter]simplify: Simplifying (/ (/ 1 (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt k)) (pow (* n (* PI 2)) (/ k 2))) * [exit]simplify: Simplified to (/ (/ 1 (sqrt k)) (pow (* n (* PI 2)) (/ k 2))) * * * * [misc]progress: [ 104 / 159 ] simplifiying candidate # * * * * [misc]progress: [ 105 / 159 ] 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: [ 106 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (/ (sqrt k) (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) * [exit]simplify: Simplified to (* (/ (sqrt k) (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) * * * * [misc]progress: [ 107 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * * [misc]simplify: iters left: 2 (45 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * * * [misc]progress: [ 108 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k))) * * * * [misc]progress: [ 109 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) 1) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (37 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: [ 110 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 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 (/ (sqrt k) (cbrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))))) * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))))) * * * * [misc]progress: [ 111 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 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 (/ (sqrt k) (sqrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))))) * * * * [misc]progress: [ 112 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (* PI 2) (/ 1 2)) (pow (* PI 2) (/ k 2)))) * * [misc]simplify: iters left: 6 (12 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 (/ (sqrt k) (/ (pow (* PI 2) (/ 1 2)) (pow (* PI 2) (/ k 2)))) * [exit]simplify: Simplified to (/ (sqrt k) (/ (pow (* PI 2) (/ 1 2)) (pow (* PI 2) (/ k 2)))) * * * * [misc]progress: [ 113 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (* PI 2) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (/ (sqrt k) (pow (* PI 2) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) * [exit]simplify: Simplified to (* (/ (sqrt k) (pow (* PI 2) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) * * * * [misc]progress: [ 114 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (* PI 2) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (/ (sqrt k) (pow (* PI 2) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) * [exit]simplify: Simplified to (* (/ (sqrt k) (pow (* PI 2) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) * * * * [misc]progress: [ 115 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (* PI 2) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (* (/ (sqrt k) (pow (* PI 2) (/ 1 2))) (pow (* 2 (* n PI)) (/ k 2))) * [exit]simplify: Simplified to (* (/ (sqrt k) (pow (* PI 2) (/ 1 2))) (pow (* 2 (* n PI)) (/ k 2))) * * * * [misc]progress: [ 116 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (* (pow (* PI 2) (/ k 2)) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ 1 2)))) * [exit]simplify: Simplified to (/ (* (pow (* PI 2) (/ k 2)) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ 1 2)))) * * * * [misc]progress: [ 117 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 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 (/ (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) * [exit]simplify: Simplified to (/ (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) * * * * [misc]progress: [ 118 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 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 (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) * [exit]simplify: Simplified to (/ (* (sqrt (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) * * * * [misc]progress: [ 119 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (* (pow (* PI (* n 2)) (/ k 2)) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ 1 2)))) * [exit]simplify: Simplified to (/ (* (pow (* PI (* n 2)) (/ k 2)) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ 1 2)))) * * * * [misc]progress: [ 120 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (* (pow (* PI 2) (/ k 2)) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ 1 2)))) * [exit]simplify: Simplified to (/ (* (pow (* PI 2) (/ k 2)) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ 1 2)))) * * * * [misc]progress: [ 121 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 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 (/ (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) (sqrt (pow (* n (* PI 2)) (/ 1 2)))) * [exit]simplify: Simplified to (/ (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) (sqrt (pow (* n (* PI 2)) (/ 1 2)))) * * * * [misc]progress: [ 122 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 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 (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) (sqrt (pow (* n (* PI 2)) (/ 1 2)))) * [exit]simplify: Simplified to (/ (* (sqrt (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) (sqrt (pow (* n (* PI 2)) (/ 1 2)))) * * * * [misc]progress: [ 123 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (* (pow (* PI (* n 2)) (/ k 2)) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ 1 2)))) * [exit]simplify: Simplified to (/ (* (pow (* PI (* n 2)) (/ k 2)) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ 1 2)))) * * * * [misc]progress: [ 124 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* PI 2) (/ k 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (* (pow (* PI 2) (/ k 2)) (sqrt k)) (pow (* (* n 2) PI) (/ 1 2))) * [exit]simplify: Simplified to (/ (* (pow (* PI 2) (/ k 2)) (sqrt k)) (pow (* (* n 2) PI) (/ 1 2))) * * * * [misc]progress: [ 125 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (* n (* PI 2)) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (* (/ (sqrt k) (pow (* PI (* n 2)) (/ 1 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))) * [exit]simplify: Simplified to (* (/ (sqrt k) (pow (* PI (* n 2)) (/ 1 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))) * * * * [misc]progress: [ 126 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (* (/ (sqrt k) (pow (* PI (* n 2)) (/ 1 2))) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * [exit]simplify: Simplified to (* (/ (sqrt k) (pow (* PI (* n 2)) (/ 1 2))) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * * * * [misc]progress: [ 127 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (/ (sqrt k) (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) * [exit]simplify: Simplified to (* (/ (sqrt k) (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) * * * * [misc]progress: [ 128 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (/ (sqrt k) (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) * [exit]simplify: Simplified to (* (/ (sqrt k) (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) * * * * [misc]progress: [ 129 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ 1 (pow (* n (* PI 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * * [misc]simplify: iters left: 2 (43 enodes) * * [misc]simplify: iters left: 1 (48 enodes) * [exit]simplify: Simplified to (* (pow (* 2 (* n PI)) (/ k 2)) (sqrt k)) * [exit]simplify: Simplified to (* (pow (* 2 (* n PI)) (/ k 2)) (sqrt k)) * * * * [misc]progress: [ 130 / 159 ] 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: [ 131 / 159 ] 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: [ 132 / 159 ] 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: [ 133 / 159 ] 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: [ 134 / 159 ] 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: [ 135 / 159 ] 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: [ 136 / 159 ] 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: [ 137 / 159 ] 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: [ 138 / 159 ] 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: [ 139 / 159 ] 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: [ 140 / 159 ] 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: [ 141 / 159 ] simplifiying candidate # * * * * [misc]progress: [ 142 / 159 ] 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: [ 143 / 159 ] 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: [ 144 / 159 ] 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: [ 145 / 159 ] 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: [ 146 / 159 ] 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: [ 147 / 159 ] simplifiying candidate # * * * * [misc]progress: [ 148 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)) (pow (* (* PI n) 2) (/ k 2))) * * * * [misc]progress: [ 149 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)) (pow (* (* PI n) 2) (/ k 2))) * * * * [misc]progress: [ 150 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)) (pow (* (* PI n) 2) (/ k 2))) * * * * [misc]progress: [ 151 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)) (pow (* (* PI n) 2) (/ k 2))) * * * * [misc]progress: [ 152 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)) (pow (* (* PI n) 2) (/ k 2))) * * * * [misc]progress: [ 153 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)) (pow (* (* PI n) 2) (/ k 2))) * * * * [misc]progress: [ 154 / 159 ] 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: [ 155 / 159 ] 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: [ 156 / 159 ] 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: [ 157 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (119 enodes) * * [misc]simplify: iters left: 2 (196 enodes) * * [misc]simplify: iters left: 1 (309 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (* PI 2)) (/ (sqrt n) (sqrt k))) (pow (* n (* PI 2)) (/ k 2))) * * * * [misc]progress: [ 158 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (112 enodes) * * [misc]simplify: iters left: 2 (241 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (* PI 2)) (/ (sqrt n) (sqrt k))) (pow (* (* PI n) 2) (/ k 2))) * * * * [misc]progress: [ 159 / 159 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (114 enodes) * * [misc]simplify: iters left: 2 (276 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (* PI -2)) (pow (/ -1 n) 1/2)) (sqrt k)) (pow (* 2 (* PI n)) (/ k 2))) * * * [misc]progress: adding candidates to table * * [misc]progress: iteration 3 / 4 * * * [misc]progress: picking best candidate * * * * [misc]pick: Picked # * * * [misc]progress: localizing error * * * [misc]progress: generating rewritten candidates * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 2 1) * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 2) * * * * [misc]progress: [ 3 / 4 ] rewriting at (2) * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 1) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2 1) * [misc]approximate: Taking taylor expansion of (pow (* PI 2) (/ (- 1 k) 2)) in (k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* PI 2) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* PI 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* 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 (* PI 2)) in k * [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 (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2) * [misc]taylor: Taking taylor expansion of (pow (* PI 2) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* PI 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* 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 (* PI 2)) in k * [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 (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2) * [misc]backup-simplify: Simplify (pow (* 2 PI) 1/2) into (pow (* 2 PI) 1/2) * [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) 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 PI)))) into (- (* 1/2 (log (* 2 PI)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1)))) into (* -1/2 (* (sqrt (* 2 PI)) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (* -1/2 (* (sqrt (* 2 PI)) (log (* 2 PI)))) into (* -1/2 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2)))) * [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 (+ 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 PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* 2 PI)) (pow (log (* 2 PI)) 2))) * [misc]backup-simplify: Simplify (* 1/8 (* (sqrt (* 2 PI)) (pow (log (* 2 PI)) 2))) into (* 1/8 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (sqrt 2)))) * [misc]backup-simplify: Simplify (+ (* (* 1/8 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (sqrt 2)))) (pow k 2)) (+ (* (* -1/2 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2)))) k) (pow (* 2 PI) 1/2))) into (- (+ (pow (* 2 PI) 1/2) (* 1/8 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (* (pow k 2) (sqrt 2)))))) (* 1/2 (* (sqrt PI) (* (log (* 2 PI)) (* k (sqrt 2)))))) * [misc]approximate: Taking taylor expansion of (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) in (k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* PI 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* 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 (* PI 2)) in k * [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 (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* PI 2)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) * [misc]taylor: Taking taylor expansion of (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* PI 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* 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 (* PI 2)) in k * [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 (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* PI 2)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) * [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 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) * [misc]approximate: Taking taylor expansion of (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) in (k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* PI 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* 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 (* PI 2)) in k * [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 (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* PI 2)))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) * [misc]taylor: Taking taylor expansion of (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* PI 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* 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 (* PI 2)) in k * [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 (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* PI 2)))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) * [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 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) * * * * [misc]progress: [ 2 / 4 ] generating series at (2 2) * [misc]approximate: Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (pow (* PI 2) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* PI 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* 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 (* PI 2)) in k * [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 (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 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 PI) 1/2) +nan.0) into (* +nan.0 (sqrt (* 2 PI))) * [misc]taylor: Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (pow (* PI 2) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* PI 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* 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 (* PI 2)) in k * [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 (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 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 PI) 1/2) +nan.0) into (* +nan.0 (sqrt (* 2 PI))) * [misc]backup-simplify: Simplify (* +nan.0 (sqrt (* 2 PI))) into (* +nan.0 (* (sqrt PI) (sqrt 2))) * [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) 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 PI)))) into (- (* 1/2 (log (* 2 PI)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1)))) into (* -1/2 (* (sqrt (* 2 PI)) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ (* -1/2 (* (sqrt (* 2 PI)) (log (* 2 PI)))) +nan.0) (+ (* (* +nan.0 (sqrt (* 2 PI))) (/ +nan.0 +nan.0)))) into (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2))))))) into (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2))))))) * [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 (+ 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 PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* 2 PI)) (pow (log (* 2 PI)) 2))) * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ (* 1/8 (* (sqrt (* 2 PI)) (pow (log (* 2 PI)) 2))) +nan.0) (+ (* (* +nan.0 (sqrt (* 2 PI))) (/ +nan.0 +nan.0)) (* (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2))))))) (/ +nan.0 +nan.0)))) into (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (sqrt 2)))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2))))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (sqrt 2)))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2))))))))) into (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (sqrt 2)))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2))))))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (sqrt 2)))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2))))))))) k) (+ (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2))))))) (* (* +nan.0 (* (sqrt PI) (sqrt 2))) (/ 1 k)))) into (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (+ (* +nan.0 (* (sqrt PI) (* k (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (* k (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt