53.935 * [progress]: [Phase 1 of 3] Setting up. 0.003 * * * [progress]: [1/2] Preparing points 0.263 * * * [progress]: [2/2] Setting up program. 0.269 * [progress]: [Phase 2 of 3] Improving. 0.269 * * * * [progress]: [ 1 / 1 ] simplifiying candidate # 0.270 * [simplify]: Simplifying: (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 0.270 * * [simplify]: iteration 0: 13 enodes 0.277 * * [simplify]: iteration 1: 31 enodes 0.288 * * [simplify]: iteration 2: 62 enodes 0.312 * * [simplify]: iteration 3: 124 enodes 0.387 * * [simplify]: iteration 4: 328 enodes 0.682 * * [simplify]: iteration 5: 970 enodes 1.076 * * [simplify]: iteration 6: 2026 enodes 1.528 * * [simplify]: iteration complete: 2026 enodes 1.528 * * [simplify]: Extracting #0: cost 1 inf + 0 1.528 * * [simplify]: Extracting #1: cost 86 inf + 0 1.530 * * [simplify]: Extracting #2: cost 311 inf + 1 1.533 * * [simplify]: Extracting #3: cost 435 inf + 46 1.537 * * [simplify]: Extracting #4: cost 405 inf + 4118 1.548 * * [simplify]: Extracting #5: cost 293 inf + 28237 1.579 * * [simplify]: Extracting #6: cost 140 inf + 129132 1.632 * * [simplify]: Extracting #7: cost 9 inf + 256512 1.677 * * [simplify]: Extracting #8: cost 0 inf + 265066 1.724 * * [simplify]: Extracting #9: cost 0 inf + 265063 1.777 * * [simplify]: Extracting #10: cost 0 inf + 264810 1.825 * [simplify]: Simplified to: (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)) 1.829 * * [progress]: iteration 1 / 4 1.829 * * * [progress]: picking best candidate 1.835 * * * * [pick]: Picked # 1.835 * * * [progress]: localizing error 1.870 * * * [progress]: generating rewritten candidates 1.870 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1) 1.903 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 1) 1.929 * * * * [progress]: [ 3 / 3 ] rewriting at (2) 1.973 * * * [progress]: generating series expansions 1.973 * * * * [progress]: [ 1 / 3 ] generating series at (2 1) 1.974 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1.974 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1.974 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1.974 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1.974 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1.974 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1.974 * [taylor]: Taking taylor expansion of 1/2 in k 1.974 * [backup-simplify]: Simplify 1/2 into 1/2 1.974 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 1.974 * [taylor]: Taking taylor expansion of 1/2 in k 1.974 * [backup-simplify]: Simplify 1/2 into 1/2 1.974 * [taylor]: Taking taylor expansion of k in k 1.974 * [backup-simplify]: Simplify 0 into 0 1.974 * [backup-simplify]: Simplify 1 into 1 1.974 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 1.974 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 1.974 * [taylor]: Taking taylor expansion of 2 in k 1.974 * [backup-simplify]: Simplify 2 into 2 1.974 * [taylor]: Taking taylor expansion of (* n PI) in k 1.974 * [taylor]: Taking taylor expansion of n in k 1.974 * [backup-simplify]: Simplify n into n 1.974 * [taylor]: Taking taylor expansion of PI in k 1.974 * [backup-simplify]: Simplify PI into PI 1.974 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.974 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1.975 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1.975 * [backup-simplify]: Simplify (* 1/2 0) into 0 1.975 * [backup-simplify]: Simplify (- 0) into 0 1.976 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 1.976 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1.976 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1.976 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1.976 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1.976 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1.976 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1.976 * [taylor]: Taking taylor expansion of 1/2 in n 1.976 * [backup-simplify]: Simplify 1/2 into 1/2 1.976 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 1.976 * [taylor]: Taking taylor expansion of 1/2 in n 1.976 * [backup-simplify]: Simplify 1/2 into 1/2 1.976 * [taylor]: Taking taylor expansion of k in n 1.976 * [backup-simplify]: Simplify k into k 1.976 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 1.976 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 1.976 * [taylor]: Taking taylor expansion of 2 in n 1.976 * [backup-simplify]: Simplify 2 into 2 1.976 * [taylor]: Taking taylor expansion of (* n PI) in n 1.976 * [taylor]: Taking taylor expansion of n in n 1.976 * [backup-simplify]: Simplify 0 into 0 1.976 * [backup-simplify]: Simplify 1 into 1 1.976 * [taylor]: Taking taylor expansion of PI in n 1.976 * [backup-simplify]: Simplify PI into PI 1.976 * [backup-simplify]: Simplify (* 0 PI) into 0 1.977 * [backup-simplify]: Simplify (* 2 0) into 0 1.978 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.979 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1.979 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.979 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 1.979 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1.979 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1.980 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.981 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1.982 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 1.982 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1.982 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1.982 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1.982 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1.982 * [taylor]: Taking taylor expansion of 1/2 in n 1.982 * [backup-simplify]: Simplify 1/2 into 1/2 1.982 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 1.982 * [taylor]: Taking taylor expansion of 1/2 in n 1.982 * [backup-simplify]: Simplify 1/2 into 1/2 1.982 * [taylor]: Taking taylor expansion of k in n 1.982 * [backup-simplify]: Simplify k into k 1.982 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 1.982 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 1.982 * [taylor]: Taking taylor expansion of 2 in n 1.982 * [backup-simplify]: Simplify 2 into 2 1.982 * [taylor]: Taking taylor expansion of (* n PI) in n 1.982 * [taylor]: Taking taylor expansion of n in n 1.982 * [backup-simplify]: Simplify 0 into 0 1.982 * [backup-simplify]: Simplify 1 into 1 1.983 * [taylor]: Taking taylor expansion of PI in n 1.983 * [backup-simplify]: Simplify PI into PI 1.983 * [backup-simplify]: Simplify (* 0 PI) into 0 1.983 * [backup-simplify]: Simplify (* 2 0) into 0 1.985 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.987 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1.988 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.988 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 1.988 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1.988 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1.990 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.991 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1.992 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 1.992 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1.992 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1.992 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1.992 * [taylor]: Taking taylor expansion of 1/2 in k 1.992 * [backup-simplify]: Simplify 1/2 into 1/2 1.992 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 1.992 * [taylor]: Taking taylor expansion of 1/2 in k 1.992 * [backup-simplify]: Simplify 1/2 into 1/2 1.992 * [taylor]: Taking taylor expansion of k in k 1.992 * [backup-simplify]: Simplify 0 into 0 1.992 * [backup-simplify]: Simplify 1 into 1 1.992 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1.993 * [taylor]: Taking taylor expansion of (log n) in k 1.993 * [taylor]: Taking taylor expansion of n in k 1.993 * [backup-simplify]: Simplify n into n 1.993 * [backup-simplify]: Simplify (log n) into (log n) 1.993 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 1.993 * [taylor]: Taking taylor expansion of (* 2 PI) in k 1.993 * [taylor]: Taking taylor expansion of 2 in k 1.993 * [backup-simplify]: Simplify 2 into 2 1.993 * [taylor]: Taking taylor expansion of PI in k 1.993 * [backup-simplify]: Simplify PI into PI 1.993 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 1.994 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.995 * [backup-simplify]: Simplify (* 1/2 0) into 0 1.995 * [backup-simplify]: Simplify (- 0) into 0 1.996 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 1.997 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.998 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1.999 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1.999 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 2.000 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.001 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 2.002 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.002 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 2.002 * [backup-simplify]: Simplify (- 0) into 0 2.002 * [backup-simplify]: Simplify (+ 0 0) into 0 2.003 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.004 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 2.005 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.005 * [taylor]: Taking taylor expansion of 0 in k 2.005 * [backup-simplify]: Simplify 0 into 0 2.005 * [backup-simplify]: Simplify 0 into 0 2.006 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.006 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.007 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.008 * [backup-simplify]: Simplify (+ 0 0) into 0 2.008 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 2.008 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.009 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.010 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2.011 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 2.013 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 2.014 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.015 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.017 * [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 2.017 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 2.017 * [backup-simplify]: Simplify (- 0) into 0 2.018 * [backup-simplify]: Simplify (+ 0 0) into 0 2.019 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.019 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 2.021 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.021 * [taylor]: Taking taylor expansion of 0 in k 2.021 * [backup-simplify]: Simplify 0 into 0 2.021 * [backup-simplify]: Simplify 0 into 0 2.021 * [backup-simplify]: Simplify 0 into 0 2.022 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.023 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.024 * [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 2.025 * [backup-simplify]: Simplify (+ 0 0) into 0 2.025 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 2.026 * [backup-simplify]: Simplify (- 0) into 0 2.026 * [backup-simplify]: Simplify (+ 0 0) into 0 2.028 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 2.032 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 2.036 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 2.047 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 2.048 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 2.048 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 2.048 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 2.048 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 2.048 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 2.048 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 2.048 * [taylor]: Taking taylor expansion of 1/2 in k 2.048 * [backup-simplify]: Simplify 1/2 into 1/2 2.048 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.048 * [taylor]: Taking taylor expansion of 1/2 in k 2.048 * [backup-simplify]: Simplify 1/2 into 1/2 2.048 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.048 * [taylor]: Taking taylor expansion of k in k 2.048 * [backup-simplify]: Simplify 0 into 0 2.048 * [backup-simplify]: Simplify 1 into 1 2.057 * [backup-simplify]: Simplify (/ 1 1) into 1 2.057 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 2.057 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 2.057 * [taylor]: Taking taylor expansion of 2 in k 2.057 * [backup-simplify]: Simplify 2 into 2 2.057 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.057 * [taylor]: Taking taylor expansion of PI in k 2.057 * [backup-simplify]: Simplify PI into PI 2.057 * [taylor]: Taking taylor expansion of n in k 2.057 * [backup-simplify]: Simplify n into n 2.057 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.057 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 2.057 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 2.058 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.058 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.059 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.059 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 2.059 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 2.059 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 2.059 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 2.059 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 2.059 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 2.059 * [taylor]: Taking taylor expansion of 1/2 in n 2.059 * [backup-simplify]: Simplify 1/2 into 1/2 2.059 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.060 * [taylor]: Taking taylor expansion of 1/2 in n 2.060 * [backup-simplify]: Simplify 1/2 into 1/2 2.060 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.060 * [taylor]: Taking taylor expansion of k in n 2.060 * [backup-simplify]: Simplify k into k 2.060 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.060 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 2.060 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.060 * [taylor]: Taking taylor expansion of 2 in n 2.060 * [backup-simplify]: Simplify 2 into 2 2.060 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.060 * [taylor]: Taking taylor expansion of PI in n 2.060 * [backup-simplify]: Simplify PI into PI 2.060 * [taylor]: Taking taylor expansion of n in n 2.060 * [backup-simplify]: Simplify 0 into 0 2.060 * [backup-simplify]: Simplify 1 into 1 2.060 * [backup-simplify]: Simplify (/ PI 1) into PI 2.061 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.062 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.062 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.062 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 2.062 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 2.064 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.065 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 2.066 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 2.066 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 2.066 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 2.066 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 2.066 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 2.066 * [taylor]: Taking taylor expansion of 1/2 in n 2.066 * [backup-simplify]: Simplify 1/2 into 1/2 2.067 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.067 * [taylor]: Taking taylor expansion of 1/2 in n 2.067 * [backup-simplify]: Simplify 1/2 into 1/2 2.067 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.067 * [taylor]: Taking taylor expansion of k in n 2.067 * [backup-simplify]: Simplify k into k 2.067 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.067 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 2.067 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.067 * [taylor]: Taking taylor expansion of 2 in n 2.067 * [backup-simplify]: Simplify 2 into 2 2.067 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.067 * [taylor]: Taking taylor expansion of PI in n 2.067 * [backup-simplify]: Simplify PI into PI 2.067 * [taylor]: Taking taylor expansion of n in n 2.067 * [backup-simplify]: Simplify 0 into 0 2.067 * [backup-simplify]: Simplify 1 into 1 2.067 * [backup-simplify]: Simplify (/ PI 1) into PI 2.068 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.069 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.069 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.069 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 2.069 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 2.071 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.072 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 2.073 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 2.073 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 2.073 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 2.073 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 2.073 * [taylor]: Taking taylor expansion of 1/2 in k 2.073 * [backup-simplify]: Simplify 1/2 into 1/2 2.073 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.073 * [taylor]: Taking taylor expansion of 1/2 in k 2.073 * [backup-simplify]: Simplify 1/2 into 1/2 2.073 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.073 * [taylor]: Taking taylor expansion of k in k 2.073 * [backup-simplify]: Simplify 0 into 0 2.073 * [backup-simplify]: Simplify 1 into 1 2.074 * [backup-simplify]: Simplify (/ 1 1) into 1 2.074 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 2.074 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 2.074 * [taylor]: Taking taylor expansion of (* 2 PI) in k 2.074 * [taylor]: Taking taylor expansion of 2 in k 2.074 * [backup-simplify]: Simplify 2 into 2 2.074 * [taylor]: Taking taylor expansion of PI in k 2.074 * [backup-simplify]: Simplify PI into PI 2.075 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.076 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.076 * [taylor]: Taking taylor expansion of (log n) in k 2.076 * [taylor]: Taking taylor expansion of n in k 2.076 * [backup-simplify]: Simplify n into n 2.076 * [backup-simplify]: Simplify (log n) into (log n) 2.076 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.077 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.077 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.077 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.078 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 2.079 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 2.081 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 2.082 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 2.082 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.083 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.084 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.084 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.084 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.085 * [backup-simplify]: Simplify (- 0) into 0 2.085 * [backup-simplify]: Simplify (+ 0 0) into 0 2.086 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.086 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 2.088 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.088 * [taylor]: Taking taylor expansion of 0 in k 2.088 * [backup-simplify]: Simplify 0 into 0 2.088 * [backup-simplify]: Simplify 0 into 0 2.088 * [backup-simplify]: Simplify 0 into 0 2.088 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.089 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.091 * [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 2.091 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.091 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.092 * [backup-simplify]: Simplify (- 0) into 0 2.092 * [backup-simplify]: Simplify (+ 0 0) into 0 2.093 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.094 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 2.095 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.095 * [taylor]: Taking taylor expansion of 0 in k 2.095 * [backup-simplify]: Simplify 0 into 0 2.095 * [backup-simplify]: Simplify 0 into 0 2.095 * [backup-simplify]: Simplify 0 into 0 2.095 * [backup-simplify]: Simplify 0 into 0 2.096 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.097 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.100 * [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 2.100 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.101 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 2.101 * [backup-simplify]: Simplify (- 0) into 0 2.101 * [backup-simplify]: Simplify (+ 0 0) into 0 2.102 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.104 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 2.105 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 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 2.105 * [taylor]: Taking taylor expansion of 0 in k 2.105 * [backup-simplify]: Simplify 0 into 0 2.105 * [backup-simplify]: Simplify 0 into 0 2.106 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 2.106 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 2.107 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 2.107 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 2.107 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 2.107 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 2.107 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.107 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.107 * [taylor]: Taking taylor expansion of 1/2 in k 2.107 * [backup-simplify]: Simplify 1/2 into 1/2 2.107 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.107 * [taylor]: Taking taylor expansion of k in k 2.107 * [backup-simplify]: Simplify 0 into 0 2.107 * [backup-simplify]: Simplify 1 into 1 2.107 * [backup-simplify]: Simplify (/ 1 1) into 1 2.107 * [taylor]: Taking taylor expansion of 1/2 in k 2.107 * [backup-simplify]: Simplify 1/2 into 1/2 2.107 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 2.107 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 2.107 * [taylor]: Taking taylor expansion of -2 in k 2.107 * [backup-simplify]: Simplify -2 into -2 2.107 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.107 * [taylor]: Taking taylor expansion of PI in k 2.107 * [backup-simplify]: Simplify PI into PI 2.107 * [taylor]: Taking taylor expansion of n in k 2.107 * [backup-simplify]: Simplify n into n 2.107 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.107 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 2.107 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 2.108 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.108 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.108 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 2.108 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 2.108 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.108 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.108 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.108 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.108 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.108 * [taylor]: Taking taylor expansion of 1/2 in n 2.108 * [backup-simplify]: Simplify 1/2 into 1/2 2.108 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.108 * [taylor]: Taking taylor expansion of k in n 2.108 * [backup-simplify]: Simplify k into k 2.108 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.108 * [taylor]: Taking taylor expansion of 1/2 in n 2.108 * [backup-simplify]: Simplify 1/2 into 1/2 2.108 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.108 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.108 * [taylor]: Taking taylor expansion of -2 in n 2.108 * [backup-simplify]: Simplify -2 into -2 2.108 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.108 * [taylor]: Taking taylor expansion of PI in n 2.108 * [backup-simplify]: Simplify PI into PI 2.108 * [taylor]: Taking taylor expansion of n in n 2.108 * [backup-simplify]: Simplify 0 into 0 2.108 * [backup-simplify]: Simplify 1 into 1 2.109 * [backup-simplify]: Simplify (/ PI 1) into PI 2.109 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.110 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.110 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.110 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.111 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.111 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 2.112 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 2.112 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.112 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.112 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.112 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.112 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.112 * [taylor]: Taking taylor expansion of 1/2 in n 2.112 * [backup-simplify]: Simplify 1/2 into 1/2 2.112 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.112 * [taylor]: Taking taylor expansion of k in n 2.112 * [backup-simplify]: Simplify k into k 2.112 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.112 * [taylor]: Taking taylor expansion of 1/2 in n 2.112 * [backup-simplify]: Simplify 1/2 into 1/2 2.112 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.112 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.112 * [taylor]: Taking taylor expansion of -2 in n 2.112 * [backup-simplify]: Simplify -2 into -2 2.112 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.112 * [taylor]: Taking taylor expansion of PI in n 2.112 * [backup-simplify]: Simplify PI into PI 2.112 * [taylor]: Taking taylor expansion of n in n 2.112 * [backup-simplify]: Simplify 0 into 0 2.112 * [backup-simplify]: Simplify 1 into 1 2.113 * [backup-simplify]: Simplify (/ PI 1) into PI 2.113 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.114 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.114 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.114 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.116 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.117 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 2.118 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 2.118 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 2.118 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 2.118 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.118 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.118 * [taylor]: Taking taylor expansion of 1/2 in k 2.118 * [backup-simplify]: Simplify 1/2 into 1/2 2.118 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.118 * [taylor]: Taking taylor expansion of k in k 2.118 * [backup-simplify]: Simplify 0 into 0 2.118 * [backup-simplify]: Simplify 1 into 1 2.119 * [backup-simplify]: Simplify (/ 1 1) into 1 2.119 * [taylor]: Taking taylor expansion of 1/2 in k 2.119 * [backup-simplify]: Simplify 1/2 into 1/2 2.119 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 2.119 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 2.119 * [taylor]: Taking taylor expansion of (* -2 PI) in k 2.119 * [taylor]: Taking taylor expansion of -2 in k 2.119 * [backup-simplify]: Simplify -2 into -2 2.119 * [taylor]: Taking taylor expansion of PI in k 2.119 * [backup-simplify]: Simplify PI into PI 2.120 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.121 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.121 * [taylor]: Taking taylor expansion of (log n) in k 2.121 * [taylor]: Taking taylor expansion of n in k 2.121 * [backup-simplify]: Simplify n into n 2.121 * [backup-simplify]: Simplify (log n) into (log n) 2.121 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.122 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.122 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.123 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 2.124 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 2.125 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 2.126 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 2.127 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.128 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 2.130 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 2.130 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.130 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.131 * [backup-simplify]: Simplify (+ 0 0) into 0 2.132 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.133 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 2.135 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.135 * [taylor]: Taking taylor expansion of 0 in k 2.136 * [backup-simplify]: Simplify 0 into 0 2.136 * [backup-simplify]: Simplify 0 into 0 2.136 * [backup-simplify]: Simplify 0 into 0 2.137 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.138 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 2.141 * [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 2.142 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.142 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.143 * [backup-simplify]: Simplify (+ 0 0) into 0 2.144 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.146 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 2.147 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.147 * [taylor]: Taking taylor expansion of 0 in k 2.147 * [backup-simplify]: Simplify 0 into 0 2.147 * [backup-simplify]: Simplify 0 into 0 2.147 * [backup-simplify]: Simplify 0 into 0 2.147 * [backup-simplify]: Simplify 0 into 0 2.148 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.149 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.152 * [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 2.152 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.153 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 2.153 * [backup-simplify]: Simplify (+ 0 0) into 0 2.154 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.156 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 2.157 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 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 2.158 * [taylor]: Taking taylor expansion of 0 in k 2.158 * [backup-simplify]: Simplify 0 into 0 2.158 * [backup-simplify]: Simplify 0 into 0 2.159 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 2.159 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 1) 2.159 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) 2.159 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 2.159 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.159 * [taylor]: Taking taylor expansion of 2 in n 2.159 * [backup-simplify]: Simplify 2 into 2 2.159 * [taylor]: Taking taylor expansion of (* n PI) in n 2.159 * [taylor]: Taking taylor expansion of n in n 2.159 * [backup-simplify]: Simplify 0 into 0 2.159 * [backup-simplify]: Simplify 1 into 1 2.159 * [taylor]: Taking taylor expansion of PI in n 2.159 * [backup-simplify]: Simplify PI into PI 2.159 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.159 * [taylor]: Taking taylor expansion of 2 in n 2.159 * [backup-simplify]: Simplify 2 into 2 2.159 * [taylor]: Taking taylor expansion of (* n PI) in n 2.159 * [taylor]: Taking taylor expansion of n in n 2.159 * [backup-simplify]: Simplify 0 into 0 2.159 * [backup-simplify]: Simplify 1 into 1 2.159 * [taylor]: Taking taylor expansion of PI in n 2.159 * [backup-simplify]: Simplify PI into PI 2.160 * [backup-simplify]: Simplify (* 0 PI) into 0 2.160 * [backup-simplify]: Simplify (* 2 0) into 0 2.160 * [backup-simplify]: Simplify 0 into 0 2.161 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.162 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 2.162 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.163 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.163 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 2.163 * [backup-simplify]: Simplify 0 into 0 2.164 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.167 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.167 * [backup-simplify]: Simplify 0 into 0 2.168 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.169 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.169 * [backup-simplify]: Simplify 0 into 0 2.170 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.170 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 2.170 * [backup-simplify]: Simplify 0 into 0 2.172 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.173 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 2.173 * [backup-simplify]: Simplify 0 into 0 2.174 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 2.176 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 2.176 * [backup-simplify]: Simplify 0 into 0 2.176 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 2.177 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) 2.177 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 2.177 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.177 * [taylor]: Taking taylor expansion of 2 in n 2.177 * [backup-simplify]: Simplify 2 into 2 2.177 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.177 * [taylor]: Taking taylor expansion of PI in n 2.177 * [backup-simplify]: Simplify PI into PI 2.177 * [taylor]: Taking taylor expansion of n in n 2.177 * [backup-simplify]: Simplify 0 into 0 2.177 * [backup-simplify]: Simplify 1 into 1 2.178 * [backup-simplify]: Simplify (/ PI 1) into PI 2.178 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.178 * [taylor]: Taking taylor expansion of 2 in n 2.178 * [backup-simplify]: Simplify 2 into 2 2.178 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.178 * [taylor]: Taking taylor expansion of PI in n 2.178 * [backup-simplify]: Simplify PI into PI 2.178 * [taylor]: Taking taylor expansion of n in n 2.178 * [backup-simplify]: Simplify 0 into 0 2.178 * [backup-simplify]: Simplify 1 into 1 2.178 * [backup-simplify]: Simplify (/ PI 1) into PI 2.179 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.179 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.180 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.181 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.181 * [backup-simplify]: Simplify 0 into 0 2.182 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.183 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.183 * [backup-simplify]: Simplify 0 into 0 2.184 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.186 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.186 * [backup-simplify]: Simplify 0 into 0 2.187 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.188 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.188 * [backup-simplify]: Simplify 0 into 0 2.189 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.191 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.191 * [backup-simplify]: Simplify 0 into 0 2.192 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.194 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.194 * [backup-simplify]: Simplify 0 into 0 2.195 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 2.195 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n)) 2.195 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 2.195 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.195 * [taylor]: Taking taylor expansion of -2 in n 2.195 * [backup-simplify]: Simplify -2 into -2 2.195 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.195 * [taylor]: Taking taylor expansion of PI in n 2.195 * [backup-simplify]: Simplify PI into PI 2.195 * [taylor]: Taking taylor expansion of n in n 2.195 * [backup-simplify]: Simplify 0 into 0 2.195 * [backup-simplify]: Simplify 1 into 1 2.196 * [backup-simplify]: Simplify (/ PI 1) into PI 2.196 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.196 * [taylor]: Taking taylor expansion of -2 in n 2.196 * [backup-simplify]: Simplify -2 into -2 2.196 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.196 * [taylor]: Taking taylor expansion of PI in n 2.196 * [backup-simplify]: Simplify PI into PI 2.196 * [taylor]: Taking taylor expansion of n in n 2.196 * [backup-simplify]: Simplify 0 into 0 2.196 * [backup-simplify]: Simplify 1 into 1 2.197 * [backup-simplify]: Simplify (/ PI 1) into PI 2.197 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.198 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.199 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.200 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 2.200 * [backup-simplify]: Simplify 0 into 0 2.201 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.202 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 2.202 * [backup-simplify]: Simplify 0 into 0 2.203 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.204 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.204 * [backup-simplify]: Simplify 0 into 0 2.205 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.206 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.206 * [backup-simplify]: Simplify 0 into 0 2.207 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.208 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.208 * [backup-simplify]: Simplify 0 into 0 2.209 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.209 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.210 * [backup-simplify]: Simplify 0 into 0 2.210 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 2.210 * * * * [progress]: [ 3 / 3 ] generating series at (2) 2.210 * [backup-simplify]: Simplify (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 2.210 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 2.211 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 2.211 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.211 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.211 * [taylor]: Taking taylor expansion of k in k 2.211 * [backup-simplify]: Simplify 0 into 0 2.211 * [backup-simplify]: Simplify 1 into 1 2.211 * [backup-simplify]: Simplify (/ 1 1) into 1 2.211 * [backup-simplify]: Simplify (sqrt 0) into 0 2.212 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.212 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 2.212 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 2.212 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 2.212 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 2.212 * [taylor]: Taking taylor expansion of 1/2 in k 2.212 * [backup-simplify]: Simplify 1/2 into 1/2 2.212 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 2.212 * [taylor]: Taking taylor expansion of 1/2 in k 2.212 * [backup-simplify]: Simplify 1/2 into 1/2 2.212 * [taylor]: Taking taylor expansion of k in k 2.212 * [backup-simplify]: Simplify 0 into 0 2.212 * [backup-simplify]: Simplify 1 into 1 2.212 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 2.212 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 2.212 * [taylor]: Taking taylor expansion of 2 in k 2.212 * [backup-simplify]: Simplify 2 into 2 2.212 * [taylor]: Taking taylor expansion of (* n PI) in k 2.212 * [taylor]: Taking taylor expansion of n in k 2.212 * [backup-simplify]: Simplify n into n 2.212 * [taylor]: Taking taylor expansion of PI in k 2.212 * [backup-simplify]: Simplify PI into PI 2.212 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.212 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 2.212 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 2.213 * [backup-simplify]: Simplify (* 1/2 0) into 0 2.213 * [backup-simplify]: Simplify (- 0) into 0 2.213 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.213 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 2.213 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 2.213 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 2.213 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 2.213 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.213 * [taylor]: Taking taylor expansion of k in n 2.213 * [backup-simplify]: Simplify k into k 2.213 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.214 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 2.214 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.214 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 2.214 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 2.214 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 2.214 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 2.214 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 2.214 * [taylor]: Taking taylor expansion of 1/2 in n 2.214 * [backup-simplify]: Simplify 1/2 into 1/2 2.214 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 2.214 * [taylor]: Taking taylor expansion of 1/2 in n 2.214 * [backup-simplify]: Simplify 1/2 into 1/2 2.214 * [taylor]: Taking taylor expansion of k in n 2.214 * [backup-simplify]: Simplify k into k 2.214 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 2.214 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.214 * [taylor]: Taking taylor expansion of 2 in n 2.214 * [backup-simplify]: Simplify 2 into 2 2.214 * [taylor]: Taking taylor expansion of (* n PI) in n 2.214 * [taylor]: Taking taylor expansion of n in n 2.214 * [backup-simplify]: Simplify 0 into 0 2.214 * [backup-simplify]: Simplify 1 into 1 2.214 * [taylor]: Taking taylor expansion of PI in n 2.214 * [backup-simplify]: Simplify PI into PI 2.214 * [backup-simplify]: Simplify (* 0 PI) into 0 2.215 * [backup-simplify]: Simplify (* 2 0) into 0 2.215 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.216 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 2.217 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.217 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 2.217 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 2.217 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 2.218 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.219 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 2.220 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 2.220 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 2.220 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 2.220 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.220 * [taylor]: Taking taylor expansion of k in n 2.220 * [backup-simplify]: Simplify k into k 2.220 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.220 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 2.220 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.220 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 2.220 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 2.220 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 2.220 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 2.220 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 2.220 * [taylor]: Taking taylor expansion of 1/2 in n 2.220 * [backup-simplify]: Simplify 1/2 into 1/2 2.220 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 2.220 * [taylor]: Taking taylor expansion of 1/2 in n 2.220 * [backup-simplify]: Simplify 1/2 into 1/2 2.220 * [taylor]: Taking taylor expansion of k in n 2.220 * [backup-simplify]: Simplify k into k 2.220 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 2.220 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.220 * [taylor]: Taking taylor expansion of 2 in n 2.220 * [backup-simplify]: Simplify 2 into 2 2.220 * [taylor]: Taking taylor expansion of (* n PI) in n 2.220 * [taylor]: Taking taylor expansion of n in n 2.220 * [backup-simplify]: Simplify 0 into 0 2.220 * [backup-simplify]: Simplify 1 into 1 2.220 * [taylor]: Taking taylor expansion of PI in n 2.220 * [backup-simplify]: Simplify PI into PI 2.220 * [backup-simplify]: Simplify (* 0 PI) into 0 2.221 * [backup-simplify]: Simplify (* 2 0) into 0 2.222 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.223 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 2.223 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.223 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 2.223 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 2.223 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 2.224 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.225 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 2.226 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 2.227 * [backup-simplify]: Simplify (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) 2.227 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k 2.227 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 2.227 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 2.227 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 2.227 * [taylor]: Taking taylor expansion of 1/2 in k 2.227 * [backup-simplify]: Simplify 1/2 into 1/2 2.227 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 2.227 * [taylor]: Taking taylor expansion of 1/2 in k 2.227 * [backup-simplify]: Simplify 1/2 into 1/2 2.227 * [taylor]: Taking taylor expansion of k in k 2.227 * [backup-simplify]: Simplify 0 into 0 2.227 * [backup-simplify]: Simplify 1 into 1 2.227 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 2.227 * [taylor]: Taking taylor expansion of (log n) in k 2.227 * [taylor]: Taking taylor expansion of n in k 2.227 * [backup-simplify]: Simplify n into n 2.227 * [backup-simplify]: Simplify (log n) into (log n) 2.227 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 2.227 * [taylor]: Taking taylor expansion of (* 2 PI) in k 2.227 * [taylor]: Taking taylor expansion of 2 in k 2.227 * [backup-simplify]: Simplify 2 into 2 2.227 * [taylor]: Taking taylor expansion of PI in k 2.227 * [backup-simplify]: Simplify PI into PI 2.227 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.228 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.228 * [backup-simplify]: Simplify (* 1/2 0) into 0 2.229 * [backup-simplify]: Simplify (- 0) into 0 2.229 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.229 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.230 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 2.231 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 2.231 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.231 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.231 * [taylor]: Taking taylor expansion of k in k 2.231 * [backup-simplify]: Simplify 0 into 0 2.231 * [backup-simplify]: Simplify 1 into 1 2.231 * [backup-simplify]: Simplify (/ 1 1) into 1 2.231 * [backup-simplify]: Simplify (sqrt 0) into 0 2.232 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.233 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0 2.233 * [backup-simplify]: Simplify 0 into 0 2.234 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.235 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 2.236 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.237 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 2.237 * [backup-simplify]: Simplify (- 0) into 0 2.238 * [backup-simplify]: Simplify (+ 0 0) into 0 2.239 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.240 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 2.242 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.243 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 2.243 * [taylor]: Taking taylor expansion of 0 in k 2.243 * [backup-simplify]: Simplify 0 into 0 2.244 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.245 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.247 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.247 * [backup-simplify]: Simplify (+ 0 0) into 0 2.248 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 2.248 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.249 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.250 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2.253 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 2.257 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 2.258 