PI) (/ (sqrt 2) k))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (* k (sqrt 2))))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2))))))))))))))) * [misc]approximate: Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* PI 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* 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 (* PI 2)) in k * [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 (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* PI 2)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) * [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 (* (- 1 (/ 1 k)) (log (* 2 PI))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* PI 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* 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 (* PI 2)) in k * [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 (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* PI 2)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) * [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 (* (- 1 (/ 1 k)) (log (* 2 PI))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) * [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 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) * [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 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI))))))) (pow (/ 1 k) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI))))))) (/ 1 k)) (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI)))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) k))))))) * [misc]approximate: Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* PI 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* 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 (* PI 2)) in k * [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 (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* PI 2)))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) * [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))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* PI 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* 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 (* PI 2)) in k * [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 (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* PI 2)))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) * [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))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 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 (/ (- 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)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 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)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (log (* 2 PI))))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (log (* 2 PI))))))) (/ 1 (- k))) (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (log (* 2 PI)))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) k))))))) * * * * [misc]progress: [ 3 / 4 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) in k * [misc]taylor: Taking taylor expansion of (pow n (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log n))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log 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 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 (* 1/2 (log n)) into (* 1/2 (log n)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) * [misc]taylor: Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (pow (* PI 2) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* PI 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* 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 (* PI 2)) in k * [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 (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 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 PI) 1/2) +nan.0) into (* +nan.0 (sqrt (* 2 PI))) * [misc]taylor: Taking taylor expansion of (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) in n * [misc]taylor: Taking taylor expansion of (pow n (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log n))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log 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 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 (log 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (log n)) into (* 1/2 (* (- 1 k) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (log n)))) into (exp (* 1/2 (* (- 1 k) (log n)))) * [misc]taylor: Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (pow (* PI 2) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* 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 (* PI 2)) in n * [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 (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (log (* 2 PI))) into (* 1/2 (* (- 1 k) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) * [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))))) (sqrt k)) into (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (sqrt (/ 1 k))) * [misc]taylor: Taking taylor expansion of (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) in n * [misc]taylor: Taking taylor expansion of (pow n (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log n))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log 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 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 (log 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (log n)) into (* 1/2 (* (- 1 k) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (log n)))) into (exp (* 1/2 (* (- 1 k) (log n)))) * [misc]taylor: Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (pow (* PI 2) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* 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 (* PI 2)) in n * [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 (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (log (* 2 PI))) into (* 1/2 (* (- 1 k) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) * [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))))) (sqrt k)) into (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (sqrt (/ 1 k))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (log n)))) (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (sqrt (/ 1 k)))) into (* (* (exp (* 1/2 (* (- 1 k) (log n)))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (sqrt (/ 1 k))) * [misc]taylor: Taking taylor expansion of (* (* (exp (* 1/2 (* (- 1 k) (log n)))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 k) (log n)))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (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 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 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 (* 1 (log n)) into (log n) * [misc]backup-simplify: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (log (* 2 PI)))) 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))) 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)) 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]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (* 1 (log (* 2 PI))) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2) * [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 (* (pow n 1/2) (pow (* 2 PI) 1/2)) into (sqrt (* n (* 2 PI))) * [misc]backup-simplify: Simplify (* (sqrt (* n (* 2 PI))) 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 (/ (* (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 (+ (* (* 1/2 (- 1 k)) 0) (* 0 (log (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (sqrt (/ 1 k))) (/ 0 (sqrt k))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 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)) 0) into (log n) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (log n))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (log n)))) 0) (* 0 (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (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 (+ (* 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) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (+ (* 1 0) (* -1 (log (* 2 PI)))) into (- (log (* 2 PI))) * [misc]backup-simplify: Simplify (+ (* 1/2 (- (log (* 2 PI)))) (* 0 (log (* 2 PI)))) into (- (* 1/2 (log (* 2 PI)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1)))) into (* -1/2 (* (sqrt (* 2 PI)) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) 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 n))) into (- (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 (- (log n))) (* 0 (log n))) into (- (* 1/2 (log n))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 1) 1)))) into (* -1/2 (* (sqrt n) (log n))) * [misc]backup-simplify: Simplify (+ (* (pow n 1/2) (* -1/2 (* (sqrt (* 2 PI)) (log (* 2 PI))))) (* (* -1/2 (* (sqrt n) (log n))) (pow (* 2 PI) 1/2))) into (- (+ (* 1/2 (* (sqrt (* n PI)) (* (log (* 2 PI)) (sqrt 2)))) (* 1/2 (* (sqrt (* n PI)) (* (log n) (sqrt 2)))))) * [misc]backup-simplify: Simplify (+ (* (sqrt (* n (* 2 PI))) +nan.0) (* (- (+ (* 1/2 (* (sqrt (* n PI)) (* (log (* 2 PI)) (sqrt 2)))) (* 1/2 (* (sqrt (* n PI)) (* (log n) (sqrt 2)))))) 0)) into (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))) into (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))) * [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 (+ 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 (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (log (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (+ (* (/ (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)) (+ (* (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (sqrt (/ 1 k))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 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)) 0) into (log n) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (log n)))) 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (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 (- (+ (* 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 (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (log (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (log (* 2 PI)))) (* 0 (log (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* 2 PI)) (pow (log (* 2 PI)) 2))) * [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 0) (+ (* -1 0) (* 0 (log n)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (log n))) (* 0 (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt n) (pow (log n) 2))) * [misc]backup-simplify: Simplify (+ (* (pow n 1/2) (* 1/8 (* (sqrt (* 2 PI)) (pow (log (* 2 PI)) 2)))) (+ (* (* -1/2 (* (sqrt n) (log n))) (* -1/2 (* (sqrt (* 2 PI)) (log (* 2 PI))))) (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (pow (* 2 PI) 1/2)))) into (+ (* 1/8 (* (sqrt (* n PI)) (* (pow (log n) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n PI)) (* (pow (log (* 2 PI)) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n PI)) (* (log (* 2 PI)) (* (log n) (sqrt 2))))))) * [misc]backup-simplify: Simplify (+ (* (sqrt (* n (* 2 PI))) +nan.0) (+ (* (- (+ (* 1/2 (* (sqrt (* n PI)) (* (log (* 2 PI)) (sqrt 2)))) (* 1/2 (* (sqrt (* n PI)) (* (log n) (sqrt 2)))))) +nan.0) (* (+ (* 1/8 (* (sqrt (* n PI)) (* (pow (log n) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n PI)) (* (pow (log (* 2 PI)) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n PI)) (* (log (* 2 PI)) (* (log n) (sqrt 2))))))) 0))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) (sqrt 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) (sqrt 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) (sqrt 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))))) * [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 (- 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 (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (+ (* (/ (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)) (+ (* (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (sqrt (/ 1 k))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 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)) 0) into (log n) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (log n)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (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 (- (+ (* 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 (- 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)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (log (* 2 PI)))) (* 0 (log (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* 2 PI)) (pow (log (* 2 PI)) 3))) * [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 0) (+ (* -1 0) (+ (* 0 0) (* 0 (log n))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (log n))) (* 0 (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 3) 6)) (* (/ (pow (- (* 1/2 (log n))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt n) (pow (log n) 3))) * [misc]backup-simplify: Simplify (+ (* (pow n 1/2) (* -1/48 (* (sqrt (* 2 PI)) (pow (log (* 2 PI)) 3)))) (+ (* (* -1/2 (* (sqrt n) (log n))) (* 1/8 (* (sqrt (* 2 PI)) (pow (log (* 2 PI)) 2)))) (+ (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (* -1/2 (* (sqrt (* 2 PI)) (log (* 2 PI))))) (* (* -1/48 (* (sqrt n) (pow (log n) 3))) (pow (* 2 PI) 1/2))))) into (- (+ (* 1/48 (* (sqrt (* n PI)) (* (pow (log (* 2 PI)) 3) (sqrt 2)))) (+ (* 1/16 (* (sqrt (* n PI)) (* (log (* 2 PI)) (* (pow (log n) 2) (sqrt 2))))) (+ (* 1/16 (* (sqrt (* n PI)) (* (pow (log (* 2 PI)) 2) (* (log n) (sqrt 2))))) (* 1/48 (* (sqrt (* n PI)) (* (pow (log n) 3) (sqrt 2)))))))) * [misc]backup-simplify: Simplify (+ (* (sqrt (* n (* 2 PI))) +nan.0) (+ (* (- (+ (* 1/2 (* (sqrt (* n PI)) (* (log (* 2 PI)) (sqrt 2)))) (* 1/2 (* (sqrt (* n PI)) (* (log n) (sqrt 2)))))) +nan.0) (+ (* (+ (* 1/8 (* (sqrt (* n PI)) (* (pow (log n) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n PI)) (* (pow (log (* 2 PI)) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n PI)) (* (log (* 2 PI)) (* (log n) (sqrt 2))))))) +nan.0) (* (- (+ (* 1/48 (* (sqrt (* n PI)) (* (pow (log (* 2 PI)) 3) (sqrt 2)))) (+ (* 1/16 (* (sqrt (* n PI)) (* (log (* 2 PI)) (* (pow (log n) 2) (sqrt 2))))) (+ (* 1/16 (* (sqrt (* n PI)) (* (pow (log (* 2 PI)) 2) (* (log n) (sqrt 2))))) (* 1/48 (* (sqrt (* n PI)) (* (pow (log n) 3) (sqrt 2)))))))) 0)))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log n) 2) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log (* 2 PI)) 2) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (* (log n) (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) (sqrt 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))))))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log n) 2) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log (* 2 PI)) 2) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (* (log n) (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) (sqrt 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))))))))))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log n) 2) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log (* 2 PI)) 2) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (* (log n) (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) (sqrt 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))))))))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log n) 2) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log (* 2 PI)) 2) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (* (log n) (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) (sqrt 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) (sqrt 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))))) (* k 1)) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) (* k (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log (* 2 PI)) 2) (* (pow k 2) (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow k 2) (* (log n) (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (* (pow k 2) (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (* k (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* k (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow k 2) (* (pow (log n) 2) (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow k 2) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (* (log (* 2 PI)) (* (pow k 2) (log n)))))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))))))))))))))))))) * [misc]approximate: Taking taylor expansion of (* (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2)) (/ (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (* (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2)) (/ (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k)))) in k * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (/ 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 (/ 1 n)) 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]backup-simplify: Simplify (log (/ 1 n)) into (log (/ 1 n)) * [misc]backup-simplify: Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (/ 1 n)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 1 n))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* PI 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* 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 (* PI 2)) in k * [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 (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* PI 2)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) * [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 (* (- 1 (/ 1 k)) (log (* 2 PI))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) * [misc]taylor: Taking taylor expansion of (* (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2)) (/ (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k)))) in n * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (/ 