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 2.259 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.260 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.262 * [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 2.262 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 2.262 * [backup-simplify]: Simplify (- 0) into 0 2.263 * [backup-simplify]: Simplify (+ 0 0) into 0 2.263 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.264 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 2.266 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.266 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.267 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 2.268 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 2.268 * [taylor]: Taking taylor expansion of 0 in k 2.268 * [backup-simplify]: Simplify 0 into 0 2.268 * [backup-simplify]: Simplify 0 into 0 2.268 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.270 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.271 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.272 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.273 * [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 2.274 * [backup-simplify]: Simplify (+ 0 0) into 0 2.274 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 2.274 * [backup-simplify]: Simplify (- 0) into 0 2.275 * [backup-simplify]: Simplify (+ 0 0) into 0 2.276 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 2.280 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 2.286 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 0))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) 2.291 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) 2.292 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.294 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.299 * [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 2.301 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 2.301 * [backup-simplify]: Simplify (- 0) into 0 2.302 * [backup-simplify]: Simplify (+ 0 0) into 0 2.303 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.305 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 2.308 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.308 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.309 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 2.311 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))))) into 0 2.311 * [taylor]: Taking taylor expansion of 0 in k 2.311 * [backup-simplify]: Simplify 0 into 0 2.311 * [backup-simplify]: Simplify 0 into 0 2.311 * [backup-simplify]: Simplify 0 into 0 2.312 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.316 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.318 * [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 2.319 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.322 * [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 2.322 * [backup-simplify]: Simplify (+ 0 0) into 0 2.323 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 2.323 * [backup-simplify]: Simplify (- 0) into 0 2.324 * [backup-simplify]: Simplify (+ 0 0) into 0 2.325 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 2.329 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (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 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 2.340 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) +nan.0) (* (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) 2.347 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) 2.358 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))) 2.359 * [backup-simplify]: Simplify (/ (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 2.359 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 2.359 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 2.359 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.359 * [taylor]: Taking taylor expansion of k in k 2.359 * [backup-simplify]: Simplify 0 into 0 2.359 * [backup-simplify]: Simplify 1 into 1 2.359 * [backup-simplify]: Simplify (sqrt 0) into 0 2.360 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.360 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 2.360 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 2.360 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 2.360 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 2.360 * [taylor]: Taking taylor expansion of 1/2 in k 2.360 * [backup-simplify]: Simplify 1/2 into 1/2 2.360 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.360 * [taylor]: Taking taylor expansion of 1/2 in k 2.360 * [backup-simplify]: Simplify 1/2 into 1/2 2.360 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.360 * [taylor]: Taking taylor expansion of k in k 2.360 * [backup-simplify]: Simplify 0 into 0 2.360 * [backup-simplify]: Simplify 1 into 1 2.360 * [backup-simplify]: Simplify (/ 1 1) into 1 2.360 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 2.360 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 2.360 * [taylor]: Taking taylor expansion of 2 in k 2.360 * [backup-simplify]: Simplify 2 into 2 2.360 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.360 * [taylor]: Taking taylor expansion of PI in k 2.360 * [backup-simplify]: Simplify PI into PI 2.360 * [taylor]: Taking taylor expansion of n in k 2.360 * [backup-simplify]: Simplify n into n 2.361 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.361 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 2.361 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 2.361 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.361 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.361 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.361 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 2.362 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 2.362 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 2.362 * [taylor]: Taking taylor expansion of (sqrt k) in n 2.362 * [taylor]: Taking taylor expansion of k in n 2.362 * [backup-simplify]: Simplify k into k 2.362 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 2.362 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 2.362 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 2.362 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 2.362 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 2.362 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 2.362 * [taylor]: Taking taylor expansion of 1/2 in n 2.362 * [backup-simplify]: Simplify 1/2 into 1/2 2.362 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.362 * [taylor]: Taking taylor expansion of 1/2 in n 2.362 * [backup-simplify]: Simplify 1/2 into 1/2 2.362 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.362 * [taylor]: Taking taylor expansion of k in n 2.362 * [backup-simplify]: Simplify k into k 2.362 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.362 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 2.362 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.362 * [taylor]: Taking taylor expansion of 2 in n 2.362 * [backup-simplify]: Simplify 2 into 2 2.362 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.362 * [taylor]: Taking taylor expansion of PI in n 2.362 * [backup-simplify]: Simplify PI into PI 2.362 * [taylor]: Taking taylor expansion of n in n 2.362 * [backup-simplify]: Simplify 0 into 0 2.362 * [backup-simplify]: Simplify 1 into 1 2.362 * [backup-simplify]: Simplify (/ PI 1) into PI 2.363 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.363 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.363 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.364 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 2.364 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 2.364 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.365 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 2.366 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 2.366 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 2.366 * [taylor]: Taking taylor expansion of (sqrt k) in n 2.366 * [taylor]: Taking taylor expansion of k in n 2.366 * [backup-simplify]: Simplify k into k 2.366 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 2.366 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 2.366 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 2.366 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 2.366 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 2.366 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 2.366 * [taylor]: Taking taylor expansion of 1/2 in n 2.366 * [backup-simplify]: Simplify 1/2 into 1/2 2.366 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.366 * [taylor]: Taking taylor expansion of 1/2 in n 2.366 * [backup-simplify]: Simplify 1/2 into 1/2 2.366 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.366 * [taylor]: Taking taylor expansion of k in n 2.366 * [backup-simplify]: Simplify k into k 2.366 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.366 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 2.366 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.366 * [taylor]: Taking taylor expansion of 2 in n 2.366 * [backup-simplify]: Simplify 2 into 2 2.366 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.366 * [taylor]: Taking taylor expansion of PI in n 2.367 * [backup-simplify]: Simplify PI into PI 2.367 * [taylor]: Taking taylor expansion of n in n 2.367 * [backup-simplify]: Simplify 0 into 0 2.367 * [backup-simplify]: Simplify 1 into 1 2.367 * [backup-simplify]: Simplify (/ PI 1) into PI 2.367 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.368 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.368 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.368 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 2.368 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 2.369 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.370 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 2.371 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 2.375 * [backup-simplify]: Simplify (* (sqrt k) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) 2.375 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 2.375 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 2.375 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 2.375 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 2.375 * [taylor]: Taking taylor expansion of 1/2 in k 2.375 * [backup-simplify]: Simplify 1/2 into 1/2 2.375 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.375 * [taylor]: Taking taylor expansion of 1/2 in k 2.375 * [backup-simplify]: Simplify 1/2 into 1/2 2.375 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.375 * [taylor]: Taking taylor expansion of k in k 2.375 * [backup-simplify]: Simplify 0 into 0 2.375 * [backup-simplify]: Simplify 1 into 1 2.376 * [backup-simplify]: Simplify (/ 1 1) into 1 2.376 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 2.376 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 2.376 * [taylor]: Taking taylor expansion of (* 2 PI) in k 2.376 * [taylor]: Taking taylor expansion of 2 in k 2.376 * [backup-simplify]: Simplify 2 into 2 2.376 * [taylor]: Taking taylor expansion of PI in k 2.376 * [backup-simplify]: Simplify PI into PI 2.377 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.378 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.378 * [taylor]: Taking taylor expansion of (log n) in k 2.378 * [taylor]: Taking taylor expansion of n in k 2.378 * [backup-simplify]: Simplify n into n 2.378 * [backup-simplify]: Simplify (log n) into (log n) 2.378 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.379 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.379 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.379 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.380 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 2.380 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 2.381 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 2.381 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.381 * [taylor]: Taking taylor expansion of k in k 2.381 * [backup-simplify]: Simplify 0 into 0 2.381 * [backup-simplify]: Simplify 1 into 1 2.382 * [backup-simplify]: Simplify (sqrt 0) into 0 2.383 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.383 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 2.383 * [backup-simplify]: Simplify 0 into 0 2.384 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.384 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.385 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.385 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.386 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.386 * [backup-simplify]: Simplify (- 0) into 0 2.386 * [backup-simplify]: Simplify (+ 0 0) into 0 2.387 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.388 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 2.389 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.390 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 2.390 * [taylor]: Taking taylor expansion of 0 in k 2.390 * [backup-simplify]: Simplify 0 into 0 2.390 * [backup-simplify]: Simplify 0 into 0 2.391 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 2.392 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 2.392 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.393 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.395 * [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 2.395 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.395 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.396 * [backup-simplify]: Simplify (- 0) into 0 2.396 * [backup-simplify]: Simplify (+ 0 0) into 0 2.397 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.398 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 2.399 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.400 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 2.401 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 2.401 * [taylor]: Taking taylor expansion of 0 in k 2.401 * [backup-simplify]: Simplify 0 into 0 2.401 * [backup-simplify]: Simplify 0 into 0 2.401 * [backup-simplify]: Simplify 0 into 0 2.403 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.404 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 2.404 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 2.405 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.406 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.412 * [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 2.412 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.413 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 2.414 * [backup-simplify]: Simplify (- 0) into 0 2.414 * [backup-simplify]: Simplify (+ 0 0) into 0 2.415 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.417 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 2.421 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 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 2.421 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 2.423 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 2.423 * [taylor]: Taking taylor expansion of 0 in k 2.423 * [backup-simplify]: Simplify 0 into 0 2.423 * [backup-simplify]: Simplify 0 into 0 2.424 * [backup-simplify]: Simplify 0 into 0 2.424 * [backup-simplify]: Simplify 0 into 0 2.428 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.430 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 2.431 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 2.433 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) 2.434 * [backup-simplify]: Simplify (/ (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 2.434 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 2.434 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 2.434 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 2.434 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 2.434 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 2.434 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.434 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.434 * [taylor]: Taking taylor expansion of 1/2 in k 2.434 * [backup-simplify]: Simplify 1/2 into 1/2 2.434 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.434 * [taylor]: Taking taylor expansion of k in k 2.434 * [backup-simplify]: Simplify 0 into 0 2.434 * [backup-simplify]: Simplify 1 into 1 2.434 * [backup-simplify]: Simplify (/ 1 1) into 1 2.434 * [taylor]: Taking taylor expansion of 1/2 in k 2.434 * [backup-simplify]: Simplify 1/2 into 1/2 2.434 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 2.434 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 2.434 * [taylor]: Taking taylor expansion of -2 in k 2.434 * [backup-simplify]: Simplify -2 into -2 2.434 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.434 * [taylor]: Taking taylor expansion of PI in k 2.434 * [backup-simplify]: Simplify PI into PI 2.434 * [taylor]: Taking taylor expansion of n in k 2.434 * [backup-simplify]: Simplify n into n 2.434 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.434 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 2.434 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 2.435 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.435 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.435 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 2.435 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 2.435 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.435 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.435 * [taylor]: Taking taylor expansion of -1 in k 2.435 * [backup-simplify]: Simplify -1 into -1 2.435 * [taylor]: Taking taylor expansion of k in k 2.435 * [backup-simplify]: Simplify 0 into 0 2.435 * [backup-simplify]: Simplify 1 into 1 2.436 * [backup-simplify]: Simplify (/ -1 1) into -1 2.436 * [backup-simplify]: Simplify (sqrt 0) into 0 2.437 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.437 * [backup-simplify]: Simplify (/ (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 2.437 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 2.437 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.437 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.437 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.437 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.437 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.437 * [taylor]: Taking taylor expansion of 1/2 in n 2.437 * [backup-simplify]: Simplify 1/2 into 1/2 2.437 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.437 * [taylor]: Taking taylor expansion of k in n 2.437 * [backup-simplify]: Simplify k into k 2.437 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.437 * [taylor]: Taking taylor expansion of 1/2 in n 2.437 * [backup-simplify]: Simplify 1/2 into 1/2 2.437 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.437 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.437 * [taylor]: Taking taylor expansion of -2 in n 2.437 * [backup-simplify]: Simplify -2 into -2 2.437 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.438 * [taylor]: Taking taylor expansion of PI in n 2.438 * [backup-simplify]: Simplify PI into PI 2.438 * [taylor]: Taking taylor expansion of n in n 2.438 * [backup-simplify]: Simplify 0 into 0 2.438 * [backup-simplify]: Simplify 1 into 1 2.438 * [backup-simplify]: Simplify (/ PI 1) into PI 2.438 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.440 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.440 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.440 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.441 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.442 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 2.442 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 2.442 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 2.442 * [taylor]: Taking taylor expansion of (/ -1 k) in n 2.442 * [taylor]: Taking taylor expansion of -1 in n 2.442 * [backup-simplify]: Simplify -1 into -1 2.442 * [taylor]: Taking taylor expansion of k in n 2.442 * [backup-simplify]: Simplify k into k 2.442 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 2.442 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 2.443 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 2.443 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 2.443 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) 2.443 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 2.443 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.443 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.443 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.443 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.443 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.443 * [taylor]: Taking taylor expansion of 1/2 in n 2.443 * [backup-simplify]: Simplify 1/2 into 1/2 2.443 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.444 * [taylor]: Taking taylor expansion of k in n 2.444 * [backup-simplify]: Simplify k into k 2.444 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.444 * [taylor]: Taking taylor expansion of 1/2 in n 2.444 * [backup-simplify]: Simplify 1/2 into 1/2 2.444 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.444 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.444 * [taylor]: Taking taylor expansion of -2 in n 2.444 * [backup-simplify]: Simplify -2 into -2 2.444 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.444 * [taylor]: Taking taylor expansion of PI in n 2.444 * [backup-simplify]: Simplify PI into PI 2.444 * [taylor]: Taking taylor expansion of n in n 2.444 * [backup-simplify]: Simplify 0 into 0 2.444 * [backup-simplify]: Simplify 1 into 1 2.444 * [backup-simplify]: Simplify (/ PI 1) into PI 2.444 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.445 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.445 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.445 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.446 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.447 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 2.448 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 2.448 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 2.448 * [taylor]: Taking taylor expansion of (/ -1 k) in n 2.448 * [taylor]: Taking taylor expansion of -1 in n 2.448 * [backup-simplify]: Simplify -1 into -1 2.448 * [taylor]: Taking taylor expansion of k in n 2.448 * [backup-simplify]: Simplify k into k 2.448 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 2.448 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 2.448 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 2.448 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 2.449 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) 2.449 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 2.449 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 2.449 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 2.449 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.449 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.449 * [taylor]: Taking taylor expansion of 1/2 in k 2.449 * [backup-simplify]: Simplify 1/2 into 1/2 2.449 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.449 * [taylor]: Taking taylor expansion of k in k 2.449 * [backup-simplify]: Simplify 0 into 0 2.449 * [backup-simplify]: Simplify 1 into 1 2.449 * [backup-simplify]: Simplify (/ 1 1) into 1 2.449 * [taylor]: Taking taylor expansion of 1/2 in k 2.449 * [backup-simplify]: Simplify 1/2 into 1/2 2.449 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 2.449 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 2.449 * [taylor]: Taking taylor expansion of (* -2 PI) in k 2.449 * [taylor]: Taking taylor expansion of -2 in k 2.449 * [backup-simplify]: Simplify -2 into -2 2.449 * [taylor]: Taking taylor expansion of PI in k 2.449 * [backup-simplify]: Simplify PI into PI 2.450 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.450 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.450 * [taylor]: Taking taylor expansion of (log n) in k 2.450 * [taylor]: Taking taylor expansion of n in k 2.450 * [backup-simplify]: Simplify n into n 2.450 * [backup-simplify]: Simplify (log n) into (log n) 2.451 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.451 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.451 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.452 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 2.452 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 2.453 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 2.453 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.453 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.453 * [taylor]: Taking taylor expansion of -1 in k 2.453 * [backup-simplify]: Simplify -1 into -1 2.453 * [taylor]: Taking taylor expansion of k in k 2.453 * [backup-simplify]: Simplify 0 into 0 2.453 * [backup-simplify]: Simplify 1 into 1 2.453 * [backup-simplify]: Simplify (/ -1 1) into -1 2.454 * [backup-simplify]: Simplify (sqrt 0) into 0 2.454 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.455 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) +nan.0) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 2.456 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 2.456 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.457 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 2.458 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 2.458 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.458 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.459 * [backup-simplify]: Simplify (+ 0 0) into 0 2.460 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.460 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 2.461 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.463 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 2.463 * [taylor]: Taking taylor expansion of 0 in k 2.463 * [backup-simplify]: Simplify 0 into 0 2.463 * [backup-simplify]: Simplify 0 into 0 2.464 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 2.466 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.469 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 2.470 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 2.471 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.472 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 2.476 * [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 2.476 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.477 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.478 * [backup-simplify]: Simplify (+ 0 0) into 0 2.479 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.485 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 2.488 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.488 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.489 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 2.491 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 2.491 * [taylor]: Taking taylor expansion of 0 in k 2.491 * [backup-simplify]: Simplify 0 into 0 2.491 * [backup-simplify]: Simplify 0 into 0 2.491 * [backup-simplify]: Simplify 0 into 0 2.492 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.496 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.500 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 2.501 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 2.505 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 2.505 * * * [progress]: simplifying candidates 2.506 * * * * [progress]: [ 1 / 445 ] simplifiying candidate # 2.506 * * * * [progress]: [ 2 / 445 ] simplifiying candidate # 2.506 * * * * [progress]: [ 3 / 445 ] simplifiying candidate # 2.506 * * * * [progress]: [ 4 / 445 ] simplifiying candidate # 2.506 * * * * [progress]: [ 5 / 445 ] simplifiying candidate # 2.506 * * * * [progress]: [ 6 / 445 ] simplifiying candidate # 2.506 * * * * [progress]: [ 7 / 445 ] simplifiying candidate # 2.506 * * * * [progress]: [ 8 / 445 ] simplifiying candidate # 2.506 * * * * [progress]: [ 9 / 445 ] simplifiying candidate # 2.506 * * * * 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* * [progress]: [ 87 / 445 ] simplifiying candidate #real (real->posit16 (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))> 2.512 * * * * [progress]: [ 88 / 445 ] simplifiying candidate # 2.512 * * * * [progress]: [ 89 / 445 ] simplifiying candidate # 2.512 * * * * [progress]: [ 90 / 445 ] simplifiying candidate # 2.512 * * * * [progress]: [ 91 / 445 ] simplifiying candidate # 2.512 * * * * [progress]: [ 92 / 445 ] simplifiying candidate # 2.512 * * * * [progress]: [ 93 / 445 ] simplifiying candidate # 2.512 * * * * [progress]: [ 94 / 445 ] simplifiying candidate # 2.512 * * * * [progress]: [ 95 / 445 ] simplifiying candidate # 2.512 * * * * [progress]: [ 96 / 445 ] simplifiying candidate # 2.513 * * * * [progress]: [ 97 / 445 ] simplifiying candidate # 2.513 * * * * [progress]: [ 98 / 445 ] simplifiying candidate # 2.513 * * * * [progress]: [ 99 / 445 ] simplifiying candidate # 2.513 * * * * [progress]: [ 100 / 445 ] simplifiying candidate # 2.513 * * * * [progress]: [ 101 / 445 ] 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candidate # 2.537 * * * * [progress]: [ 438 / 445 ] simplifiying candidate # 2.537 * * * * [progress]: [ 439 / 445 ] simplifiying candidate # 2.537 * * * * [progress]: [ 440 / 445 ] simplifiying candidate # 2.537 * * * * [progress]: [ 441 / 445 ] simplifiying candidate # 2.537 * * * * [progress]: [ 442 / 445 ] simplifiying candidate # 2.537 * * * * [progress]: [ 443 / 445 ] simplifiying candidate # 2.537 * * * * [progress]: [ 444 / 445 ] simplifiying candidate # 2.537 * * * * [progress]: [ 445 / 445 ] simplifiying candidate # 2.544 * [simplify]: Simplifying: (expm1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (log1p (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))) (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2))) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (/ k 2)) (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) 1) (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2)))) (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (pow (* n (* 2 PI)) 1) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) (/ 1 1))))) (pow (* n (* 2 PI)) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1)))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) 1)))) (pow (* n (* 2 PI)) (fma (- (/ k 2)) 1 (* (/ k 2) 1))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ 1 2) k)))) (pow (* n (* 2 PI)) (fma (- (/ 1 2)) k (* (/ 1 2) k))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) 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(* 2 (* n PI)) (* 2 (* n PI)) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 2.562 * * [simplify]: iteration 0: 695 enodes 2.828 * * [simplify]: iteration 1: 1526 enodes 3.266 * * [simplify]: iteration 2: 2001 enodes 3.695 * * [simplify]: iteration complete: 2001 enodes 3.695 * * [simplify]: Extracting #0: cost 233 inf + 0 3.698 * * [simplify]: Extracting #1: cost 515 inf + 1 3.702 * * [simplify]: Extracting #2: cost 739 inf + 1881 3.710 * * [simplify]: Extracting #3: cost 804 inf + 11914 3.724 * * [simplify]: Extracting #4: cost 562 inf + 88070 3.755 * * [simplify]: Extracting #5: cost 346 inf + 180910 3.819 * * [simplify]: Extracting #6: cost 193 inf + 273665 3.898 * * [simplify]: Extracting #7: cost 60 inf + 356856 3.956 * * [simplify]: Extracting #8: cost 23 inf + 387667 4.046 * * [simplify]: Extracting #9: cost 23 inf + 390493 4.143 * * [simplify]: Extracting #10: cost 15 inf + 395110 4.199 * * [simplify]: Extracting #11: cost 10 inf + 400340 4.262 * * [simplify]: Extracting #12: cost 4 inf + 408621 4.344 * * [simplify]: Extracting #13: cost 0 inf + 415390 4.419 * * [simplify]: Extracting #14: cost 0 inf + 415265 4.498 * * [simplify]: Extracting #15: cost 0 inf + 415190 4.602 * [simplify]: Simplified to: (expm1 (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (log1p (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (* (log (* (* PI 2) n)) (- 1/2 (/ k 2))) (* (log (* (* PI 2) n)) (- 1/2 (/ k 2))) (* (log (* (* PI 2) n)) (- 1/2 (/ k 2))) (* (log (* (* PI 2) n)) (- 1/2 (/ k 2))) (- 1/2 (/ k 2)) (- 1/2 (/ k 2)) (- 1/2 (/ k 2)) (sqrt (* (* PI 2) n)) (pow (* (* PI 2) n) (/ k 2)) (pow (* (* PI 2) n) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (pow (* (* PI 2) n) (sqrt 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1/2 (/ k 2)))) (sqrt k)) (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))) (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt k)) (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (fabs (cbrt k))) (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (cbrt k))) (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt k)) (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt k)) (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1 (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1 (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k)) (/ (/ (pow (* (* PI 2) n) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1/2 (/ k 2)) 2)) (fabs (cbrt k))) (/ (pow (* (* PI 2) n) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k))) (/ (pow (* (* PI 2) n) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))) (pow (* (* PI 2) n) (/ (- 1/2 (/ k 2)) 2)) (/ (pow (* (* PI 2) n) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)) (/ (pow (* (* PI 2) n) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))) (pow (* (* PI 2) n) (/ (- 1/2 (/ k 2)) 2)) (/ (pow (* (* PI 2) n) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (fabs (cbrt k))) (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (* -1/2 k) (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (/ k 2) -1 (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (/ (cbrt k) (cbrt 2)) (- (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2)))) (* (/ (cbrt k) (cbrt 2)) (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))))))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (- (* (/ (cbrt k) (sqrt 2)) (/ (cbrt k) (/ (sqrt 2) (cbrt k))))) (* (/ (cbrt k) (sqrt 2)) (/ (cbrt k) (/ (sqrt 2) (cbrt k))))))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (- (* (/ (cbrt k) 2) (* (cbrt k) (cbrt k)))) (* (/ (cbrt k) 2) (* (cbrt k) (cbrt k)))))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (- (/ (sqrt k) (cbrt 2))) (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)) (* (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)) (/ (sqrt k) (cbrt 2)))))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (* -1/2 k) (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (- (/ (/ k (cbrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ k (cbrt 2)) (* (cbrt 2) (cbrt 2)))))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (- (/ (/ k (sqrt 2)) (sqrt 2))) (/ (/ k (sqrt 2)) (sqrt 2))))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (/ k 2) -1 (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (/ k 2) -1 (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (fma -1/2 k (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (* -1/2 k) (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (/ k 2) -1 (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (/ (cbrt k) (cbrt 2)) (- (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2)))) (* (/ (cbrt k) (cbrt 2)) (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))))))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (- (* (/ (cbrt k) (sqrt 2)) (/ (cbrt k) (/ (sqrt 2) (cbrt k))))) (* (/ (cbrt k) (sqrt 2)) (/ (cbrt k) (/ (sqrt 2) (cbrt k))))))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (- (* (/ (cbrt k) 2) (* (cbrt k) (cbrt k)))) (* (/ (cbrt k) 2) (* (cbrt k) (cbrt k)))))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (- (/ (sqrt k) (cbrt 2))) (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)) (* (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)) (/ (sqrt k) (cbrt 2)))))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (* -1/2 k) (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (- (/ (/ k (cbrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ k (cbrt 2)) (* (cbrt 2) (cbrt 2)))))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (- (/ (/ k (sqrt 2)) (sqrt 2))) (/ (/ k (sqrt 2)) (sqrt 2))))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (/ k 2) -1 (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (/ k 2) -1 (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (fma -1/2 k (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (* -1/2 k) (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (/ k 2) -1 (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (/ (cbrt k) (cbrt 2)) (- (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2)))) (* (/ (cbrt k) (cbrt 2)) (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))))))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (- (* (/ (cbrt k) (sqrt 2)) (/ (cbrt k) (/ (sqrt 2) (cbrt k))))) (* (/ (cbrt k) (sqrt 2)) (/ (cbrt k) (/ (sqrt 2) (cbrt k))))))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (- (* (/ (cbrt k) 2) (* (cbrt k) (cbrt k)))) (* (/ (cbrt k) 2) (* (cbrt k) (cbrt k)))))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (- (/ (sqrt k) (cbrt 2))) (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)) (* (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)) (/ (sqrt k) (cbrt 2)))))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (* -1/2 k) (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (- (/ (/ k (cbrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ k (cbrt 2)) (* (cbrt 2) (cbrt 2)))))) (/ (sqrt k) (pow (* (* PI 2) n) (+ (- (/ (/ k (sqrt 2)) (sqrt 2))) (/ (/ k (sqrt 2)) (sqrt 2))))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (/ k 2) -1 (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (fma (/ k 2) -1 (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (fma -1/2 k (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (/ (- k) 2))) (/ (sqrt k) (pow (* (* PI 2) n) (/ (- k) 2))) (/ (sqrt k) (pow (* PI 2) (- 1/2 (/ k 2)))) (/ (sqrt k) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (/ (sqrt k) (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1/2 (/ k 2)) 2))) (* (pow (* (* PI 2) n) (/ k 2)) (sqrt k)) (real->posit16 (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k))) (fma (* (* (log (* PI 2)) (exp (* 1/2 (log (* (* PI 2) n))))) (* (* k k) (log n))) 1/4 (- (fma (* (* (* (log n) (log n)) (* k k)) (exp (* 1/2 (log (* (* PI 2) n))))) 1/8 (fma 1/8 (* (* (* (log (* PI 2)) (log (* PI 2))) (exp (* 1/2 (log (* (* PI 2) n))))) (* k k)) (exp (* 1/2 (log (* (* PI 2) n)))))) (* 1/2 (fma (* k (log n)) (exp (* 1/2 (log (* (* PI 2) n)))) (* (* (log (* PI 2)) (exp (* 1/2 (log (* (* PI 2) n))))) k))))) (exp (* (log (* (* PI 2) n)) (- 1/2 (/ k 2)))) (exp (* (- 1/2 (/ k 2)) (- (log (* -2 PI)) (log (/ -1 n))))) (* (* PI 2) n) (* (* PI 2) n) (* (* PI 2) n) (- (- (* +nan.0 (* (* (log (* PI 2)) (exp (* 1/2 (log (* (* PI 2) n))))) (* (* k k) (log n)))) (fma (* (* (log (* PI 2)) (exp (* 1/2 (log (* (* PI 2) n))))) (* k k)) +nan.0 (- (fma (* (exp (* 1/2 (log (* (* PI 2) n)))) +nan.0) (* (* (log n) (log n)) (* k k)) (- (fma (* (exp (* 1/2 (log (* (* PI 2) n)))) +nan.0) k (- (- (* (exp (* 1/2 (log (* (* PI 2) n)))) +nan.0) (- (* +nan.0 (* (* (* (log (* PI 2)) (log (* PI 2))) (exp (* 1/2 (log (* (* PI 2) n))))) (* k k))) (- (* (* (exp (* 1/2 (log (* (* PI 2) n)))) +nan.0) (* (* k k) (log n))) (- (* (* (exp (* 1/2 (log (* (* PI 2) n)))) +nan.0) (* k k)) (- (* (* (* (log (* PI 2)) (exp (* 1/2 (log (* (* PI 2) n))))) k) +nan.0) (* +nan.0 (* (exp (* 1/2 (log (* (* PI 2) n)))) (* k (log n))))))))))))))))) (+ (- (* +nan.0 (/ (exp (* (log (* (* PI 2) n)) (- 1/2 (/ k 2)))) (* (* k k) k)))) (- (/ (* +nan.0 (exp (* (log (* (* PI 2) n)) (- 1/2 (/ k 2))))) k) (* (/ (exp (* (log (* (* PI 2) n)) (- 1/2 (/ k 2)))) (* k k)) +nan.0))) (+ (- (/ (* (exp (* (- 1/2 (/ k 2)) (- (log (* -2 PI)) (log (/ -1 n))))) +nan.0) k)) (- (/ (* (exp (* (- 1/2 (/ k 2)) (- (log (* -2 PI)) (log (/ -1 n))))) +nan.0) (* k k)) (* (exp (* (- 1/2 (/ k 2)) (- (log (* -2 PI)) (log (/ -1 n))))) +nan.0))) 4.714 * * * [progress]: adding candidates to table 7.615 * * [progress]: iteration 2 / 4 7.615 * * * [progress]: picking best candidate 7.661 * * * * [pick]: Picked # 7.661 * * * [progress]: localizing error 7.706 * * * [progress]: generating rewritten candidates 7.706 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 7.727 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1) 7.752 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2) 7.778 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 7.911 * * * [progress]: generating series expansions 7.911 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 7.912 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 7.912 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 7.912 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 7.912 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 7.912 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 7.912 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 7.912 * [taylor]: Taking taylor expansion of 1/2 in k 7.912 * [backup-simplify]: Simplify 1/2 into 1/2 7.912 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 7.912 * [taylor]: Taking taylor expansion of 1/2 in k 7.912 * [backup-simplify]: Simplify 1/2 into 1/2 7.912 * [taylor]: Taking taylor expansion of k in k 7.912 * [backup-simplify]: Simplify 0 into 0 7.912 * [backup-simplify]: Simplify 1 into 1 7.912 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 7.912 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 7.912 * [taylor]: Taking taylor expansion of 2 in k 7.912 * [backup-simplify]: Simplify 2 into 2 7.912 * [taylor]: Taking taylor expansion of (* n PI) in k 7.912 * [taylor]: Taking taylor expansion of n in k 7.912 * [backup-simplify]: Simplify n into n 7.912 * [taylor]: Taking taylor expansion of PI in k 7.913 * [backup-simplify]: Simplify PI into PI 7.913 * [backup-simplify]: Simplify (* n PI) into (* n PI) 7.913 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 7.913 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 7.913 * [backup-simplify]: Simplify (* 1/2 0) into 0 7.914 * [backup-simplify]: Simplify (- 0) into 0 7.914 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 7.914 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 7.914 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 7.914 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 7.914 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 7.914 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 7.914 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 7.914 * [taylor]: Taking taylor expansion of 1/2 in n 7.914 * [backup-simplify]: Simplify 1/2 into 1/2 7.914 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 7.915 * [taylor]: Taking taylor expansion of 1/2 in n 7.915 * [backup-simplify]: Simplify 1/2 into 1/2 7.915 * [taylor]: Taking taylor expansion of k in n 7.915 * [backup-simplify]: Simplify k into k 7.915 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 7.915 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 7.915 * [taylor]: Taking taylor expansion of 2 in n 7.915 * [backup-simplify]: Simplify 2 into 2 7.915 * [taylor]: Taking taylor expansion of (* n PI) in n 7.915 * [taylor]: Taking taylor expansion of n in n 7.915 * [backup-simplify]: Simplify 0 into 0 7.915 * [backup-simplify]: Simplify 1 into 1 7.915 * [taylor]: Taking taylor expansion of PI in n 7.915 * [backup-simplify]: Simplify PI into PI 7.915 * [backup-simplify]: Simplify (* 0 PI) into 0 7.916 * [backup-simplify]: Simplify (* 2 0) into 0 7.917 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 7.919 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 7.920 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 7.920 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 7.920 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 7.920 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 7.922 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 7.923 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 7.924 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 7.924 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 7.924 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 7.924 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 7.924 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 7.924 * [taylor]: Taking taylor expansion of 1/2 in n 7.924 * [backup-simplify]: Simplify 1/2 into 1/2 7.924 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 7.924 * [taylor]: Taking taylor expansion of 1/2 in n 7.924 * [backup-simplify]: Simplify 1/2 into 1/2 7.924 * [taylor]: Taking taylor expansion of k in n 7.924 * [backup-simplify]: Simplify k into k 7.925 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 7.925 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 7.925 * [taylor]: Taking taylor expansion of 2 in n 7.925 * [backup-simplify]: Simplify 2 into 2 7.925 * [taylor]: Taking taylor expansion of (* n PI) in n 7.925 * [taylor]: Taking taylor expansion of n in n 7.925 * [backup-simplify]: Simplify 0 into 0 7.925 * [backup-simplify]: Simplify 1 into 1 7.925 * [taylor]: Taking taylor expansion of PI in n 7.925 * [backup-simplify]: Simplify PI into PI 7.925 * [backup-simplify]: Simplify (* 0 PI) into 0 7.926 * [backup-simplify]: Simplify (* 2 0) into 0 7.927 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 7.929 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 7.930 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 7.930 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 7.930 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 7.930 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 7.932 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 7.933 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 7.934 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 7.934 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 7.934 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 7.934 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 7.934 * [taylor]: Taking taylor expansion of 1/2 in k 7.934 * [backup-simplify]: Simplify 1/2 into 1/2 7.934 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 7.934 * [taylor]: Taking taylor expansion of 1/2 in k 7.934 * [backup-simplify]: Simplify 1/2 into 1/2 7.935 * [taylor]: Taking taylor expansion of k in k 7.935 * [backup-simplify]: Simplify 0 into 0 7.935 * [backup-simplify]: Simplify 1 into 1 7.935 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 7.935 * [taylor]: Taking taylor expansion of (log n) in k 7.935 * [taylor]: Taking taylor expansion of n in k 7.935 * [backup-simplify]: Simplify n into n 7.935 * [backup-simplify]: Simplify (log n) into (log n) 7.935 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 7.935 * [taylor]: Taking taylor expansion of (* 2 PI) in k 7.935 * [taylor]: Taking taylor expansion of 2 in k 7.935 * [backup-simplify]: Simplify 2 into 2 7.935 * [taylor]: Taking taylor expansion of PI in k 7.935 * [backup-simplify]: Simplify PI into PI 7.935 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 7.936 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 7.937 * [backup-simplify]: Simplify (* 1/2 0) into 0 7.937 * [backup-simplify]: Simplify (- 0) into 0 7.938 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 7.939 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 7.940 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 7.941 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 7.942 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 7.943 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 7.945 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 7.946 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 7.947 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 7.947 * [backup-simplify]: Simplify (- 0) into 0 7.948 * [backup-simplify]: Simplify (+ 0 0) into 0 7.949 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 7.950 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 7.952 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 7.952 * [taylor]: Taking taylor expansion of 0 in k 7.952 * [backup-simplify]: Simplify 0 into 0 7.952 * [backup-simplify]: Simplify 0 into 0 7.953 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 7.954 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 7.956 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 7.956 * [backup-simplify]: Simplify (+ 0 0) into 0 7.957 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 7.957 * [backup-simplify]: Simplify (- 1/2) into -1/2 7.958 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 7.959 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 7.963 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 7.966 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 7.967 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 7.969 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 7.972 * [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 7.973 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 7.973 * [backup-simplify]: Simplify (- 0) into 0 7.974 * [backup-simplify]: Simplify (+ 0 0) into 0 7.975 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 7.977 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 7.980 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 7.980 * [taylor]: Taking taylor expansion of 0 in k 7.980 * [backup-simplify]: Simplify 0 into 0 7.980 * [backup-simplify]: Simplify 0 into 0 7.980 * [backup-simplify]: Simplify 0 into 0 7.981 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 7.983 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 7.986 * [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 7.987 * [backup-simplify]: Simplify (+ 0 0) into 0 7.988 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 7.988 * [backup-simplify]: Simplify (- 0) into 0 7.989 * [backup-simplify]: Simplify (+ 0 0) into 0 7.991 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 7.995 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 8.001 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 8.025 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 8.027 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 8.027 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 8.027 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 8.027 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 8.027 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 8.027 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 8.027 * [taylor]: Taking taylor expansion of 1/2 in k 8.027 * [backup-simplify]: Simplify 1/2 into 1/2 8.027 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 8.027 * [taylor]: Taking taylor expansion of 1/2 in k 8.027 * [backup-simplify]: Simplify 1/2 into 1/2 8.027 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.027 * [taylor]: Taking taylor expansion of k in k 8.027 * [backup-simplify]: Simplify 0 into 0 8.027 * [backup-simplify]: Simplify 1 into 1 8.028 * [backup-simplify]: Simplify (/ 1 1) into 1 8.028 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 8.028 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 8.028 * [taylor]: Taking taylor expansion of 2 in k 8.028 * [backup-simplify]: Simplify 2 into 2 8.028 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.028 * [taylor]: Taking taylor expansion of PI in k 8.028 * [backup-simplify]: Simplify PI into PI 8.028 * [taylor]: Taking taylor expansion of n in k 8.028 * [backup-simplify]: Simplify n into n 8.028 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.028 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 8.028 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 8.029 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 8.029 * [backup-simplify]: Simplify (- 1/2) into -1/2 8.030 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 8.030 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 8.030 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 8.030 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 8.030 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 8.030 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 8.030 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 8.030 * [taylor]: Taking taylor expansion of 1/2 in n 8.030 * [backup-simplify]: Simplify 1/2 into 1/2 8.030 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.030 * [taylor]: Taking taylor expansion of 1/2 in n 8.030 * [backup-simplify]: Simplify 1/2 into 1/2 8.030 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.030 * [taylor]: Taking taylor expansion of k in n 8.030 * [backup-simplify]: Simplify k into k 8.030 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.030 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 8.030 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 8.030 * [taylor]: Taking taylor expansion of 2 in n 8.030 * [backup-simplify]: Simplify 2 into 2 8.031 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.031 * [taylor]: Taking taylor expansion of PI in n 8.031 * [backup-simplify]: Simplify PI into PI 8.031 * [taylor]: Taking taylor expansion of n in n 8.031 * [backup-simplify]: Simplify 0 into 0 8.031 * [backup-simplify]: Simplify 1 into 1 8.031 * [backup-simplify]: Simplify (/ PI 1) into PI 8.032 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 8.033 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.033 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.033 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 8.033 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 8.035 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 8.036 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 8.037 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 8.037 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 8.037 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 8.037 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 8.037 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 8.037 * [taylor]: Taking taylor expansion of 1/2 in n 8.037 * [backup-simplify]: Simplify 1/2 into 1/2 8.037 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.038 * [taylor]: Taking taylor expansion of 1/2 in n 8.038 * [backup-simplify]: Simplify 1/2 into 1/2 8.038 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.038 * [taylor]: Taking taylor expansion of k in n 8.038 * [backup-simplify]: Simplify k into k 8.038 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.038 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 8.038 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 8.038 * [taylor]: Taking taylor expansion of 2 in n 8.038 * [backup-simplify]: Simplify 2 into 2 8.038 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.038 * [taylor]: Taking taylor expansion of PI in n 8.038 * [backup-simplify]: Simplify PI into PI 8.038 * [taylor]: Taking taylor expansion of n in n 8.038 * [backup-simplify]: Simplify 0 into 0 8.038 * [backup-simplify]: Simplify 1 into 1 8.038 * [backup-simplify]: Simplify (/ PI 1) into PI 8.039 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 8.040 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.040 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.040 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 8.040 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 8.042 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 8.043 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 8.044 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 8.044 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 8.044 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 8.044 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 8.044 * [taylor]: Taking taylor expansion of 1/2 in k 8.044 * [backup-simplify]: Simplify 1/2 into 1/2 8.044 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 8.044 * [taylor]: Taking taylor expansion of 1/2 in k 8.044 * [backup-simplify]: Simplify 1/2 into 1/2 8.044 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.044 * [taylor]: Taking taylor expansion of k in k 8.044 * [backup-simplify]: Simplify 0 into 0 8.044 * [backup-simplify]: Simplify 1 into 1 8.045 * [backup-simplify]: Simplify (/ 1 1) into 1 8.045 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 8.045 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 8.045 * [taylor]: Taking taylor expansion of (* 2 PI) in k 8.045 * [taylor]: Taking taylor expansion of 2 in k 8.045 * [backup-simplify]: Simplify 2 into 2 8.045 * [taylor]: Taking taylor expansion of PI in k 8.045 * [backup-simplify]: Simplify PI into PI 8.045 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 8.046 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.047 * [taylor]: Taking taylor expansion of (log n) in k 8.047 * [taylor]: Taking taylor expansion of n in k 8.047 * [backup-simplify]: Simplify n into n 8.047 * [backup-simplify]: Simplify (log n) into (log n) 8.047 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 8.047 * [backup-simplify]: Simplify (- 1/2) into -1/2 8.048 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 8.048 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 8.049 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 8.050 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 8.051 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 8.052 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 8.053 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.054 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 8.056 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 8.056 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.057 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 8.057 * [backup-simplify]: Simplify (- 0) into 0 8.057 * [backup-simplify]: Simplify (+ 0 0) into 0 8.059 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 8.060 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 8.062 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 8.062 * [taylor]: Taking taylor expansion of 0 in k 8.062 * [backup-simplify]: Simplify 0 into 0 8.062 * [backup-simplify]: Simplify 0 into 0 8.062 * [backup-simplify]: Simplify 0 into 0 8.063 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.064 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 8.068 * [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 8.068 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.069 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 8.069 * [backup-simplify]: Simplify (- 0) into 0 8.070 * [backup-simplify]: Simplify (+ 0 0) into 0 8.071 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 8.073 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 8.075 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 8.075 * [taylor]: Taking taylor expansion of 0 in k 8.075 * [backup-simplify]: Simplify 0 into 0 8.075 * [backup-simplify]: Simplify 0 into 0 8.075 * [backup-simplify]: Simplify 0 into 0 8.075 * [backup-simplify]: Simplify 0 into 0 8.077 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.078 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.084 * [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 8.084 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.085 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 8.086 * [backup-simplify]: Simplify (- 0) into 0 8.086 * [backup-simplify]: Simplify (+ 0 0) into 0 8.088 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 8.090 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 8.093 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 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 8.093 * [taylor]: Taking taylor expansion of 0 in k 8.093 * [backup-simplify]: Simplify 0 into 0 8.093 * [backup-simplify]: Simplify 0 into 0 8.094 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 8.095 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 8.095 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 8.095 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 8.095 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 8.095 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 8.095 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 8.095 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 8.095 * [taylor]: Taking taylor expansion of 1/2 in k 8.095 * [backup-simplify]: Simplify 1/2 into 1/2 8.095 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.095 * [taylor]: Taking taylor expansion of k in k 8.095 * [backup-simplify]: Simplify 0 into 0 8.095 * [backup-simplify]: Simplify 1 into 1 8.096 * [backup-simplify]: Simplify (/ 1 1) into 1 8.096 * [taylor]: Taking taylor expansion of 1/2 in k 8.096 * [backup-simplify]: Simplify 1/2 into 1/2 8.096 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 8.096 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 8.096 * [taylor]: Taking taylor expansion of -2 in k 8.096 * [backup-simplify]: Simplify -2 into -2 8.096 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.096 * [taylor]: Taking taylor expansion of PI in k 8.096 * [backup-simplify]: Simplify PI into PI 8.096 * [taylor]: Taking taylor expansion of n in k 8.096 * [backup-simplify]: Simplify n into n 8.096 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.096 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 8.096 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 8.097 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 8.097 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 8.097 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 8.097 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 8.097 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 8.097 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 8.097 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 8.098 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 8.098 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.098 * [taylor]: Taking taylor expansion of 1/2 in n 8.098 * [backup-simplify]: Simplify 1/2 into 1/2 8.098 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.098 * [taylor]: Taking taylor expansion of k in n 8.098 * [backup-simplify]: Simplify k into k 8.098 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.098 * [taylor]: Taking taylor expansion of 1/2 in n 8.098 * [backup-simplify]: Simplify 1/2 into 1/2 8.098 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 8.098 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 8.098 * [taylor]: Taking taylor expansion of -2 in n 8.098 * [backup-simplify]: Simplify -2 into -2 8.098 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.098 * [taylor]: Taking taylor expansion of PI in n 8.098 * [backup-simplify]: Simplify PI into PI 8.098 * [taylor]: Taking taylor expansion of n in n 8.098 * [backup-simplify]: Simplify 0 into 0 8.098 * [backup-simplify]: Simplify 1 into 1 8.099 * [backup-simplify]: Simplify (/ PI 1) into PI 8.099 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 8.100 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 8.100 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.100 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 8.102 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 8.103 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 8.104 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 8.104 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 8.104 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 8.104 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 8.104 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 8.104 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.104 * [taylor]: Taking taylor expansion of 1/2 in n 8.104 * [backup-simplify]: Simplify 1/2 into 1/2 8.104 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.104 * [taylor]: Taking taylor expansion of k in n 8.104 * [backup-simplify]: Simplify k into k 8.105 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.105 * [taylor]: Taking taylor expansion of 1/2 in n 8.105 * [backup-simplify]: Simplify 1/2 into 1/2 8.105 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 8.105 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 8.105 * [taylor]: Taking taylor expansion of -2 in n 8.105 * [backup-simplify]: Simplify -2 into -2 8.105 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.105 * [taylor]: Taking taylor expansion of PI in n 8.105 * [backup-simplify]: Simplify PI into PI 8.105 * [taylor]: Taking taylor expansion of n in n 8.105 * [backup-simplify]: Simplify 0 into 0 8.105 * [backup-simplify]: Simplify 1 into 1 8.105 * [backup-simplify]: Simplify (/ PI 1) into PI 8.106 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 8.107 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 8.107 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.107 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 8.108 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 8.110 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 8.111 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 8.111 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 8.111 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 8.111 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 8.111 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 8.111 * [taylor]: Taking taylor expansion of 1/2 in k 8.111 * [backup-simplify]: Simplify 1/2 into 1/2 8.111 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.111 * [taylor]: Taking taylor expansion of k in k 8.111 * [backup-simplify]: Simplify 0 into 0 8.111 * [backup-simplify]: Simplify 1 into 1 8.112 * [backup-simplify]: Simplify (/ 1 1) into 1 8.112 * [taylor]: Taking taylor expansion of 1/2 in k 8.112 * [backup-simplify]: Simplify 1/2 into 1/2 8.112 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 8.112 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 8.112 * [taylor]: Taking taylor expansion of (* -2 PI) in k 8.112 * [taylor]: Taking taylor expansion of -2 in k 8.112 * [backup-simplify]: Simplify -2 into -2 8.112 * [taylor]: Taking taylor expansion of PI in k 8.112 * [backup-simplify]: Simplify PI into PI 8.112 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 8.113 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 8.113 * [taylor]: Taking taylor expansion of (log n) in k 8.113 * [taylor]: Taking taylor expansion of n in k 8.113 * [backup-simplify]: Simplify n into n 8.114 * [backup-simplify]: Simplify (log n) into (log n) 8.114 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 8.114 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 8.114 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 8.116 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 8.117 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 8.119 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 8.120 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 8.121 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.122 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 8.124 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 8.124 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.124 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 8.125 * [backup-simplify]: Simplify (+ 0 0) into 0 8.126 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 8.127 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 8.129 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 8.129 * [taylor]: Taking taylor expansion of 0 in k 8.129 * [backup-simplify]: Simplify 0 into 0 8.129 * [backup-simplify]: Simplify 0 into 0 8.129 * [backup-simplify]: Simplify 0 into 0 8.131 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.132 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 8.135 * [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 8.135 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.136 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 8.137 * [backup-simplify]: Simplify (+ 0 0) into 0 8.138 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 8.140 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 8.142 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 8.142 * [taylor]: Taking taylor expansion of 0 in k 8.142 * [backup-simplify]: Simplify 0 into 0 8.142 * [backup-simplify]: Simplify 0 into 0 8.142 * [backup-simplify]: Simplify 0 into 0 8.142 * [backup-simplify]: Simplify 0 into 0 8.143 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.145 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.151 * [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 8.151 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.153 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 8.154 * [backup-simplify]: Simplify (+ 0 0) into 0 8.155 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 8.157 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 8.160 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 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 8.160 * [taylor]: Taking taylor expansion of 0 in k 8.160 * [backup-simplify]: Simplify 0 into 0 8.160 * [backup-simplify]: Simplify 0 into 0 8.162 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 8.162 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1) 8.162 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) 8.162 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 8.162 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 8.162 * [taylor]: Taking taylor expansion of 2 in n 8.162 * [backup-simplify]: Simplify 2 into 2 8.162 * [taylor]: Taking taylor expansion of (* n PI) in n 8.162 * [taylor]: Taking taylor expansion of n in n 8.162 * [backup-simplify]: Simplify 0 into 0 8.162 * [backup-simplify]: Simplify 1 into 1 8.163 * [taylor]: Taking taylor expansion of PI in n 8.163 * [backup-simplify]: Simplify PI into PI 8.163 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 8.163 * [taylor]: Taking taylor expansion of 2 in n 8.163 * [backup-simplify]: Simplify 2 into 2 8.163 * [taylor]: Taking taylor expansion of (* n PI) in n 8.163 * [taylor]: Taking taylor expansion of n in n 8.163 * [backup-simplify]: Simplify 0 into 0 8.163 * [backup-simplify]: Simplify 1 into 1 8.163 * [taylor]: Taking taylor expansion of PI in n 8.163 * [backup-simplify]: Simplify PI into PI 8.163 * [backup-simplify]: Simplify (* 0 PI) into 0 8.164 * [backup-simplify]: Simplify (* 2 0) into 0 8.164 * [backup-simplify]: Simplify 0 into 0 8.166 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.168 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 8.168 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 8.176 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.177 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 8.177 * [backup-simplify]: Simplify 0 into 0 8.178 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 8.180 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 8.180 * [backup-simplify]: Simplify 0 into 0 8.181 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 8.182 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 8.182 * [backup-simplify]: Simplify 0 into 0 8.184 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 8.186 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 8.186 * [backup-simplify]: Simplify 0 into 0 8.188 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 8.189 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 8.189 * [backup-simplify]: Simplify 