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 (/ 1 n)) 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]backup-simplify: Simplify (log 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log n))) into (* -1/2 (* (- 1 (/ 1 k)) (log n))) * [misc]backup-simplify: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) * [misc]taylor: Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* 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 (* PI 2)) in n * [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 (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI))) into (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) * [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))))) (sqrt (/ 1 k))) into (* (sqrt k) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) * [misc]taylor: Taking taylor expansion of (* (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2)) (/ (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k)))) in n * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (/ 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 (/ 1 n)) 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]backup-simplify: Simplify (log 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log n))) into (* -1/2 (* (- 1 (/ 1 k)) (log n))) * [misc]backup-simplify: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) * [misc]taylor: Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* 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 (* PI 2)) in n * [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 (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI))) into (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) * [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))))) (sqrt (/ 1 k))) into (* (sqrt k) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) * [misc]backup-simplify: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (* (sqrt k) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) into (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))) 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))) 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)) 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]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (* -1 (log (* 2 PI))) into (* -1 (log (* 2 PI))) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (log (* 2 PI)))) into (* -1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* -1/2 (* (- 1 (/ 1 k)) (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 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 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 (* -1 (log n)) into (* -1 (log n)) * [misc]backup-simplify: Simplify (* -1/2 (* -1 (log n))) into (* 1/2 (log n)) * [misc]backup-simplify: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (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))))) (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))) into (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) * [misc]backup-simplify: Simplify (* (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) 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 (/ (* (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 (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (log (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (sqrt k) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 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)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) 0) (* 0 (* (sqrt k) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) 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))))) 0) (* 0 (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) into (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) * [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 (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (log (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (+ (* (/ (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))) (+ (* (* (sqrt k) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) (/ 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 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 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)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) 0) (+ (* 0 0) (* 0 (* (sqrt k) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))))) 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))))) 0) (+ (* 0 0) (* 0 (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) into (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) * [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 (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (+ (* (/ (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))) (+ (* (* (sqrt k) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) (/ 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 (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 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)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt k) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))))) 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))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) into (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 (/ 1 k))) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 (/ 1 k))) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 (/ 1 k))) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* -1/2 (* (- 1 k) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* -1/2 (* (- 1 k) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* -1/2 (* (- 1 k) (log (/ 1 n)))))) (pow k 3)))))))) * [misc]approximate: Taking taylor expansion of (* (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2)) (/ (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k))))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (* (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2)) (/ (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k))))) in k * [misc]taylor: Taking taylor expansion of (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 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 (/ 1 (- n))) 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]backup-simplify: Simplify (log (/ -1 n)) into (log (/ -1 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 1 (- n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (/ -1 n))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* PI 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* 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 (* PI 2)) in k * [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 (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* PI 2)))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) * [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))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))) * [misc]taylor: Taking taylor expansion of (* (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2)) (/ (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k))))) in n * [misc]taylor: Taking taylor expansion of (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 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 (/ 1 (- n))) 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]backup-simplify: Simplify (log -1) into (log -1) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log -1) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* 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 (* PI 2)) in n * [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 (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (log (* 2 PI))) into (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) * [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))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) (sqrt (/ -1 k))) * [misc]taylor: Taking taylor expansion of (* (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2)) (/ (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k))))) in n * [misc]taylor: Taking taylor expansion of (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 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 (/ 1 (- n))) 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]backup-simplify: Simplify (log -1) into (log -1) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log -1) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* PI 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* 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 (* PI 2)) in n * [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 (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (log (* 2 PI))) into (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) * [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))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) (sqrt (/ -1 k))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) (sqrt (/ -1 k)))) into (/ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))) (sqrt (/ -1 k))) * [misc]taylor: Taking taylor expansion of (/ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))) (sqrt (/ -1 k))) in k * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (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 -1) (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 -1) (log n)) in k * [misc]taylor: Taking taylor expansion of (log -1) in k * [misc]taylor: Taking taylor expansion of -1 in k * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify (log -1) into (log -1) * [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 -1) (- (log n))) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (* 1 (- (log -1) (log n))) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log -1) (log n))) into (* 1/2 (- (log -1) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))) 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))) 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)) 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]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (* 1 (log (* 2 PI))) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) * [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 -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))) into (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))) * [misc]backup-simplify: Simplify (/ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))) +nan.0) into (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))) into (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))) * [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 (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (* 0 (log (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) 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 (/ (* (pow (* 1 0) 1)) (pow -1 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 -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (* 0 (- (log -1) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) 0) (* 0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) (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 -1) (log n))))) 0) (* 0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))) 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 -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))))) * [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 (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (log (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) (+ (* (/ (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))))) (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 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 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 -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) 0) (+ (* 0 0) (* 0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) (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 (+ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))))) 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 -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log -1) (log (/ 1 (- n))))))) (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (log (* 2 PI)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log -1) (log (/ 1 (- n))))))) (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (log (* 2 PI)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log -1) (log (/ 1 (- n))))))) (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n))))))) k)) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n))))))) (pow k 2))) (- (* +nan.0 (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n))))))))))))) * * * * [misc]progress: [ 4 / 4 ] generating series at (2 1) * [misc]approximate: Taking taylor expansion of (pow n (/ (- 1 k) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow n (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log n))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log 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 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 (* 1/2 (log n)) into (* 1/2 (log n)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) * [misc]taylor: Taking taylor expansion of (pow n (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log n))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log 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 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 (log 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (log n)) into (* 1/2 (* (- 1 k) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (log n)))) into (exp (* 1/2 (* (- 1 k) (log n)))) * [misc]taylor: Taking taylor expansion of (pow n (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log n))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log 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 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 (log 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (log n)) into (* 1/2 (* (- 1 k) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (log n)))) into (exp (* 1/2 (* (- 1 k) (log n)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (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 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 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 (* 1 (log n)) into (log n) * [misc]backup-simplify: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) * [misc]backup-simplify: Simplify (pow n 1/2) into (pow n 1/2) * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 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)) 0) into (log n) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (log n))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (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 (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) 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 n))) into (- (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 (- (log n))) (* 0 (log n))) into (- (* 1/2 (log n))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 1) 1)))) into (* -1/2 (* (sqrt n) (log n))) * [misc]backup-simplify: Simplify (* -1/2 (* (sqrt n) (log n))) into (* -1/2 (* (sqrt n) (log n))) * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 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)) 0) into (log n) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (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 (/ (+ (* -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 0) (+ (* -1 0) (* 0 (log n)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (log n))) (* 0 (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt n) (pow (log n) 2))) * [misc]backup-simplify: Simplify (* 1/8 (* (sqrt n) (pow (log n) 2))) into (* 1/8 (* (sqrt n) (pow (log n) 2))) * [misc]backup-simplify: Simplify (+ (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (pow (* k 1) 2)) (+ (* (* -1/2 (* (sqrt n) (log n))) (* k 1)) (pow n 1/2))) into (- (+ (* 1/8 (* (sqrt n) (* (pow (log n) 2) (pow k 2)))) (pow n 1/2)) (* 1/2 (* (sqrt n) (* (log n) k)))) * [misc]approximate: Taking taylor expansion of (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (/ 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 (/ 1 n)) 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]backup-simplify: Simplify (log (/ 1 n)) into (log (/ 1 n)) * [misc]backup-simplify: Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (/ 1 n)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 1 n))))) * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (/ 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 (/ 1 n)) 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]backup-simplify: Simplify (log 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log n))) into (* -1/2 (* (- 1 (/ 1 k)) (log n))) * [misc]backup-simplify: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (/ 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 (/ 1 n)) 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]backup-simplify: Simplify (log 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log n))) into (* -1/2 (* (- 1 (/ 1 k)) (log n))) * [misc]backup-simplify: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* -1/2 (* (- 1 (/ 1 k)) (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 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 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 (* -1 (log n)) into (* -1 (log n)) * [misc]backup-simplify: Simplify (* -1/2 (* -1 (log n))) into (* 1/2 (log n)) * [misc]backup-simplify: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) * [misc]backup-simplify: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 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)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (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 (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 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)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (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 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 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)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (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 (/ 1 n))))) into (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) * [misc]approximate: Taking taylor expansion of (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 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 (/ 1 (- n))) 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]backup-simplify: Simplify (log (/ -1 n)) into (log (/ -1 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 1 (- n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (/ -1 n))))) * [misc]taylor: Taking taylor expansion of (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 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 (/ 1 (- n))) 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]backup-simplify: Simplify (log -1) into (log -1) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log -1) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 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 (/ 1 (- n))) 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]backup-simplify: Simplify (log -1) into (log -1) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log -1) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (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 -1) (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 -1) (log n)) in k * [misc]taylor: Taking taylor expansion of (log -1) in k * [misc]taylor: Taking taylor expansion of -1 in k * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify (log -1) into (log -1) * [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 -1) (- (log n))) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (* 1 (- (log -1) (log n))) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log -1) (log n))) into (* 1/2 (- (log -1) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (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 (/ (* (pow (* 1 0) 1)) (pow -1 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 -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (* 0 (- (log -1) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (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 (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 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 -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (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 (/ (* (pow (* 1 0) 3)) (pow -1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow -1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow -1 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 -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -1) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (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 -1) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (pow (* PI 2) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 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 (expm1 (pow (* 2 PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (expm1 (pow (* 2 PI) (/ (- 1 k) 2))) * * * * [misc]progress: [ 2 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (pow (* PI 2) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 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 (log1p (pow (* 2 PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (log1p (pow (* 2 PI) (/ (- 1 k) 2))) * * * * [misc]progress: [ 3 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* PI 2)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (395 enodes) * [exit]simplify: Simplified to (* (log (* 2 PI)) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (* (log (* 2 PI)) (/ (- 1 k) 2)) * * * * [misc]progress: [ 4 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* PI 2)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (395 enodes) * [exit]simplify: Simplified to (* (log (* 2 PI)) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (* (log (* 2 PI)) (/ (- 1 k) 2)) * * * * [misc]progress: [ 5 / 123 ] 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: [ 6 / 123 ] simplifiying candidate # * [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)) * [enter]simplify: Simplifying (pow (* PI 2) (/ k 2)) * * [misc]simplify: iters left: 3 (6 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * [exit]simplify: Simplified to (pow (* 2 PI) (/ k 2)) * [exit]simplify: Simplified to (pow (* 2 PI) (/ k 2)) * * * * [misc]progress: [ 7 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* PI 2) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 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 (pow (* 2 PI) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (pow (* 2 PI) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * * * [misc]progress: [ 8 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* PI 2) (sqrt (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 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 (* 2 PI) (sqrt (/ (- 1 k) 2))) * [exit]simplify: Simplified to (pow (* 2 PI) (sqrt (/ (- 1 k) 2))) * * * * [misc]progress: [ 9 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* PI 2) 1) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (8 enodes) * [exit]simplify: Simplified to (* 2 PI) * [exit]simplify: Simplified to (* 2 PI) * * * * [misc]progress: [ 10 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* PI 2) (- 1 k)) * * [misc]simplify: iters left: 3 (7 enodes) * * [misc]simplify: iters left: 2 (12 enodes) * * [misc]simplify: iters left: 1 (13 enodes) * [exit]simplify: Simplified to (pow (* 2 PI) (- 1 k)) * [exit]simplify: Simplified to (pow (* 2 PI) (- 1 k)) * * * * [misc]progress: [ 11 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (pow PI (/ (- 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 PI (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow PI (/ (- 1 k) 2)) * [enter]simplify: Simplifying (pow 2 (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (pow 2 (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow 2 (/ (- 1 k) 2)) * * * * [misc]progress: [ 12 / 123 ] simplifiying candidate # * * * * [misc]progress: [ 13 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (log (pow (* PI 2) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (132 enodes) * * [misc]simplify: iters left: 1 (490 enodes) * [exit]simplify: Simplified to (* (log (* 2 PI)) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (* (log (* 2 PI)) (/ (- 1 k) 2)) * * * * [misc]progress: [ 14 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (pow (* PI 2) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 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 (exp (pow (* 2 PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (exp (pow (* 2 PI) (/ (- 1 k) 2))) * * * * [misc]progress: [ 15 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (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 (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) * [enter]simplify: Simplifying (cbrt (pow (* PI 2) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 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 (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) * * * * [misc]progress: [ 16 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (pow (* PI 2) (/ (- 1 k) 2)) (pow (* PI 2) (/ (- 1 k) 2))) (pow (* PI 2) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (pow (pow (* 2 PI) (/ (- 1 k) 2)) 3) * [exit]simplify: Simplified to (pow (pow (* 2 PI) (/ (- 1 k) 2)) 3) * * * * [misc]progress: [ 17 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (pow (* PI 2) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 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 (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) * [enter]simplify: Simplifying (sqrt (pow (* PI 2) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 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 (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) * * * * [misc]progress: [ 18 / 123 ] simplifiying candidate # * * * * [misc]progress: [ 19 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (/ (pow (* PI 2) (/ (- 1 k) 2)) (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 (expm1 (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (expm1 (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 20 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (/ (pow (* PI 2) (/ (- 1 k) 2)) (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 (log1p (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (log1p (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 21 / 123 ] simplifiying candidate # * * * * [misc]progress: [ 22 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* PI 2)) (/ (- 1 k) 2)) (log (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (125 enodes) * * [misc]simplify: iters left: 2 (455 enodes) * [exit]simplify: Simplified to (- (/ (log (* 2 PI)) (/ 2 (- 1 k))) (log (sqrt k))) * [exit]simplify: Simplified to (- (/ (log (* 2 PI)) (/ 2 (- 1 k))) (log (sqrt k))) * * * * [misc]progress: [ 23 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* PI 2)) (/ (- 1 k) 2)) (log (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (125 enodes) * * [misc]simplify: iters left: 2 (455 enodes) * [exit]simplify: Simplified to (- (/ (log (* 2 PI)) (/ 2 (- 1 k))) (log (sqrt k))) * [exit]simplify: Simplified to (- (/ (log (* 2 PI)) (/ 2 (- 1 k))) (log (sqrt k))) * * * * [misc]progress: [ 24 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (pow (* PI 2) (/ (- 1 k) 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (176 enodes) * [exit]simplify: Simplified to (- (/ (log (* 2 PI)) (/ 2 (- 1 k))) (log (sqrt k))) * [exit]simplify: Simplified to (- (/ (log (* 2 PI)) (/ 2 (- 1 k))) (log (sqrt k))) * * * * [misc]progress: [ 25 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (log (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * * [misc]simplify: iters left: 2 (69 enodes) * * [misc]simplify: iters left: 1 (192 enodes) * [exit]simplify: Simplified to (- (/ (log (* 2 PI)) (/ 2 (- 1 k))) (log (sqrt k))) * [exit]simplify: Simplified to (- (/ (log (* 2 PI)) (/ 2 (- 1 k))) (log (sqrt k))) * * * * [misc]progress: [ 26 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (/ (pow (* PI 2) (/ (- 1 k) 2)) (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 (exp (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (exp (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 27 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (pow (* PI 2) (/ (- 1 k) 2)) (pow (* PI 2) (/ (- 1 k) 2))) (pow (* PI 2) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (120 enodes) * * [misc]simplify: iters left: 2 (204 enodes) * * [misc]simplify: iters left: 1 (341 enodes) * [exit]simplify: Simplified to (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (* k (sqrt k))) (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (* k (sqrt k))) (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 28 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 (* (cbrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))) * [enter]simplify: Simplifying (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (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 (cbrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (cbrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 29 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (77 enodes) * * [misc]simplify: iters left: 2 (112 enodes) * * [misc]simplify: iters left: 1 (143 enodes) * [exit]simplify: Simplified to (/ (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* 2 PI) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* 2 PI) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 30 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (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 (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) * [enter]simplify: Simplifying (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (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 (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 31 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (- (pow (* PI 2) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 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 (* 2 PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (- (pow (* 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: [ 32 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow PI (/ (- 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 PI (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (pow 2 (/ (- 1 k) 2)) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (/ (pow 2 (/ (- 1 k) 2)) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow 2 (/ (- 1 k) 2)) (cbrt (sqrt k))) * * * * [misc]progress: [ 33 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow PI (/ (- 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 PI (/ (- 1 k) 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k))) * * * * [misc]progress: [ 34 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow PI (/ (- 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 PI (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow PI (/ (- 1 k) 2)) * [enter]simplify: Simplifying (/ (pow 2 (/ (- 1 k) 2)) (sqrt k)) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * [exit]simplify: Simplified to (/ (pow 2 (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow 2 (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 35 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (12 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 (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) * * * * [misc]progress: [ 36 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (/ (sqrt (sqrt k)) (cbrt (pow (* 2 PI) (/ (- 1 k) 2))))) * [exit]simplify: Simplified to (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (/ (sqrt (sqrt k)) (cbrt (pow (* 2 PI) (/ (- 1 k) 2))))) * [enter]simplify: Simplifying (/ (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (12 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 (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * * * [misc]progress: [ 37 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))) 1) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) * [enter]simplify: Simplifying (/ (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (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 (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k)) * [exit]simplify: Simplified to (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k)) * * * * [misc]progress: [ 38 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (12 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 (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) * * * * [misc]progress: [ 39 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (12 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 (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (12 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 (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * * * [misc]progress: [ 40 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) 1) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) * [enter]simplify: Simplifying (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (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 (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k)) * * * * [misc]progress: [ 41 / 123 ] 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 (* 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: [ 42 / 123 ] 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 (* 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: [ 43 / 123 ] 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 (* 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: [ 44 / 123 ] simplifiying candidate # * * * * [misc]progress: [ 45 / 123 ] 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: [ 46 / 123 ] 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: [ 47 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* PI 2) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (27 enodes) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * * * [misc]progress: [ 48 / 123 ] simplifiying candidate # * [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: [ 49 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* PI 2) (/ (- 1 k) 2)) 1) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 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)) * [exit]simplify: Simplified to (pow (* 2 PI) (/ (- 1 k) 2)) * * * * [misc]progress: [ 50 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (pow 2 (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (pow 2 (/ (- 1 k) 2))) * [exit]simplify: Simplified to (/ (sqrt k) (pow 2 (/ (- 1 k) 2))) * * * * [misc]progress: [ 51 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))) * * [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 (/ (sqrt k) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 52 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (pow (* PI 2) (/ (- 1 k) 2)))) * * [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 (/ (sqrt k) (sqrt (pow (* PI 2) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (pow (* PI 2) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 53 / 123 ] 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: [ 54 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt k) (pow (* PI 