0 into 0 8.191 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 8.193 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 8.193 * [backup-simplify]: Simplify 0 into 0 8.194 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 8.194 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) 8.194 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 8.194 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 8.194 * [taylor]: Taking taylor expansion of 2 in n 8.194 * [backup-simplify]: Simplify 2 into 2 8.194 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.194 * [taylor]: Taking taylor expansion of PI in n 8.194 * [backup-simplify]: Simplify PI into PI 8.194 * [taylor]: Taking taylor expansion of n in n 8.194 * [backup-simplify]: Simplify 0 into 0 8.194 * [backup-simplify]: Simplify 1 into 1 8.195 * [backup-simplify]: Simplify (/ PI 1) into PI 8.195 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 8.195 * [taylor]: Taking taylor expansion of 2 in n 8.195 * [backup-simplify]: Simplify 2 into 2 8.195 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.195 * [taylor]: Taking taylor expansion of PI in n 8.195 * [backup-simplify]: Simplify PI into PI 8.195 * [taylor]: Taking taylor expansion of n in n 8.195 * [backup-simplify]: Simplify 0 into 0 8.195 * [backup-simplify]: Simplify 1 into 1 8.195 * [backup-simplify]: Simplify (/ PI 1) into PI 8.196 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 8.196 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 8.197 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.197 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 8.197 * [backup-simplify]: Simplify 0 into 0 8.198 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.198 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 8.198 * [backup-simplify]: Simplify 0 into 0 8.199 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.200 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.200 * [backup-simplify]: Simplify 0 into 0 8.200 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.201 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 8.201 * [backup-simplify]: Simplify 0 into 0 8.202 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.203 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 8.203 * [backup-simplify]: Simplify 0 into 0 8.204 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.205 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 8.205 * [backup-simplify]: Simplify 0 into 0 8.205 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 8.205 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n)) 8.205 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 8.205 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 8.205 * [taylor]: Taking taylor expansion of -2 in n 8.205 * [backup-simplify]: Simplify -2 into -2 8.205 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.205 * [taylor]: Taking taylor expansion of PI in n 8.205 * [backup-simplify]: Simplify PI into PI 8.205 * [taylor]: Taking taylor expansion of n in n 8.205 * [backup-simplify]: Simplify 0 into 0 8.205 * [backup-simplify]: Simplify 1 into 1 8.206 * [backup-simplify]: Simplify (/ PI 1) into PI 8.206 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 8.206 * [taylor]: Taking taylor expansion of -2 in n 8.206 * [backup-simplify]: Simplify -2 into -2 8.206 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.206 * [taylor]: Taking taylor expansion of PI in n 8.206 * [backup-simplify]: Simplify PI into PI 8.206 * [taylor]: Taking taylor expansion of n in n 8.206 * [backup-simplify]: Simplify 0 into 0 8.206 * [backup-simplify]: Simplify 1 into 1 8.206 * [backup-simplify]: Simplify (/ PI 1) into PI 8.207 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 8.207 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 8.207 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.208 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 8.208 * [backup-simplify]: Simplify 0 into 0 8.209 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.209 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 8.209 * [backup-simplify]: Simplify 0 into 0 8.210 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.211 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.211 * [backup-simplify]: Simplify 0 into 0 8.211 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.212 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 8.212 * [backup-simplify]: Simplify 0 into 0 8.213 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.214 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 8.214 * [backup-simplify]: Simplify 0 into 0 8.214 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.215 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 8.215 * [backup-simplify]: Simplify 0 into 0 8.216 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 8.216 * * * * [progress]: [ 3 / 4 ] generating series at (2 2) 8.216 * [backup-simplify]: Simplify (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) into (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) 8.216 * [approximate]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in (k n) around 0 8.216 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in n 8.216 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 8.216 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 8.216 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 8.216 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 8.216 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 8.216 * [taylor]: Taking taylor expansion of 1/2 in n 8.216 * [backup-simplify]: Simplify 1/2 into 1/2 8.216 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 8.216 * [taylor]: Taking taylor expansion of 1/2 in n 8.216 * [backup-simplify]: Simplify 1/2 into 1/2 8.216 * [taylor]: Taking taylor expansion of k in n 8.216 * [backup-simplify]: Simplify k into k 8.216 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 8.217 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 8.217 * [taylor]: Taking taylor expansion of 2 in n 8.217 * [backup-simplify]: Simplify 2 into 2 8.217 * [taylor]: Taking taylor expansion of (* n PI) in n 8.217 * [taylor]: Taking taylor expansion of n in n 8.217 * [backup-simplify]: Simplify 0 into 0 8.217 * [backup-simplify]: Simplify 1 into 1 8.217 * [taylor]: Taking taylor expansion of PI in n 8.217 * [backup-simplify]: Simplify PI into PI 8.217 * [backup-simplify]: Simplify (* 0 PI) into 0 8.217 * [backup-simplify]: Simplify (* 2 0) into 0 8.218 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.219 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 8.220 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.220 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 8.220 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 8.220 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 8.221 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 8.221 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 8.223 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 8.224 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 8.224 * [taylor]: Taking taylor expansion of (sqrt k) in n 8.224 * [taylor]: Taking taylor expansion of k in n 8.224 * [backup-simplify]: Simplify k into k 8.224 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 8.224 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 8.224 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k 8.224 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 8.224 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 8.224 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 8.224 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 8.224 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 8.224 * [taylor]: Taking taylor expansion of 1/2 in k 8.224 * [backup-simplify]: Simplify 1/2 into 1/2 8.224 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 8.224 * [taylor]: Taking taylor expansion of 1/2 in k 8.224 * [backup-simplify]: Simplify 1/2 into 1/2 8.224 * [taylor]: Taking taylor expansion of k in k 8.224 * [backup-simplify]: Simplify 0 into 0 8.224 * [backup-simplify]: Simplify 1 into 1 8.224 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 8.224 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 8.224 * [taylor]: Taking taylor expansion of 2 in k 8.225 * [backup-simplify]: Simplify 2 into 2 8.225 * [taylor]: Taking taylor expansion of (* n PI) in k 8.225 * [taylor]: Taking taylor expansion of n in k 8.225 * [backup-simplify]: Simplify n into n 8.225 * [taylor]: Taking taylor expansion of PI in k 8.225 * [backup-simplify]: Simplify PI into PI 8.225 * [backup-simplify]: Simplify (* n PI) into (* n PI) 8.225 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 8.225 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 8.225 * [backup-simplify]: Simplify (* 1/2 0) into 0 8.226 * [backup-simplify]: Simplify (- 0) into 0 8.226 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 8.226 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 8.226 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 8.226 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 8.226 * [taylor]: Taking taylor expansion of (sqrt k) in k 8.227 * [taylor]: Taking taylor expansion of k in k 8.227 * [backup-simplify]: Simplify 0 into 0 8.227 * [backup-simplify]: Simplify 1 into 1 8.227 * [backup-simplify]: Simplify (sqrt 0) into 0 8.228 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.228 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k 8.228 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 8.228 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 8.228 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 8.228 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 8.229 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 8.229 * [taylor]: Taking taylor expansion of 1/2 in k 8.229 * [backup-simplify]: Simplify 1/2 into 1/2 8.229 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 8.229 * [taylor]: Taking taylor expansion of 1/2 in k 8.229 * [backup-simplify]: Simplify 1/2 into 1/2 8.229 * [taylor]: Taking taylor expansion of k in k 8.229 * [backup-simplify]: Simplify 0 into 0 8.229 * [backup-simplify]: Simplify 1 into 1 8.229 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 8.229 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 8.229 * [taylor]: Taking taylor expansion of 2 in k 8.229 * [backup-simplify]: Simplify 2 into 2 8.229 * [taylor]: Taking taylor expansion of (* n PI) in k 8.229 * [taylor]: Taking taylor expansion of n in k 8.229 * [backup-simplify]: Simplify n into n 8.229 * [taylor]: Taking taylor expansion of PI in k 8.229 * [backup-simplify]: Simplify PI into PI 8.229 * [backup-simplify]: Simplify (* n PI) into (* n PI) 8.229 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 8.229 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 8.230 * [backup-simplify]: Simplify (* 1/2 0) into 0 8.230 * [backup-simplify]: Simplify (- 0) into 0 8.230 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 8.231 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 8.231 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 8.231 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 8.231 * [taylor]: Taking taylor expansion of (sqrt k) in k 8.231 * [taylor]: Taking taylor expansion of k in k 8.231 * [backup-simplify]: Simplify 0 into 0 8.231 * [backup-simplify]: Simplify 1 into 1 8.231 * [backup-simplify]: Simplify (sqrt 0) into 0 8.233 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.233 * [backup-simplify]: Simplify (* (sqrt (/ 1 (* PI (* n 2)))) 0) into 0 8.233 * [taylor]: Taking taylor expansion of 0 in n 8.233 * [backup-simplify]: Simplify 0 into 0 8.233 * [backup-simplify]: Simplify 0 into 0 8.233 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 8.234 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 8.235 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 8.235 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 8.236 * [backup-simplify]: Simplify (- 1/2) into -1/2 8.236 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 8.237 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 8.237 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 8.238 * [backup-simplify]: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) 8.239 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) 8.239 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n 8.239 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n 8.240 * [taylor]: Taking taylor expansion of +nan.0 in n 8.240 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.240 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n 8.240 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 8.240 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n 8.240 * [taylor]: Taking taylor expansion of (* n PI) in n 8.240 * [taylor]: Taking taylor expansion of n in n 8.240 * [backup-simplify]: Simplify 0 into 0 8.240 * [backup-simplify]: Simplify 1 into 1 8.240 * [taylor]: Taking taylor expansion of PI in n 8.240 * [backup-simplify]: Simplify PI into PI 8.240 * [backup-simplify]: Simplify (* 0 PI) into 0 8.242 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.242 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 8.243 * [backup-simplify]: Simplify (sqrt 0) into 0 8.245 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 8.245 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n 8.245 * [taylor]: Taking taylor expansion of 1/2 in n 8.245 * [backup-simplify]: Simplify 1/2 into 1/2 8.245 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2) 8.246 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 8.249 * [backup-simplify]: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 8.250 * [backup-simplify]: Simplify (* 0 (sqrt 1/2)) into 0 8.256 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 8.259 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 8.262 * [backup-simplify]: Simplify (- (* +nan.0 (/ (sqrt 1/2) PI))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 8.262 * [backup-simplify]: Simplify 0 into 0 8.265 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.266 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 8.267 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 8.268 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0 8.269 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 8.270 * [backup-simplify]: Simplify (- 0) into 0 8.270 * [backup-simplify]: Simplify (+ 0 0) into 0 8.271 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 8.272 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 8.275 * [backup-simplify]: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) (pow (* 2 (* n PI)) 1/2))) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))) 8.281 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (+ (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) +nan.0) (* (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) 8.281 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) in n 8.281 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))))) in n 8.282 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) in n 8.282 * [taylor]: Taking taylor expansion of +nan.0 in n 8.282 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.282 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))) in n 8.282 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) in n 8.282 * [taylor]: Taking taylor expansion of (sqrt 2) in n 8.282 * [taylor]: Taking taylor expansion of 2 in n 8.282 * [backup-simplify]: Simplify 2 into 2 8.282 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 8.283 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 8.283 * [taylor]: Taking taylor expansion of (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2)) in n 8.283 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 8.283 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 8.283 * [taylor]: Taking taylor expansion of 2 in n 8.283 * [backup-simplify]: Simplify 2 into 2 8.283 * [taylor]: Taking taylor expansion of (* n PI) in n 8.283 * [taylor]: Taking taylor expansion of n in n 8.283 * [backup-simplify]: Simplify 0 into 0 8.283 * [backup-simplify]: Simplify 1 into 1 8.283 * [taylor]: Taking taylor expansion of PI in n 8.283 * [backup-simplify]: Simplify PI into PI 8.284 * [backup-simplify]: Simplify (* 0 PI) into 0 8.284 * [backup-simplify]: Simplify (* 2 0) into 0 8.286 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.287 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 8.288 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.288 * [taylor]: Taking taylor expansion of (pow (sqrt 1/2) 2) in n 8.288 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n 8.288 * [taylor]: Taking taylor expansion of 1/2 in n 8.289 * [backup-simplify]: Simplify 1/2 into 1/2 8.289 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2) 8.290 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 8.290 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 8.290 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n 8.290 * [taylor]: Taking taylor expansion of (* n PI) in n 8.290 * [taylor]: Taking taylor expansion of n in n 8.290 * [backup-simplify]: Simplify 0 into 0 8.290 * [backup-simplify]: Simplify 1 into 1 8.290 * [taylor]: Taking taylor expansion of PI in n 8.290 * [backup-simplify]: Simplify PI into PI 8.290 * [backup-simplify]: Simplify (* 0 PI) into 0 8.292 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.293 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 8.293 * [backup-simplify]: Simplify (sqrt 0) into 0 8.295 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 8.295 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n 8.295 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n 8.295 * [taylor]: Taking taylor expansion of +nan.0 in n 8.295 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.295 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n 8.295 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 8.295 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n 8.295 * [taylor]: Taking taylor expansion of (* n PI) in n 8.295 * [taylor]: Taking taylor expansion of n in n 8.295 * [backup-simplify]: Simplify 0 into 0 8.295 * [backup-simplify]: Simplify 1 into 1 8.295 * [taylor]: Taking taylor expansion of PI in n 8.295 * [backup-simplify]: Simplify PI into PI 8.296 * [backup-simplify]: Simplify (* 0 PI) into 0 8.297 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.298 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 8.298 * [backup-simplify]: Simplify (sqrt 0) into 0 8.300 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 8.300 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n 8.300 * [taylor]: Taking taylor expansion of 1/2 in n 8.300 * [backup-simplify]: Simplify 1/2 into 1/2 8.301 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2) 8.301 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 8.310 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 8.311 * [backup-simplify]: Simplify (* (sqrt 1/2) (sqrt 1/2)) into (pow (sqrt 1/2) 2) 8.313 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (pow (sqrt 1/2) 2)) into (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))) 8.315 * [backup-simplify]: Simplify (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) into (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) 8.317 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 8.318 * [backup-simplify]: Simplify (+ (* (sqrt 1/2) 0) (* 0 (sqrt 1/2))) into 0 8.318 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.319 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 8.320 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 8.321 * [backup-simplify]: Simplify (+ (* (+ (log n) (log (* 2 PI))) 0) (* 0 (pow (sqrt 1/2) 2))) into 0 8.323 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))))) into 0 8.325 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) (/ +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) 8.327 * [backup-simplify]: Simplify (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) 0) into 0 8.335 * [backup-simplify]: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) 8.337 * [backup-simplify]: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 8.338 * [backup-simplify]: Simplify (* 0 (sqrt 1/2)) into 0 8.341 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 8.343 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 8.352 * [backup-simplify]: Simplify (+ (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 8.364 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 8.383 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 8.384 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1/2))) into 0 8.385 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.385 * [backup-simplify]: Simplify (- (+ (* (/ 1 PI) (/ 0 PI)))) into 0 8.388 * [backup-simplify]: Simplify (/ (- 0 (pow (/ +nan.0 PI) 2) (+)) (* 2 0)) into (/ +nan.0 (pow PI 2)) 8.392 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* (/ +nan.0 PI) 0) (* (/ +nan.0 (pow PI 2)) (sqrt 1/2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 8.398 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 8.401 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 8.403 * [backup-simplify]: Simplify (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 8.423 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) (* n k)) (+ (* (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) (pow (* 1 k) 2)) (* (- (* +nan.0 (/ (sqrt 1/2) PI))) (* 1 k)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (+ (* +nan.0 (/ (* n (* (sqrt 1/2) k)) (pow PI 2))) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI))))))))))) 8.424 * [backup-simplify]: Simplify (/ (sqrt (/ 1 k)) (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2)))) into (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) 8.424 * [approximate]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in (k n) around 0 8.424 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in n 8.424 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 8.424 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 8.424 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 8.424 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 8.424 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 8.424 * [taylor]: Taking taylor expansion of 1/2 in n 8.424 * [backup-simplify]: Simplify 1/2 into 1/2 8.424 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.424 * [taylor]: Taking taylor expansion of 1/2 in n 8.424 * [backup-simplify]: Simplify 1/2 into 1/2 8.424 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.424 * [taylor]: Taking taylor expansion of k in n 8.424 * [backup-simplify]: Simplify k into k 8.424 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.424 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 8.424 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 8.424 * [taylor]: Taking taylor expansion of 2 in n 8.424 * [backup-simplify]: Simplify 2 into 2 8.424 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.424 * [taylor]: Taking taylor expansion of PI in n 8.424 * [backup-simplify]: Simplify PI into PI 8.424 * [taylor]: Taking taylor expansion of n in n 8.424 * [backup-simplify]: Simplify 0 into 0 8.424 * [backup-simplify]: Simplify 1 into 1 8.425 * [backup-simplify]: Simplify (/ PI 1) into PI 8.425 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 8.426 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.426 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.426 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 8.426 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 8.427 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 8.428 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 8.428 