2) (/ k 2))) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * [exit]simplify: Simplified to (* (pow (* PI 2) (/ k 2)) (sqrt k)) * [exit]simplify: Simplified to (* (pow (* PI 2) (/ k 2)) (sqrt k)) * * * * [misc]progress: [ 55 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (* (pow n (/ (- 1 k) 2)) (/ (pow (* 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 (32 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 (expm1 (* (/ (pow n (/ (- 1 k) 2)) (sqrt k)) (pow (* PI 2) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (expm1 (* (/ (pow n (/ (- 1 k) 2)) (sqrt k)) (pow (* PI 2) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 56 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (* (pow n (/ (- 1 k) 2)) (/ (pow (* 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 (32 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 (log1p (* (/ (pow n (/ (- 1 k) 2)) (sqrt k)) (pow (* PI 2) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (log1p (* (/ (pow n (/ (- 1 k) 2)) (sqrt k)) (pow (* PI 2) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 57 / 123 ] simplifiying candidate # * * * * [misc]progress: [ 58 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (log n) (/ (- 1 k) 2)) (- (* (log (* PI 2)) (/ (- 1 k) 2)) (log (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (242 enodes) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (+ (log n) (log (* PI 2))) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (+ (log n) (log (* PI 2))) (- (log (sqrt k)))) * * * * [misc]progress: [ 59 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (log n) (/ (- 1 k) 2)) (- (* (log (* PI 2)) (/ (- 1 k) 2)) (log (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (242 enodes) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (+ (log n) (log (* PI 2))) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (+ (log n) (log (* PI 2))) (- (log (sqrt k)))) * * * * [misc]progress: [ 60 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (log n) (/ (- 1 k) 2)) (- (log (pow (* PI 2) (/ (- 1 k) 2))) (log (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (171 enodes) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (+ (log n) (log (* PI 2))) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (+ (log n) (log (* PI 2))) (- (log (sqrt k)))) * * * * [misc]progress: [ 61 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (log n) (/ (- 1 k) 2)) (log (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (117 enodes) * * [misc]simplify: iters left: 2 (313 enodes) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (+ (log (* PI 2)) (log n)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (+ (log (* PI 2)) (log n)) (- (log (sqrt k)))) * * * * [misc]progress: [ 62 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (pow n (/ (- 1 k) 2))) (- (* (log (* PI 2)) (/ (- 1 k) 2)) (log (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (194 enodes) * [exit]simplify: Simplified to (fma (+ (log n) (log (* PI 2))) (/ (- 1 k) 2) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (+ (log n) (log (* PI 2))) (/ (- 1 k) 2) (- (log (sqrt k)))) * * * * [misc]progress: [ 63 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (pow n (/ (- 1 k) 2))) (- (* (log (* PI 2)) (/ (- 1 k) 2)) (log (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (194 enodes) * [exit]simplify: Simplified to (fma (+ (log n) (log (* PI 2))) (/ (- 1 k) 2) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (+ (log n) (log (* PI 2))) (/ (- 1 k) 2) (- (log (sqrt k)))) * * * * [misc]progress: [ 64 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (pow n (/ (- 1 k) 2))) (- (log (pow (* PI 2) (/ (- 1 k) 2))) (log (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (388 enodes) * [exit]simplify: Simplified to (fma (+ (log n) (log (* PI 2))) (/ (- 1 k) 2) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (+ (log n) (log (* PI 2))) (/ (- 1 k) 2) (- (log (sqrt k)))) * * * * [misc]progress: [ 65 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (pow n (/ (- 1 k) 2))) (log (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (79 enodes) * * [misc]simplify: iters left: 2 (196 enodes) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (+ (log (* PI 2)) (log n)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (+ (log (* PI 2)) (log n)) (- (log (sqrt k)))) * * * * [misc]progress: [ 66 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (110 enodes) * * [misc]simplify: iters left: 1 (289 enodes) * [exit]simplify: Simplified to (fma (+ (log (* PI 2)) (log n)) (/ (- 1 k) 2) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (+ (log (* PI 2)) (log n)) (/ (- 1 k) 2) (- (log (sqrt k)))) * * * * [misc]progress: [ 67 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * * [misc]simplify: iters left: 2 (40 enodes) * * [misc]simplify: iters left: 1 (41 enodes) * [exit]simplify: Simplified to (pow (exp (pow n (/ (- 1 k) 2))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (pow (exp (pow n (/ (- 1 k) 2))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 68 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (pow n (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))) (/ (* (* (pow (* PI 2) (/ (- 1 k) 2)) (pow (* PI 2) (/ (- 1 k) 2))) (pow (* PI 2) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (448 enodes) * [exit]simplify: Simplified to (* (/ (* (pow n (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (/ k (pow n (/ (- 1 k) 2)))) (/ (* (pow (* PI 2) (/ (- 1 k) 2)) (pow (* PI 2) (/ (- 1 k) 2))) (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2))))) * [exit]simplify: Simplified to (* (/ (* (pow n (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (/ k (pow n (/ (- 1 k) 2)))) (/ (* (pow (* PI 2) (/ (- 1 k) 2)) (pow (* PI 2) (/ (- 1 k) 2))) (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2))))) * * * * [misc]progress: [ 69 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (pow n (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))) (* (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (232 enodes) * [exit]simplify: Simplified to (* (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (* (pow n (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (/ (* (pow (* PI 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (/ k (pow (* PI 2) (/ (- 1 k) 2))))) * [exit]simplify: Simplified to (* (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (* (pow n (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (/ (* (pow (* PI 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (/ k (pow (* PI 2) (/ (- 1 k) 2))))) * * * * [misc]progress: [ 70 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (33 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 (* (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (/ (sqrt k) (pow n (/ (- 1 k) 2))))) (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (/ (sqrt k) (pow n (/ (- 1 k) 2)))))) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (/ (sqrt k) (pow n (/ (- 1 k) 2))))) (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (/ (sqrt k) (pow n (/ (- 1 k) 2)))))) * [enter]simplify: Simplifying (cbrt (* (pow n (/ (- 1 k) 2)) (/ (pow (* 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 (32 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 (cbrt (* (/ (pow n (/ (- 1 k) 2)) (sqrt k)) (pow (* PI 2) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (cbrt (* (/ (pow n (/ (- 1 k) 2)) (sqrt k)) (pow (* PI 2) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 71 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))) (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (74 enodes) * * [misc]simplify: iters left: 3 (195 enodes) * [exit]simplify: Simplified to (pow (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))) 3) * [exit]simplify: Simplified to (pow (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))) 3) * * * * [misc]progress: [ 72 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (pow n (/ (- 1 k) 2)) (/ (pow (* 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 (32 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 (* (/ (pow n (/ (- 1 k) 2)) (sqrt k)) (pow (* PI 2) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (sqrt (* (/ (pow n (/ (- 1 k) 2)) (sqrt k)) (pow (* PI 2) (/ (- 1 k) 2)))) * [enter]simplify: Simplifying (sqrt (* (pow n (/ (- 1 k) 2)) (/ (pow (* 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 (32 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 (* (/ (pow n (/ (- 1 k) 2)) (sqrt k)) (pow (* PI 2) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (sqrt (* (/ (pow n (/ (- 1 k) 2)) (sqrt k)) (pow (* PI 2) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 73 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow n (/ 1 2)) (pow (* PI 2) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (12 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 (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) * [exit]simplify: Simplified to (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) * [enter]simplify: Simplifying (* (pow n (/ k 2)) (sqrt k)) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * [exit]simplify: Simplified to (* (sqrt k) (pow n (/ k 2))) * [exit]simplify: Simplified to (* (sqrt k) (pow n (/ k 2))) * * * * [misc]progress: [ 74 / 123 ] simplifiying candidate # * * * * [misc]progress: [ 75 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow n (/ (- 1 k) 2)) (* (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (* (* (pow n (/ (- 1 k) 2)) (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (* (pow n (/ (- 1 k) 2)) (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 76 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow n (/ (- 1 k) 2)) (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (* (pow n (/ (- 1 k) 2)) (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (pow n (/ (- 1 k) 2)) (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 77 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow n (/ (- 1 k) 2)) (/ (pow PI (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (61 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (/ (* (pow PI (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (* (pow PI (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * * * [misc]progress: [ 78 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow n (/ (- 1 k) 2)) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * * [misc]simplify: iters left: 2 (36 enodes) * * [misc]simplify: iters left: 1 (37 enodes) * [exit]simplify: Simplified to (/ (pow n (/ (- 1 k) 2)) (/ (sqrt (sqrt k)) (pow PI (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (pow n (/ (- 1 k) 2)) (/ (sqrt (sqrt k)) (pow PI (/ (- 1 k) 2)))) * * * * [misc]progress: [ 79 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow n (/ (- 1 k) 2)) (/ (pow PI (/ (- 1 k) 2)) 1)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * * [misc]simplify: iters left: 2 (43 enodes) * * [misc]simplify: iters left: 1 (49 enodes) * [exit]simplify: Simplified to (* (pow PI (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) * [exit]simplify: Simplified to (* (pow PI (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) * * * * [misc]progress: [ 80 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow n (/ (- 1 k) 2)) (/ (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (150 enodes) * * [misc]simplify: iters left: 1 (176 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (/ (- 1 k) 2))) (cbrt (pow (* PI 2) (/ (- 1 k) 2))))) * [exit]simplify: Simplified to (/ (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (/ (- 1 k) 2))) (cbrt (pow (* PI 2) (/ (- 1 k) 2))))) * * * * [misc]progress: [ 81 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow n (/ (- 1 k) 2)) (/ (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (76 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))))) * [exit]simplify: Simplified to (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 82 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow n (/ (- 1 k) 2)) (/ (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))) 1)) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (153 enodes) * * [misc]simplify: iters left: 1 (297 enodes) * [exit]simplify: Simplified to (* (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 83 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow n (/ (- 1 k) 2)) (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (56 enodes) * * [misc]simplify: iters left: 2 (64 enodes) * * [misc]simplify: iters left: 1 (72 enodes) * [exit]simplify: Simplified to (* (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* PI 2) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* PI 2) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 84 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow n (/ (- 1 k) 2)) (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (33 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 (pow (* PI 2) (/ (- 1 k) 2))) (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))) * [exit]simplify: Simplified to (* (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))) * * * * [misc]progress: [ 85 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow n (/ (- 1 k) 2)) (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) 1)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (46 enodes) * * [misc]simplify: iters left: 1 (52 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))) * [exit]simplify: Simplified to (* (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))) * * * * [misc]progress: [ 86 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow n (/ (- 1 k) 2)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (105 enodes) * * [misc]simplify: iters left: 1 (129 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)))) * * * * [misc]progress: [ 87 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow n (/ (- 1 k) 2)) (/ 1 (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * * [misc]simplify: iters left: 2 (54 enodes) * * [misc]simplify: iters left: 1 (55 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))) * * * * [misc]progress: [ 88 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow n (/ (- 1 k) 2)) (/ 1 1)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * * * * [misc]progress: [ 89 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow n (/ (- 1 k) 2)) 1) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * * * * [misc]progress: [ 90 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow n (/ (- 1 k) 2)) (pow (* PI 2) (/ (- 1 k) 2))) * * [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)) (pow (* PI 2) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (* (pow n (/ (- 1 k) 2)) (pow (* PI 2) (/ (- 1 k) 2))) * * * * [misc]progress: [ 91 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (pow n (/ (- 1 k) 2))) (/ (pow (* 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 (32 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 (/ (cbrt (pow n (/ (- 1 k) 2))) (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (cbrt (pow n (/ (- 1 k) 2))) (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 92 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow n (/ (- 1 k) 2))) (/ (pow (* 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 (32 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 (pow n (/ (- 1 k) 2))) (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (sqrt (pow n (/ (- 1 k) 2))) (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 93 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow n (/ (- 1 k) 2)) (/ (pow (* 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 (31 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (37 enodes) * * [misc]simplify: iters left: 1 (38 enodes) * [exit]simplify: Simplified to (/ (pow (* PI 2) (/ (- 1 k) 2)) (/ (sqrt k) (pow n (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (pow (* PI 2) (/ (- 1 k) 2)) (/ (sqrt k) (pow n (/ (- 1 k) 2)))) * * * * [misc]progress: [ 94 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow n (/ (- 1 k) 2)) (pow (* PI 2) (/ (- 1 k) 2))) * * [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)) (pow (* PI 2) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (* (pow n (/ (- 1 k) 2)) (pow (* PI 2) (/ (- 1 k) 2))) * * * * [misc]progress: [ 95 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow n (/ 1 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (37 enodes) * * [misc]simplify: iters left: 1 (38 enodes) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (/ (sqrt k) (pow n (/ 1 2)))) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (/ (sqrt k) (pow n (/ 1 2)))) * * * * [misc]progress: [ 96 / 123 ] simplifiying candidate # * * * * [misc]progress: [ 97 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * [exit]simplify: Simplified to (expm1 (pow n (/ (- 1 k) 2))) * [exit]simplify: Simplified to (expm1 (pow n (/ (- 1 k) 2))) * * * * [misc]progress: [ 98 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * [exit]simplify: Simplified to (log1p (pow n (/ (- 1 k) 2))) * [exit]simplify: Simplified to (log1p (pow n (/ (- 1 k) 2))) * * * * [misc]progress: [ 99 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log n) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (73 enodes) * * [misc]simplify: iters left: 2 (161 enodes) * * [misc]simplify: iters left: 1 (345 enodes) * [exit]simplify: Simplified to (* (/ (log n) 2) (- 1 k)) * [exit]simplify: Simplified to (* (/ (log n) 2) (- 1 k)) * * * * [misc]progress: [ 100 / 123 ] 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 n (/ k 2)) * * [misc]simplify: iters left: 3 (5 enodes) * [exit]simplify: Simplified to (pow n (/ k 2)) * [exit]simplify: Simplified to (pow n (/ k 2)) * * * * [misc]progress: [ 101 