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 8.429 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 8.429 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 8.429 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.429 * [taylor]: Taking taylor expansion of k in n 8.429 * [backup-simplify]: Simplify k into k 8.429 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.429 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 8.429 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.429 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 8.429 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 8.429 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 8.429 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 8.429 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 8.429 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 8.429 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 8.429 * [taylor]: Taking taylor expansion of 1/2 in k 8.429 * [backup-simplify]: Simplify 1/2 into 1/2 8.429 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 8.429 * [taylor]: Taking taylor expansion of 1/2 in k 8.429 * [backup-simplify]: Simplify 1/2 into 1/2 8.429 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.430 * [taylor]: Taking taylor expansion of k in k 8.430 * [backup-simplify]: Simplify 0 into 0 8.430 * [backup-simplify]: Simplify 1 into 1 8.430 * [backup-simplify]: Simplify (/ 1 1) into 1 8.430 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 8.430 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 8.430 * [taylor]: Taking taylor expansion of 2 in k 8.430 * [backup-simplify]: Simplify 2 into 2 8.430 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.430 * [taylor]: Taking taylor expansion of PI in k 8.430 * [backup-simplify]: Simplify PI into PI 8.430 * [taylor]: Taking taylor expansion of n in k 8.430 * [backup-simplify]: Simplify n into n 8.430 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.430 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 8.430 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 8.430 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 8.431 * [backup-simplify]: Simplify (- 1/2) into -1/2 8.431 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 8.431 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 8.431 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 8.431 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 8.431 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.431 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.431 * [taylor]: Taking taylor expansion of k in k 8.431 * [backup-simplify]: Simplify 0 into 0 8.431 * [backup-simplify]: Simplify 1 into 1 8.432 * [backup-simplify]: Simplify (/ 1 1) into 1 8.432 * [backup-simplify]: Simplify (sqrt 0) into 0 8.433 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.433 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 8.433 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 8.433 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 8.433 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 8.433 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 8.433 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 8.433 * [taylor]: Taking taylor expansion of 1/2 in k 8.433 * [backup-simplify]: Simplify 1/2 into 1/2 8.433 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 8.433 * [taylor]: Taking taylor expansion of 1/2 in k 8.433 * [backup-simplify]: Simplify 1/2 into 1/2 8.433 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.433 * [taylor]: Taking taylor expansion of k in k 8.433 * [backup-simplify]: Simplify 0 into 0 8.433 * [backup-simplify]: Simplify 1 into 1 8.433 * [backup-simplify]: Simplify (/ 1 1) into 1 8.433 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 8.433 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 8.433 * [taylor]: Taking taylor expansion of 2 in k 8.433 * [backup-simplify]: Simplify 2 into 2 8.433 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.433 * [taylor]: Taking taylor expansion of PI in k 8.433 * [backup-simplify]: Simplify PI into PI 8.433 * [taylor]: Taking taylor expansion of n in k 8.433 * [backup-simplify]: Simplify n into n 8.433 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.434 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 8.434 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 8.434 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 8.434 * [backup-simplify]: Simplify (- 1/2) into -1/2 8.435 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 8.435 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 8.435 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 8.435 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 8.435 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.435 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.436 * [taylor]: Taking taylor expansion of k in k 8.436 * [backup-simplify]: Simplify 0 into 0 8.436 * [backup-simplify]: Simplify 1 into 1 8.436 * [backup-simplify]: Simplify (/ 1 1) into 1 8.436 * [backup-simplify]: Simplify (sqrt 0) into 0 8.438 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.438 * [backup-simplify]: Simplify (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0 8.438 * [taylor]: Taking taylor expansion of 0 in n 8.438 * [backup-simplify]: Simplify 0 into 0 8.438 * [backup-simplify]: Simplify 0 into 0 8.439 * [backup-simplify]: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 8.440 * [backup-simplify]: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 8.440 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 8.440 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 8.440 * [taylor]: Taking taylor expansion of +nan.0 in n 8.440 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.440 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 8.440 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 8.440 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 8.440 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 8.440 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 8.440 * [taylor]: Taking taylor expansion of 1/2 in n 8.440 * [backup-simplify]: Simplify 1/2 into 1/2 8.440 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.440 * [taylor]: Taking taylor expansion of 1/2 in n 8.440 * [backup-simplify]: Simplify 1/2 into 1/2 8.440 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.440 * [taylor]: Taking taylor expansion of k in n 8.440 * [backup-simplify]: Simplify k into k 8.440 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.440 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 8.440 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 8.440 * [taylor]: Taking taylor expansion of 2 in n 8.440 * [backup-simplify]: Simplify 2 into 2 8.440 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.440 * [taylor]: Taking taylor expansion of PI in n 8.440 * [backup-simplify]: Simplify PI into PI 8.440 * [taylor]: Taking taylor expansion of n in n 8.440 * [backup-simplify]: Simplify 0 into 0 8.440 * [backup-simplify]: Simplify 1 into 1 8.441 * [backup-simplify]: Simplify (/ PI 1) into PI 8.442 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 8.443 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.443 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.443 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 8.443 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 8.444 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 8.446 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 8.447 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 8.448 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 8.450 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 8.450 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 8.451 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 8.451 * [backup-simplify]: Simplify 0 into 0 8.452 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 8.454 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.454 * [backup-simplify]: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 8.455 * [backup-simplify]: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 8.455 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 8.455 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 8.455 * [taylor]: Taking taylor expansion of +nan.0 in n 8.455 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.455 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 8.455 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 8.455 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 8.455 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 8.455 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 8.455 * [taylor]: Taking taylor expansion of 1/2 in n 8.455 * [backup-simplify]: Simplify 1/2 into 1/2 8.455 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.455 * [taylor]: Taking taylor expansion of 1/2 in n 8.455 * [backup-simplify]: Simplify 1/2 into 1/2 8.455 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.455 * [taylor]: Taking taylor expansion of k in n 8.455 * [backup-simplify]: Simplify k into k 8.455 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.455 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 8.455 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 8.455 * [taylor]: Taking taylor expansion of 2 in n 8.455 * [backup-simplify]: Simplify 2 into 2 8.455 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.455 * [taylor]: Taking taylor expansion of PI in n 8.455 * [backup-simplify]: Simplify PI into PI 8.455 * [taylor]: Taking taylor expansion of n in n 8.455 * [backup-simplify]: Simplify 0 into 0 8.455 * [backup-simplify]: Simplify 1 into 1 8.455 * [backup-simplify]: Simplify (/ PI 1) into PI 8.456 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 8.456 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.456 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.456 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 8.456 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 8.457 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 8.458 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 8.459 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 8.460 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 8.460 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 8.461 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 8.462 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 8.462 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.463 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 8.464 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 8.464 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.464 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 8.465 * [backup-simplify]: Simplify (- 0) into 0 8.465 * [backup-simplify]: Simplify (+ 0 0) into 0 8.466 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 8.467 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 8.468 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 8.469 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 8.470 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 8.471 * [backup-simplify]: Simplify (- 0) into 0 8.471 * [backup-simplify]: Simplify 0 into 0 8.471 * [backup-simplify]: Simplify 0 into 0 8.471 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.474 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.474 * [backup-simplify]: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 8.475 * [backup-simplify]: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 8.475 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 8.475 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 8.475 * [taylor]: Taking taylor expansion of +nan.0 in n 8.475 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.475 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 8.475 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 8.475 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 8.475 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 8.475 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 8.475 * [taylor]: Taking taylor expansion of 1/2 in n 8.475 * [backup-simplify]: Simplify 1/2 into 1/2 8.475 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.475 * [taylor]: Taking taylor expansion of 1/2 in n 8.475 * [backup-simplify]: Simplify 1/2 into 1/2 8.475 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.475 * [taylor]: Taking taylor expansion of k in n 8.475 * [backup-simplify]: Simplify k into k 8.475 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.475 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 8.475 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 8.475 * [taylor]: Taking taylor expansion of 2 in n 8.475 * [backup-simplify]: Simplify 2 into 2 8.475 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.475 * [taylor]: Taking taylor expansion of PI in n 8.475 * [backup-simplify]: Simplify PI into PI 8.475 * [taylor]: Taking taylor expansion of n in n 8.475 * [backup-simplify]: Simplify 0 into 0 8.475 * [backup-simplify]: Simplify 1 into 1 8.475 * [backup-simplify]: Simplify (/ PI 1) into PI 8.476 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 8.476 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.476 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.477 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 8.477 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 8.478 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 8.478 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 8.479 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 8.480 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 8.480 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 8.481 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 8.482 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 8.486 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))))))))) 8.487 * [backup-simplify]: Simplify (/ (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2)))) into (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) 8.487 * [approximate]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in (k n) around 0 8.487 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 8.488 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 8.488 * [taylor]: Taking taylor expansion of (/ -1 k) in n 8.488 * [taylor]: Taking taylor expansion of -1 in n 8.488 * [backup-simplify]: Simplify -1 into -1 8.488 * [taylor]: Taking taylor expansion of k in n 8.488 * [backup-simplify]: Simplify k into k 8.488 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 8.488 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 8.488 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 8.488 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 8.488 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 8.488 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 8.488 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 8.488 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 8.488 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.488 * [taylor]: Taking taylor expansion of 1/2 in n 8.488 * [backup-simplify]: Simplify 1/2 into 1/2 8.488 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.488 * [taylor]: Taking taylor expansion of k in n 8.488 * [backup-simplify]: Simplify k into k 8.488 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.488 * [taylor]: Taking taylor expansion of 1/2 in n 8.488 * [backup-simplify]: Simplify 1/2 into 1/2 8.488 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 8.488 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 8.488 * [taylor]: Taking taylor expansion of -2 in n 8.489 * [backup-simplify]: Simplify -2 into -2 8.489 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.489 * [taylor]: Taking taylor expansion of PI in n 8.489 * [backup-simplify]: Simplify PI into PI 8.489 * [taylor]: Taking taylor expansion of n in n 8.489 * [backup-simplify]: Simplify 0 into 0 8.489 * [backup-simplify]: Simplify 1 into 1 8.489 * [backup-simplify]: Simplify (/ PI 1) into PI 8.490 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 8.491 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 8.491 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.491 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 8.493 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 8.494 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 8.496 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 8.497 * [backup-simplify]: Simplify (/ (sqrt (/ -1 k)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ (sqrt (/ -1 k)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 8.497 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 8.497 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.497 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.497 * [taylor]: Taking taylor expansion of -1 in k 8.497 * [backup-simplify]: Simplify -1 into -1 8.497 * [taylor]: Taking taylor expansion of k in k 8.497 * [backup-simplify]: Simplify 0 into 0 8.497 * [backup-simplify]: Simplify 1 into 1 8.498 * [backup-simplify]: Simplify (/ -1 1) into -1 8.498 * [backup-simplify]: Simplify (sqrt 0) into 0 8.499 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.499 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 8.499 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 8.499 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 8.499 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 8.499 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 8.499 * [taylor]: Taking taylor expansion of 1/2 in k 8.500 * [backup-simplify]: Simplify 1/2 into 1/2 8.500 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.500 * [taylor]: Taking taylor expansion of k in k 8.500 * [backup-simplify]: Simplify 0 into 0 8.500 * [backup-simplify]: Simplify 1 into 1 8.500 * [backup-simplify]: Simplify (/ 1 1) into 1 8.500 * [taylor]: Taking taylor expansion of 1/2 in k 8.500 * [backup-simplify]: Simplify 1/2 into 1/2 8.500 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 8.500 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 8.500 * [taylor]: Taking taylor expansion of -2 in k 8.500 * [backup-simplify]: Simplify -2 into -2 8.500 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.500 * [taylor]: Taking taylor expansion of PI in k 8.500 * [backup-simplify]: Simplify PI into PI 8.500 * [taylor]: Taking taylor expansion of n in k 8.500 * [backup-simplify]: Simplify n into n 8.500 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.500 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 8.500 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 8.501 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 8.501 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 8.501 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 8.502 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 8.502 * [backup-simplify]: Simplify (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 8.502 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 8.502 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.502 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.502 * [taylor]: Taking taylor expansion of -1 in k 8.502 * [backup-simplify]: Simplify -1 into -1 8.502 * [taylor]: Taking taylor expansion of k in k 8.502 * [backup-simplify]: Simplify 0 into 0 8.502 * [backup-simplify]: Simplify 1 into 1 8.502 * [backup-simplify]: Simplify (/ -1 1) into -1 8.503 * [backup-simplify]: Simplify (sqrt 0) into 0 8.505 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.505 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 8.505 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 8.505 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 8.505 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 8.505 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 8.505 * [taylor]: Taking taylor expansion of 1/2 in k 8.505 * [backup-simplify]: Simplify 1/2 into 1/2 8.505 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.505 * [taylor]: Taking taylor expansion of k in k 8.505 * [backup-simplify]: Simplify 0 into 0 8.505 * [backup-simplify]: Simplify 1 into 1 8.506 * [backup-simplify]: Simplify (/ 1 1) into 1 8.506 * [taylor]: Taking taylor expansion of 1/2 in k 8.506 * [backup-simplify]: Simplify 1/2 into 1/2 8.506 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 8.506 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 8.506 * [taylor]: Taking taylor expansion of -2 in k 8.506 * [backup-simplify]: Simplify -2 into -2 8.506 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.506 * [taylor]: Taking taylor expansion of PI in k 8.506 * [backup-simplify]: Simplify PI into PI 8.506 * [taylor]: Taking taylor expansion of n in k 8.506 * [backup-simplify]: Simplify n into n 8.506 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.506 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 8.506 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 8.507 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 8.507 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 8.507 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 8.507 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 8.508 * [backup-simplify]: Simplify (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 8.508 * [taylor]: Taking taylor expansion of (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 8.508 * [taylor]: Taking taylor expansion of +nan.0 in n 8.508 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.508 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 8.508 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 8.508 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 8.508 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 8.508 * [taylor]: Taking taylor expansion of -2 in n 8.508 * [backup-simplify]: Simplify -2 into -2 8.508 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.508 * [taylor]: Taking taylor expansion of PI in n 8.508 * [backup-simplify]: Simplify PI into PI 8.508 * [taylor]: Taking taylor expansion of n in n 8.508 * [backup-simplify]: Simplify 0 into 0 8.508 * [backup-simplify]: Simplify 1 into 1 8.509 * [backup-simplify]: Simplify (/ PI 1) into PI 8.509 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 8.510 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 8.510 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 8.510 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.510 * [taylor]: Taking taylor expansion of 1/2 in n 8.510 * [backup-simplify]: Simplify 1/2 into 1/2 8.510 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.510 * [taylor]: Taking taylor expansion of k in n 8.510 * [backup-simplify]: Simplify k into k 8.510 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.510 * [taylor]: Taking taylor expansion of 1/2 in n 8.510 * [backup-simplify]: Simplify 1/2 into 1/2 8.512 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 8.512 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.512 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 8.513 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 8.515 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 8.516 * [backup-simplify]: Simplify (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 8.524 * [backup-simplify]: Simplify (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 8.525 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 8.528 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.529 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) 8.529 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 8.529 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 8.529 * [taylor]: Taking taylor expansion of +nan.0 in n 8.529 