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (pow n (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (pow n (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (pow n (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * * * [misc]progress: [ 102 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (pow n (sqrt (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * [exit]simplify: Simplified to (pow n (sqrt (/ (- 1 k) 2))) * [exit]simplify: Simplified to (pow n (sqrt (/ (- 1 k) 2))) * * * * [misc]progress: [ 103 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (pow n 1) * * [misc]simplify: iters left: 1 (3 enodes) * [exit]simplify: Simplified to n * [exit]simplify: Simplified to n * * * * [misc]progress: [ 104 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (pow n (- 1 k)) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (9 enodes) * * [misc]simplify: iters left: 1 (10 enodes) * [exit]simplify: Simplified to (pow n (- 1 k)) * [exit]simplify: Simplified to (pow n (- 1 k)) * * * * [misc]progress: [ 105 / 123 ] simplifiying candidate # * * * * [misc]progress: [ 106 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (log (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (58 enodes) * * [misc]simplify: iters left: 1 (128 enodes) * [exit]simplify: Simplified to (/ (* (- 1 k) (log n)) 2) * [exit]simplify: Simplified to (/ (* (- 1 k) (log n)) 2) * * * * [misc]progress: [ 107 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * [exit]simplify: Simplified to (exp (pow n (/ (- 1 k) 2))) * [exit]simplify: Simplified to (exp (pow n (/ (- 1 k) 2))) * * * * [misc]progress: [ 108 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (pow n (/ (- 1 k) 2))) (cbrt (pow n (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (* (cbrt (pow n (/ (- 1 k) 2))) (cbrt (pow n (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (cbrt (pow n (/ (- 1 k) 2))) (cbrt (pow n (/ (- 1 k) 2)))) * [enter]simplify: Simplifying (cbrt (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * [exit]simplify: Simplified to (cbrt (pow n (/ (- 1 k) 2))) * [exit]simplify: Simplified to (cbrt (pow n (/ (- 1 k) 2))) * * * * [misc]progress: [ 109 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (pow n (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (pow (pow n (/ (- 1 k) 2)) 3) * [exit]simplify: Simplified to (pow (pow n (/ (- 1 k) 2)) 3) * * * * [misc]progress: [ 110 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * [exit]simplify: Simplified to (sqrt (pow n (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow n (/ (- 1 k) 2))) * [enter]simplify: Simplifying (sqrt (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * [exit]simplify: Simplified to (sqrt (pow n (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow n (/ (- 1 k) 2))) * * * * [misc]progress: [ 111 / 123 ] simplifiying candidate # * * * * [misc]progress: [ 112 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow n (/ (- 1 k) 2)) (/ (- (+ (pow (* 2 PI) 1/2) (* 1/8 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (* (pow k 2) (sqrt 2)))))) (* 1/2 (* (sqrt PI) (* (log (* 2 PI)) (* k (sqrt 2)))))) (sqrt k))) * * [misc]simplify: iters left: 6 (30 enodes) * * [misc]simplify: iters left: 5 (75 enodes) * * [misc]simplify: iters left: 4 (227 enodes) * [exit]simplify: Simplified to (* (/ (pow n (/ (- 1 k) 2)) (sqrt k)) (fma (* (* 1/8 (sqrt PI)) (* (log (* PI 2)) (log (* PI 2)))) (* (sqrt 2) (* k k)) (- (sqrt (* PI 2)) (* (log (* PI 2)) (* (sqrt PI) (* (sqrt 2) (* k 1/2))))))) * * * * [misc]progress: [ 113 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow n (/ (- 1 k) 2)) (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (167 enodes) * [exit]simplify: Simplified to (/ (pow (* PI 2) (- 1/2 (* 1/2 k))) (/ (sqrt k) (pow n (/ (- 1 k) 2)))) * * * * [misc]progress: [ 114 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow n (/ (- 1 k) 2)) (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (167 enodes) * [exit]simplify: Simplified to (/ (pow (* PI 2) (- 1/2 (* 1/2 k))) (/ (sqrt k) (pow n (/ (- 1 k) 2)))) * * * * [misc]progress: [ 115 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow n (/ (- 1 k) 2)) (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (+ (* +nan.0 (* (sqrt PI) (* k (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (* k (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt PI) (/ (sqrt 2) k))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (* k (sqrt 2))))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2)))))))))))))))) * * * * [misc]progress: [ 116 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow n (/ (- 1 k) 2)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) k)))))))) * * * * [misc]progress: [ 117 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow n (/ (- 1 k) 2)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) k)))))))) * * * * [misc]progress: [ 118 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) (* k (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log (* 2 PI)) 2) (* (pow k 2) (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow k 2) (* (log n) (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (* (pow k 2) (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (* k (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* k (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow k 2) (* (pow (log n) 2) (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow k 2) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (* (log (* 2 PI)) (* (pow k 2) (log n)))))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))))))))))))))))))) * * * * [misc]progress: [ 119 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* -1/2 (* (- 1 k) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* -1/2 (* (- 1 k) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* -1/2 (* (- 1 k) (log (/ 1 n)))))) (pow k 3)))))))) * * * * [misc]progress: [ 120 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n))))))) k)) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n))))))) (pow k 2))) (- (* +nan.0 (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n))))))))))))) * * * * [misc]progress: [ 121 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (- (+ (* 1/8 (* (sqrt n) (* (pow (log n) 2) (pow k 2)))) (pow n 1/2)) (* 1/2 (* (sqrt n) (* (log n) k)))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (60 enodes) * * [misc]simplify: iters left: 4 (159 enodes) * [exit]simplify: Simplified to (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (fma (- 1/2) (* (* (sqrt n) (log n)) k) (fma 1/8 (* (* (sqrt n) (log n)) (* (log n) (* k k))) (sqrt n)))) * * * * [misc]progress: [ 122 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * [exit]simplify: Simplified to (/ (pow (/ 1 n) (- -1/2 (* -1/2 k))) (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 123 / 123 ] simplifiying candidate # * [enter]simplify: Simplifying (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (232 enodes) * [exit]simplify: Simplified to (* (/ (pow (exp (log n)) (- 1/2 (* 1/2 k))) (sqrt k)) (pow (* PI 2) (/ (- 1 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) * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 2 1 1) * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 1 1 1) * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 2 1 1 1) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 4 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (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)) (sqrt k))) in k * [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]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ (* +nan.0 (sqrt (* n (* 2 PI)))) (* 2 (sqrt 0))) into (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))) * [misc]taylor: Taking taylor expansion of (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) in k * [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]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ (* +nan.0 (sqrt (* n (* 2 PI)))) (* 2 (sqrt 0))) into (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (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)) (sqrt k))) in 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]backup-simplify: Simplify (sqrt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))) into (* (pow (/ 1 k) 1/4) (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 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) (/ 0 (sqrt k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* (sqrt (/ 1 k)) (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 (/ (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]backup-simplify: Simplify (sqrt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))) into (* (pow (/ 1 k) 1/4) (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 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) (/ 0 (sqrt k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* (sqrt (/ 1 k)) (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))) (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)) (sqrt k))) in 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]backup-simplify: Simplify (sqrt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))) into (* (pow (/ 1 k) 1/4) (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 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) (/ 0 (sqrt k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* (sqrt (/ 1 k)) (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 (/ (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]backup-simplify: Simplify (sqrt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))) into (* (pow (/ 1 k) 1/4) (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 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) (/ 0 (sqrt k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (* (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))) (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))))) 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 (+ (* (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))) 0) (* 0 (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [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 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]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))))) 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) 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]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))) 0) (+ (* 0 0) (* 0 (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))))))) 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 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]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))))) 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) 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]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))))))) 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 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 (- 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)) (* 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 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 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 (pow 0 2) (+ (* 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))) (* 0 (/ 0 (sqrt k))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))))) 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 (- 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)) (* 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 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 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 (pow 0 2) (+ (* 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))) (* 0 (/ 0 (sqrt k))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))))))))) 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 (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k)))) (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 (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k)))) (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)) (sqrt (/ 1 k)))) in k * [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]backup-simplify: Simplify (sqrt (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) into (* (sqrt +nan.0) (sqrt (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) * [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 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (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))))))) (* 2 (sqrt (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))))) into (* +nan.0 (* (/ 1 (sqrt +nan.0)) (sqrt (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))))) * [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 (/ (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]backup-simplify: Simplify (sqrt (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) into (* (sqrt +nan.0) (sqrt (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) * [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 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (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))))))) (* 2 (sqrt (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))))) into (* +nan.0 (* (/ 1 (sqrt +nan.0)) (sqrt (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))))) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k)))) (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)) (sqrt (/ 1 k)))) in 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]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]backup-simplify: Simplify (sqrt (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))) into (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)) * [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]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))))) 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 (/ (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]backup-simplify: Simplify (sqrt (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))) into (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)) * [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]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))))) into 0 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k)))) (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)) (sqrt (/ 1 k)))) in 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]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]backup-simplify: Simplify (sqrt (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))) into (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)) * [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]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))))) 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 (/ (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]backup-simplify: Simplify (sqrt (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))) into (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)) * [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]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))))) into 0 * [misc]backup-simplify: Simplify (* (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)) (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4))) 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 (+ (* (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)) 0) (* 0 (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)))) 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]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)))) 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]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]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)) 0) (+ (* 0 0) (* 0 (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4))))) 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]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)))) 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]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]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)))))) 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 (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k))))) (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 (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k))))) (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)) (sqrt (/ 1 (- k))))) in k * [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]backup-simplify: Simplify (sqrt (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) into (* (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) (sqrt +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 (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (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)))))))) (* 2 (sqrt (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))))) into (* +nan.0 (* (/ 1 (sqrt +nan.0)) (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))))) * [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 (/ (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]backup-simplify: Simplify (sqrt (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) into (* (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) (sqrt +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 (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (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)))))))) (* 2 (sqrt (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))))) into (* +nan.0 (* (/ 1 (sqrt +nan.0)) (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))))) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k))))) (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)) (sqrt (/ 1 (- k))))) in 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]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))))) (sqrt (/ -1 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 (- 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]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))))) 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 (/ (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]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))))) (sqrt (/ -1 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 (- 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]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k))))) (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)) (sqrt (/ 1 (- k))))) in 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]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))))) (sqrt (/ -1 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 (- 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]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))))) 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 (/ (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]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))))) (sqrt (/ -1 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 (- 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]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))))) into 0 * [misc]backup-simplify: Simplify (* (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))) (sqrt (/ (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 (+ (* (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))) 0) (* 0 (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (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]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))))) 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]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]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))) 0) (+ (* 0 0) (* 0 (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (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: [ 2 / 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: [ 3 / 4 ] generating series at (2 1 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: [ 4 / 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: simplifying candidates * * * * [misc]progress: [ 1 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (* (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 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (expm1 (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (expm1 (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 2 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (* (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 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (log1p (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (log1p (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 3 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (+ 1/2 1/2) * * [misc]simplify: iters left: 2 (2 enodes) * [exit]simplify: Simplified to (+ 1/2 1/2) * [exit]simplify: Simplified to (+ 1/2 1/2) * * * * [misc]progress: [ 4 / 120 ] 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 1) * [exit]simplify: Simplified to (+ 1 1) * * * * [misc]progress: [ 5 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * [exit]simplify: Simplified to (/ (* (pow (* PI (* n 2)) (/ (- 1 k) 2)) (pow (* PI (* n 2)) (/ (- 1 k) 2))) k) * [exit]simplify: Simplified to (/ (* (pow (* PI (* n 2)) (/ (- 1 k) 2)) (pow (* PI (* n 2)) (/ (- 1 k) 2))) k) * * * * [misc]progress: [ 6 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (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 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 7 / 120 ] simplifiying candidate # * * * * [misc]progress: [ 8 / 120 ] 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 1) * [exit]simplify: Simplified to (+ 1 1) * * * * [misc]progress: [ 9 / 120 ] simplifiying candidate # * * * * [misc]progress: [ 10 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (log (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (+ (log (sqrt (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)))) (log (sqrt (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))))) * [exit]simplify: Simplified to (+ (log (sqrt (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)))) (log (sqrt (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))))) * * * * [misc]progress: [ 11 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* (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 (15 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * * [misc]simplify: iters left: 2 (65 enodes) * * [misc]simplify: iters left: 1 (132 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: [ 12 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* (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 (15 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (exp (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (exp (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 13 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (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)))) (* (* (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 (16 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (162 enodes) * * [misc]simplify: iters left: 1 (268 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: [ 14 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))) (cbrt (* (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 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* 2 (* PI n)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* 2 (* PI n)) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* 2 (* PI n)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* 2 (* PI n)) (/ (- 1 k) 2)) (sqrt k)))) * [enter]simplify: Simplifying (cbrt (* (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 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (cbrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (cbrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 15 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (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))) (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 (16 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (117 enodes) * * [misc]simplify: iters left: 2 (178 enodes) * * [misc]simplify: iters left: 1 (301 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: [ 16 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * [exit]simplify: Simplified to (/ (* (pow (* PI (* n 2)) (/ (- 1 k) 2)) (pow (* PI (* n 2)) (/ (- 1 k) 2))) k) * [exit]simplify: Simplified to (/ (* (pow (* PI (* n 2)) (/ (- 1 k) 2)) (pow (* PI (* n 2)) (/ (- 1 k) 2))) k) * * * * [misc]progress: [ 17 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (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 (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 (* 2 (* PI n)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (pow (* 2 (* PI n)) (/ (- 1 k) 2)) (sqrt k))) * [enter]simplify: Simplifying (sqrt (* (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 (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 (* 2 (* PI n)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (pow (* 2 (* PI n)) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 18 / 120 ] simplifiying candidate # * * * * [misc]progress: [ 19 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (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 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (pow (* PI (* n 2)) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (* PI (* n 2)) (/ (- 1 k) 2)) * [enter]simplify: Simplifying (* (sqrt (sqrt k)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 4 (4 enodes) * [exit]simplify: Simplified to (sqrt k) * [exit]simplify: Simplified to (sqrt k) * * * * [misc]progress: [ 20 / 120 ] simplifiying candidate # * * * * [misc]progress: [ 21 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (* (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 (16 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))) (* (cbrt (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))))) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))) (* (cbrt (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))))) * * * * [misc]progress: [ 22 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (* (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 (17 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (* (fabs (cbrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (fabs (cbrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 23 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (sqrt (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 24 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (sqrt (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 25 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))))) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 26 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * [exit]simplify: Simplified to (* (sqrt (pow n (/ (- 1 k) 2))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (sqrt (pow n (/ (- 1 k) 2))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 27 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (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 (20 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * [exit]simplify: Simplified to (* (fabs (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (fabs (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 28 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (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 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (* (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (sqrt (/ (* (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 29 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) 1))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (56 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))) (fabs (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))))) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))) (fabs (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))))) * * * * [misc]progress: [ 30 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (sqrt (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 31 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (sqrt (sqrt k))))) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (sqrt (sqrt k))))) * * * * [misc]progress: [ 32 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) 1))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (sqrt (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 33 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))))) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))))) * * * * [misc]progress: [ 34 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 35 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ 1 1))) * * [misc]simplify: iters left: 6 (16 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 (* 2 (* PI n)) (/ (- 1 k) 2)) (sqrt k))) (sqrt 1)) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* 2 (* PI n)) (/ (- 1 k) 2)) (sqrt k))) (sqrt 1)) * * * * [misc]progress: [ 36 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt 1)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (* (sqrt 1) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (sqrt 1) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 37 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 38 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (sqrt (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 39 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) 1) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 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: [ 40 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (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 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (cbrt (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 41 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (/ (pow (* 2 (* PI n)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* 2 (* PI n)) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (sqrt (cbrt (/ (pow (* 2 (* PI n)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* 2 (* PI n)) (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 42 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (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 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (sqrt (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 43 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 44 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 45 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 46 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (sqrt (/ (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 47 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (sqrt (/ (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 48 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt k)))) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt k)))) * * * * [misc]progress: [ 49 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (sqrt (/ (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 50 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (sqrt (/ (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 51 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (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 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt k)))) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt k)))) * * * * [misc]progress: [ 52 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (cbrt (sqrt k))))) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (cbrt (sqrt k))))) * * * * [misc]progress: [ 53 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt (sqrt k))))) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 54 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (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 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 55 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (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 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 56 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ 1 (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (16 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)) (sqrt k))) (sqrt (/ 1 (sqrt k)))) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ 1 (sqrt k)))) * * * * [misc]progress: [ 57 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (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 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (sqrt (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 58 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (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 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 59 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 60 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 61 / 120 ] simplifiying candidate # * * * * [misc]progress: [ 62 / 120 ] 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: [ 63 / 120 ] 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: [ 64 / 120 ] 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: [ 65 / 120 ] 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: [ 66 / 120 ] 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: [ 67 / 120 ] 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: [ 68 / 120 ] 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: [ 69 / 120 ] 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: [ 70 / 120 ] 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: [ 71 / 120 ] 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: [ 72 / 120 ] 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: [ 73 / 120 ] simplifiying candidate # * * * * [misc]progress: [ 74 / 120 ] 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: [ 75 / 120 ] 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: [ 76 / 120 ] 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: [ 77 / 120 ] 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: [ 78 / 120 ] 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: [ 79 / 120 ] simplifiying candidate # * * * * [misc]progress: [ 80 / 120 ] 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: [ 81 / 120 ] 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: [ 82 / 120 ] 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: [ 83 / 120 ] 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: [ 84 / 120 ] 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: [ 85 / 120 ] 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: [ 86 / 120 ] 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: [ 87 / 120 ] 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: [ 88 / 120 ] 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: [ 89 / 120 ] 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: [ 90 / 120 ] 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: [ 91 / 120 ] simplifiying candidate # * * * * [misc]progress: [ 92 / 120 ] 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: [ 93 / 120 ] 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: [ 94 / 120 ] 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: [ 95 / 120 ] 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: [ 96 / 120 ] 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: [ 97 / 120 ] simplifiying candidate # * * * * [misc]progress: [ 98 / 120 ] 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: [ 99 / 120 ] 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: [ 100 / 120 ] simplifiying candidate # * * * * [misc]progress: [ 101 / 120 ] 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: [ 102 / 120 ] 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: [ 103 / 120 ] 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: [ 104 / 120 ] 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: [ 105 / 120 ] 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: [ 106 / 120 ] simplifiying candidate # * * * * [misc]progress: [ 107 / 120 ] 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: [ 108 / 120 ] simplifiying candidate # * * * * [misc]progress: [ 109 / 120 ] 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: [ 110 / 120 ] 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: [ 111 / 120 ] 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: [ 112 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (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 (49 enodes) * * [misc]simplify: iters left: 5 (133 enodes) * * [misc]simplify: iters left: 4 (406 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (+ (* (* (exp (fma (log (* 2 PI)) 1/2 (* 1/2 (log n)))) (* (* k k) 1/8)) (+ (* (log n) (log n)) (* (log (* 2 PI)) (log (* 2 PI))))) (- (fma (* (* (* k k) (log (* 2 PI))) (* (log n) 1/4)) (exp (fma (log (* 2 PI)) 1/2 (* 1/2 (log n)))) (exp (fma (log (* 2 PI)) 1/2 (* 1/2 (log n))))) (* (exp (fma (log (* 2 PI)) 1/2 (* 1/2 (log n)))) (* (fma (log (* 2 PI)) k (* (log n) k)) 1/2)))) (sqrt k)))) * * * * [misc]progress: [ 113 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (sqrt k)))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (100 enodes) * * [misc]simplify: iters left: 3 (292 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) (sqrt k)))) * * * * [misc]progress: [ 114 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt k)))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (54 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (305 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) (sqrt k)))) * * * * [misc]progress: [ 115 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (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))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (49 enodes) * * [misc]simplify: iters left: 5 (133 enodes) * * [misc]simplify: iters left: 4 (406 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (+ (* (* (exp (fma (log (* PI 2)) 1/2 (* 1/2 (log n)))) (* k (* k 1/8))) (+ (* (log n) (log n)) (* (log (* PI 2)) (log (* PI 2))))) (- (fma (exp (fma (log (* PI 2)) 1/2 (* 1/2 (log n)))) (* (* (log (* PI 2)) (* (log n) k)) (* k 1/4)) (exp (fma (log (* PI 2)) 1/2 (* 1/2 (log n))))) (* (exp (fma (log (* PI 2)) 1/2 (* 1/2 (log n)))) (* 1/2 (fma k (log (* PI 2)) (* (log n) k)))))) (sqrt k))) (sqrt (/ (pow (* 2 (* PI n)) (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 116 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (100 enodes) * * [misc]simplify: iters left: 3 (297 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (* (pow n (- 1/2 (* 1/2 k))) (pow (* PI 2) (- 1/2 (* 1/2 k)))) (sqrt k)))) * * * * [misc]progress: [ 117 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (54 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (305 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)))) (sqrt k)))) * * * * [misc]progress: [ 118 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * [exit]simplify: Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 119 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * [exit]simplify: Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 120 / 120 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * [exit]simplify: Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)) * * * [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 (cbrt (/ (* (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (* (pow (* (* PI n) 2) (/ k 2)) (/ (* (sqrt k) k) (pow (* (* PI n) 2) (/ 1 2)))))) +nan.0)) , with alts (#) * [enter]simplify: Simplifying (pow (* n (* PI 2)) (/ 1 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (12 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 (10 enodes) * [exit]simplify: Simplified to (pow (* (* 2 PI) n) (/ k 2)) * [exit]simplify: Simplified to (pow (* (* 2 PI) n) (/ k 2)) * * * * [misc]points: Sampling 8000 additional inputs, on iter 0 have 0 / 8000 * * * * [misc]points: Computing exacts on every 500 of 8000 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 8000 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 8000 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 62 of 8000 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 8000 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 8000 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 8000 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 8000 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 8000 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 6496 additional inputs, on iter 1 have 1504 / 8000 * * * * [misc]points: Computing exacts on every 406 of 6496 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 203 of 6496 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 6496 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 6496 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 6496 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 6496 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 6496 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 6496 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 6496 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 5226 additional inputs, on iter 2 have 2774 / 8000 * * * * [misc]points: Computing exacts on every 326 of 5226 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 163 of 5226 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 5226 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 40 of 5226 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 5226 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 5226 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 5226 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 5226 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 5226 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 4254 additional inputs, on iter 3 have 3746 / 8000 * * * * [misc]points: Computing exacts on every 265 of 4254 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 132 of 4254 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 66 of 4254 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 4254 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 4254 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 4254 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 4254 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 4254 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 4254 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 3438 additional inputs, on iter 4 have 4562 / 8000 * * * * [misc]points: Computing exacts on every 214 of 3438 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 107 of 3438 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 3438 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 26 of 3438 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 3438 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 3438 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 3438 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 3438 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 2786 additional inputs, on iter 5 have 5214 / 8000 * * * * [misc]points: Computing exacts on every 174 of 2786 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 87 of 2786 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 2786 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 21 of 2786 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 2786 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 2786 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 2786 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 2786 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 2263 additional inputs, on iter 6 have 5737 / 8000 * * * * [misc]points: Computing exacts on every 141 of 2263 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 2263 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 2263 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 17 of 2263 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 2263 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 2263 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 2263 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 2263 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 1821 additional inputs, on iter 7 have 6179 / 8000 * * * * [misc]points: Computing exacts on every 113 of 1821 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 1821 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 1821 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 1821 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 1821 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 1821 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 1821 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 1483 additional inputs, on iter 8 have 6517 / 8000 * * * * [misc]points: Computing exacts on every 92 of 1483 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 46 of 1483 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 23 of 1483 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 1483 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 1483 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 1483 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 1483 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 1207 additional inputs, on iter 9 have 6793 / 8000 * * * * [misc]points: Computing exacts on every 75 of 1207 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 37 of 1207 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 1207 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 1207 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 1207 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 1207 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 1207 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 994 additional inputs, on iter 10 have 7006 / 8000 * * * * [misc]points: Computing exacts on every 62 of 994 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 994 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 994 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 994 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 994 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 994 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 796 additional inputs, on iter 11 have 7204 / 8000 * * * * [misc]points: Computing exacts on every 49 of 796 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 796 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 796 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 796 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 796 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 796 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 641 additional inputs, on iter 12 have 7359 / 8000 * * * * [misc]points: Computing exacts on every 40 of 641 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 641 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 641 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 641 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 641 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 641 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 522 additional inputs, on iter 13 have 7478 / 8000 * * * * [misc]points: Computing exacts on every 32 of 522 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 522 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 522 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 522 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 522 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 522 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 437 additional inputs, on iter 14 have 7563 / 8000 * * * * [misc]points: Computing exacts on every 27 of 437 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 437 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 437 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 437 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 437 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 368 additional inputs, on iter 15 have 7632 / 8000 * * * * [misc]points: Computing exacts on every 23 of 368 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 368 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 368 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 368 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 368 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 291 additional inputs, on iter 16 have 7709 / 8000 * * * * [misc]points: Computing exacts on every 18 of 291 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 291 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 291 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 291 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 291 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 232 additional inputs, on iter 17 have 7768 / 8000 * * * * [misc]points: Computing exacts on every 14 of 232 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 232 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 232 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 232 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 192 additional inputs, on iter 18 have 7808 / 8000 * * * * [misc]points: Computing exacts on every 12 of 192 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 192 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 192 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 192 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 153 additional inputs, on iter 19 have 7847 / 8000 * * * * [misc]points: Computing exacts on every 9 of 153 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 153 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 153 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 153 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 128 additional inputs, on iter 20 have 7872 / 8000 * * * * [misc]points: Computing exacts on every 8 of 128 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 128 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 128 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 128 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 107 additional inputs, on iter 21 have 7893 / 8000 * * * * [misc]points: Computing exacts on every 6 of 107 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 107 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 107 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 81 additional inputs, on iter 22 have 7919 / 8000 * * * * [misc]points: Computing exacts on every 5 of 81 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 81 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 81 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 69 additional inputs, on iter 23 have 7931 / 8000 * * * * [misc]points: Computing exacts on every 4 of 69 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 69 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 69 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 50 additional inputs, on iter 24 have 7950 / 8000 * * * * [misc]points: Computing exacts on every 3 of 50 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 50 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 44 additional inputs, on iter 25 have 7956 / 8000 * * * * [misc]points: Computing exacts on every 2 of 44 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 44 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 36 additional inputs, on iter 26 have 7964 / 8000 * * * * [misc]points: Computing exacts on every 2 of 36 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 36 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 27 have 7973 / 8000 * * * * [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 23 additional inputs, on iter 28 have 7977 / 8000 * * * * [misc]points: Computing exacts for 23 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 21 additional inputs, on iter 29 have 7979 / 8000 * * * * [misc]points: Computing exacts for 21 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 15 additional inputs, on iter 30 have 7985 / 8000 * * * * [misc]points: Computing exacts for 15 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 31 have 7986 / 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 9 additional inputs, on iter 32 have 7991 / 8000 * * * * [misc]points: Computing exacts for 9 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 4 additional inputs, on iter 33 have 7996 / 8000 * * * * [misc]points: Computing exacts for 4 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 4 additional inputs, on iter 34 have 7996 / 8000 * * * * [misc]points: Computing exacts for 4 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 4 additional inputs, on iter 35 have 7996 / 8000 * * * * [misc]points: Computing exacts for 4 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 4 additional inputs, on iter 36 have 7996 / 8000 * * * * [misc]points: Computing exacts for 4 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 4 additional inputs, on iter 37 have 7998 / 8000 * * * * [misc]points: Computing exacts for 4 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 4 additional inputs, on iter 38 have 7999 / 8000 * * * * [misc]points: Computing exacts for 4 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 8001 points with exact outputs