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.529 * [taylor]: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 8.529 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 8.529 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 8.529 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 8.529 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 8.529 * [taylor]: Taking taylor expansion of -2 in n 8.529 * [backup-simplify]: Simplify -2 into -2 8.529 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.529 * [taylor]: Taking taylor expansion of PI in n 8.529 * [backup-simplify]: Simplify PI into PI 8.529 * [taylor]: Taking taylor expansion of n in n 8.529 * [backup-simplify]: Simplify 0 into 0 8.530 * [backup-simplify]: Simplify 1 into 1 8.530 * [backup-simplify]: Simplify (/ PI 1) into PI 8.531 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 8.532 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 8.532 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 8.532 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.532 * [taylor]: Taking taylor expansion of 1/2 in n 8.532 * [backup-simplify]: Simplify 1/2 into 1/2 8.532 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.532 * [taylor]: Taking taylor expansion of k in n 8.532 * [backup-simplify]: Simplify k into k 8.532 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.532 * [taylor]: Taking taylor expansion of 1/2 in n 8.533 * [backup-simplify]: Simplify 1/2 into 1/2 8.534 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 8.534 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.535 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 8.536 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 8.537 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 8.538 * [backup-simplify]: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 8.540 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 8.541 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 8.542 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 8.543 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 8.543 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.543 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 8.544 * [backup-simplify]: Simplify (+ 0 0) into 0 8.544 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.545 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 8.546 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 8.547 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 8.548 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 8.550 * [backup-simplify]: Simplify (- (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0 8.550 * [backup-simplify]: Simplify 0 into 0 8.551 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.553 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.553 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) (* (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) 8.553 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 8.553 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 8.553 * [taylor]: Taking taylor expansion of +nan.0 in n 8.553 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.553 * [taylor]: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 8.553 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 8.554 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 8.554 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 8.554 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 8.554 * [taylor]: Taking taylor expansion of -2 in n 8.554 * [backup-simplify]: Simplify -2 into -2 8.554 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.554 * [taylor]: Taking taylor expansion of PI in n 8.554 * [backup-simplify]: Simplify PI into PI 8.554 * [taylor]: Taking taylor expansion of n in n 8.554 * [backup-simplify]: Simplify 0 into 0 8.554 * [backup-simplify]: Simplify 1 into 1 8.554 * [backup-simplify]: Simplify (/ PI 1) into PI 8.554 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 8.555 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 8.555 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 8.555 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.555 * [taylor]: Taking taylor expansion of 1/2 in n 8.555 * [backup-simplify]: Simplify 1/2 into 1/2 8.555 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.555 * [taylor]: Taking taylor expansion of k in n 8.555 * [backup-simplify]: Simplify k into k 8.555 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.555 * [taylor]: Taking taylor expansion of 1/2 in n 8.555 * [backup-simplify]: Simplify 1/2 into 1/2 8.556 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 8.556 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.556 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 8.557 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 8.558 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 8.558 * [backup-simplify]: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 8.559 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 8.560 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 8.561 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 8.563 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) 8.563 * * * * [progress]: [ 4 / 4 ] generating series at (2) 8.564 * [backup-simplify]: Simplify (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 8.564 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (k n) around 0 8.564 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 8.564 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 8.564 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.564 * [taylor]: Taking taylor expansion of k in n 8.564 * [backup-simplify]: Simplify k into k 8.564 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.564 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 8.564 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.564 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 8.564 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 8.564 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 8.564 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 8.564 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 8.564 * [taylor]: Taking taylor expansion of 1/2 in n 8.564 * [backup-simplify]: Simplify 1/2 into 1/2 8.564 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 8.564 * [taylor]: Taking taylor expansion of 1/2 in n 8.564 * [backup-simplify]: Simplify 1/2 into 1/2 8.564 * [taylor]: Taking taylor expansion of k in n 8.564 * [backup-simplify]: Simplify k into k 8.564 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 8.564 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 8.564 * [taylor]: Taking taylor expansion of 2 in n 8.564 * [backup-simplify]: Simplify 2 into 2 8.564 * [taylor]: Taking taylor expansion of (* n PI) in n 8.564 * [taylor]: Taking taylor expansion of n in n 8.564 * [backup-simplify]: Simplify 0 into 0 8.564 * [backup-simplify]: Simplify 1 into 1 8.564 * [taylor]: Taking taylor expansion of PI in n 8.564 * [backup-simplify]: Simplify PI into PI 8.565 * [backup-simplify]: Simplify (* 0 PI) into 0 8.565 * [backup-simplify]: Simplify (* 2 0) into 0 8.566 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.567 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 8.568 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.568 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 8.568 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 8.568 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 8.569 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 8.569 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 8.570 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 8.570 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 8.570 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.570 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.570 * [taylor]: Taking taylor expansion of k in k 8.570 * [backup-simplify]: Simplify 0 into 0 8.570 * [backup-simplify]: Simplify 1 into 1 8.571 * [backup-simplify]: Simplify (/ 1 1) into 1 8.571 * [backup-simplify]: Simplify (sqrt 0) into 0 8.572 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.572 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 8.572 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 8.572 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 8.572 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 8.572 * [taylor]: Taking taylor expansion of 1/2 in k 8.572 * [backup-simplify]: Simplify 1/2 into 1/2 8.572 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 8.572 * [taylor]: Taking taylor expansion of 1/2 in k 8.572 * [backup-simplify]: Simplify 1/2 into 1/2 8.572 * [taylor]: Taking taylor expansion of k in k 8.572 * [backup-simplify]: Simplify 0 into 0 8.572 * [backup-simplify]: Simplify 1 into 1 8.572 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 8.572 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 8.572 * [taylor]: Taking taylor expansion of 2 in k 8.572 * [backup-simplify]: Simplify 2 into 2 8.572 * [taylor]: Taking taylor expansion of (* n PI) in k 8.572 * [taylor]: Taking taylor expansion of n in k 8.572 * [backup-simplify]: Simplify n into n 8.572 * [taylor]: Taking taylor expansion of PI in k 8.572 * [backup-simplify]: Simplify PI into PI 8.572 * [backup-simplify]: Simplify (* n PI) into (* n PI) 8.572 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 8.572 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 8.572 * [backup-simplify]: Simplify (* 1/2 0) into 0 8.573 * [backup-simplify]: Simplify (- 0) into 0 8.573 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 8.573 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 8.573 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 8.573 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 8.573 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.573 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.573 * [taylor]: Taking taylor expansion of k in k 8.573 * [backup-simplify]: Simplify 0 into 0 8.573 * [backup-simplify]: Simplify 1 into 1 8.573 * [backup-simplify]: Simplify (/ 1 1) into 1 8.574 * [backup-simplify]: Simplify (sqrt 0) into 0 8.574 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.574 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 8.574 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 8.574 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 8.574 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 8.574 * [taylor]: Taking taylor expansion of 1/2 in k 8.574 * [backup-simplify]: Simplify 1/2 into 1/2 8.575 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 8.575 * [taylor]: Taking taylor expansion of 1/2 in k 8.575 * [backup-simplify]: Simplify 1/2 into 1/2 8.575 * [taylor]: Taking taylor expansion of k in k 8.575 * [backup-simplify]: Simplify 0 into 0 8.575 * [backup-simplify]: Simplify 1 into 1 8.575 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 8.575 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 8.575 * [taylor]: Taking taylor expansion of 2 in k 8.575 * [backup-simplify]: Simplify 2 into 2 8.575 * [taylor]: Taking taylor expansion of (* n PI) in k 8.575 * [taylor]: Taking taylor expansion of n in k 8.575 * [backup-simplify]: Simplify n into n 8.575 * [taylor]: Taking taylor expansion of PI in k 8.575 * [backup-simplify]: Simplify PI into PI 8.575 * [backup-simplify]: Simplify (* n PI) into (* n PI) 8.575 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 8.575 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 8.575 * [backup-simplify]: Simplify (* 1/2 0) into 0 8.575 * [backup-simplify]: Simplify (- 0) into 0 8.576 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 8.576 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 8.576 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 8.576 * [backup-simplify]: Simplify (* 0 (pow (* 2 (* n PI)) 1/2)) into 0 8.576 * [taylor]: Taking taylor expansion of 0 in n 8.576 * [backup-simplify]: Simplify 0 into 0 8.576 * [backup-simplify]: Simplify 0 into 0 8.576 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 8.577 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 8.577 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 8.578 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 8.578 * [backup-simplify]: Simplify (- 1/2) into -1/2 8.578 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 8.579 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 8.579 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 8.579 * [backup-simplify]: Simplify (+ (* 0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2))) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 8.579 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 8.579 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 8.579 * [taylor]: Taking taylor expansion of +nan.0 in n 8.579 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.579 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 8.579 * [taylor]: Taking taylor expansion of (sqrt 2) in n 8.580 * [taylor]: Taking taylor expansion of 2 in n 8.580 * [backup-simplify]: Simplify 2 into 2 8.580 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 8.581 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 8.581 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 8.581 * [taylor]: Taking taylor expansion of (* n PI) in n 8.581 * [taylor]: Taking taylor expansion of n in n 8.581 * [backup-simplify]: Simplify 0 into 0 8.581 * [backup-simplify]: Simplify 1 into 1 8.581 * [taylor]: Taking taylor expansion of PI in n 8.581 * [backup-simplify]: Simplify PI into PI 8.581 * [backup-simplify]: Simplify (* 0 PI) into 0 8.583 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.583 * [backup-simplify]: Simplify (sqrt 0) into 0 8.584 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 8.585 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 8.585 * [backup-simplify]: Simplify (* +nan.0 0) into 0 8.586 * [backup-simplify]: Simplify (- 0) into 0 8.586 * [backup-simplify]: Simplify 0 into 0 8.586 * [backup-simplify]: Simplify 0 into 0 8.586 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 8.587 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 8.589 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0 8.590 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 8.590 * [backup-simplify]: Simplify (- 0) into 0 8.591 * [backup-simplify]: Simplify (+ 0 0) into 0 8.592 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 8.593 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 8.593 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 8.596 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.597 * [backup-simplify]: Simplify (+ (* 0 (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))) (+ (* +nan.0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) 8.597 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n 8.597 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n 8.597 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 8.597 * [taylor]: Taking taylor expansion of +nan.0 in n 8.597 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.597 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 8.597 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 8.597 * [taylor]: Taking taylor expansion of (sqrt 2) in n 8.597 * [taylor]: Taking taylor expansion of 2 in n 8.597 * [backup-simplify]: Simplify 2 into 2 8.598 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 8.598 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 8.598 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 8.598 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 8.598 * [taylor]: Taking taylor expansion of 2 in n 8.598 * [backup-simplify]: Simplify 2 into 2 8.598 * [taylor]: Taking taylor expansion of (* n PI) in n 8.598 * [taylor]: Taking taylor expansion of n in n 8.599 * [backup-simplify]: Simplify 0 into 0 8.599 * [backup-simplify]: Simplify 1 into 1 8.599 * [taylor]: Taking taylor expansion of PI in n 8.599 * [backup-simplify]: Simplify PI into PI 8.599 * [backup-simplify]: Simplify (* 0 PI) into 0 8.599 * [backup-simplify]: Simplify (* 2 0) into 0 8.601 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.603 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 8.604 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.604 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 8.604 * [taylor]: Taking taylor expansion of (* n PI) in n 8.604 * [taylor]: Taking taylor expansion of n in n 8.604 * [backup-simplify]: Simplify 0 into 0 8.604 * [backup-simplify]: Simplify 1 into 1 8.604 * [taylor]: Taking taylor expansion of PI in n 8.604 * [backup-simplify]: Simplify PI into PI 8.604 * [backup-simplify]: Simplify (* 0 PI) into 0 8.606 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.606 * [backup-simplify]: Simplify (sqrt 0) into 0 8.608 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 8.608 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 8.608 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 8.608 * [taylor]: Taking taylor expansion of +nan.0 in n 8.608 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.608 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 8.608 * [taylor]: Taking taylor expansion of (sqrt 2) in n 8.608 * [taylor]: Taking taylor expansion of 2 in n 8.608 * [backup-simplify]: Simplify 2 into 2 8.608 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 8.609 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 8.609 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 8.609 * [taylor]: Taking taylor expansion of (* n PI) in n 8.609 * [taylor]: Taking taylor expansion of n in n 8.609 * [backup-simplify]: Simplify 0 into 0 8.609 * [backup-simplify]: Simplify 1 into 1 8.609 * [taylor]: Taking taylor expansion of PI in n 8.609 * [backup-simplify]: Simplify PI into PI 8.610 * [backup-simplify]: Simplify (* 0 PI) into 0 8.611 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.611 * [backup-simplify]: Simplify (sqrt 0) into 0 8.613 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 8.614 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 8.616 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 8.618 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 8.618 * [backup-simplify]: Simplify (* +nan.0 0) into 0 8.619 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 8.619 * [backup-simplify]: Simplify (* +nan.0 0) into 0 8.620 * [backup-simplify]: Simplify (- 0) into 0 8.620 * [backup-simplify]: Simplify (+ 0 0) into 0 8.621 * [backup-simplify]: Simplify (- 0) into 0 8.621 * [backup-simplify]: Simplify 0 into 0 8.624 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 8.629 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 8.633 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 8.635 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 8.636 * [backup-simplify]: Simplify 0 into 0 8.636 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.638 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 8.641 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 (* n PI)) 1)))) 6) into 0 8.649 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 8.650 * [backup-simplify]: Simplify (- 0) into 0 8.650 * [backup-simplify]: Simplify (+ 0 0) into 0 8.652 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0 8.653 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 8.654 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.659 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.660 * [backup-simplify]: Simplify (+ (* 0 (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3)))) (+ (* +nan.0 (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))) (+ (* +nan.0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))) 8.660 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))) in n 8.660 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))) in n 8.660 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 8.660 * [taylor]: Taking taylor expansion of +nan.0 in n 8.660 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.660 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 8.661 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 8.661 * [taylor]: Taking taylor expansion of (sqrt 2) in n 8.661 * [taylor]: Taking taylor expansion of 2 in n 8.661 * [backup-simplify]: Simplify 2 into 2 8.661 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 8.662 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 8.662 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 8.662 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 8.662 * [taylor]: Taking taylor expansion of 2 in n 8.662 * [backup-simplify]: Simplify 2 into 2 8.662 * [taylor]: Taking taylor expansion of (* n PI) in n 8.662 * [taylor]: Taking taylor expansion of n in n 8.662 * [backup-simplify]: Simplify 0 into 0 8.662 * [backup-simplify]: Simplify 1 into 1 8.662 * [taylor]: Taking taylor expansion of PI in n 8.662 * [backup-simplify]: Simplify PI into PI 8.663 * [backup-simplify]: Simplify (* 0 PI) into 0 8.663 * [backup-simplify]: Simplify (* 2 0) into 0 8.665 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.666 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 8.667 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.667 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 8.668 * [taylor]: Taking taylor expansion of (* n PI) in n 8.668 * [taylor]: Taking taylor expansion of n in n 8.668 * [backup-simplify]: Simplify 0 into 0 8.668 * [backup-simplify]: Simplify 1 into 1 8.668 * [taylor]: Taking taylor expansion of PI in n 8.668 * [backup-simplify]: Simplify PI into PI 8.668 * [backup-simplify]: Simplify (* 0 PI) into 0 8.670 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.670 * [backup-simplify]: Simplify (sqrt 0) into 0 8.672 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 8.672 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n 8.672 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n 8.672 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n 8.672 * [taylor]: Taking taylor expansion of +nan.0 in n 8.672 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.672 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n 8.672 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n 8.672 * [taylor]: Taking taylor expansion of (sqrt 2) in n 8.672 * [taylor]: Taking taylor expansion of 2 in n 8.672 * [backup-simplify]: Simplify 2 into 2 8.672 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 8.673 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 8.673 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 8.673 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 8.673 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 8.673 * [taylor]: Taking taylor expansion of 2 in n 8.673 * [backup-simplify]: Simplify 2 into 2 8.673 * [taylor]: Taking taylor expansion of (* n PI) in n 8.673 * [taylor]: Taking taylor expansion of n in n 8.673 * [backup-simplify]: Simplify 0 into 0 8.673 * [backup-simplify]: Simplify 1 into 1 8.673 * [taylor]: Taking taylor expansion of PI in n 8.673 * [backup-simplify]: Simplify PI into PI 8.674 * [backup-simplify]: Simplify (* 0 PI) into 0 8.674 * [backup-simplify]: Simplify (* 2 0) into 0 8.676 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.678 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 8.679 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.681 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 8.681 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 8.681 * [taylor]: Taking taylor expansion of (* n PI) in n 8.681 * [taylor]: Taking taylor expansion of n in n 8.681 * [backup-simplify]: Simplify 0 into 0 8.681 * [backup-simplify]: Simplify 1 into 1 8.681 * [taylor]: Taking taylor expansion of PI in n 8.681 * [backup-simplify]: Simplify PI into PI 8.681 * [backup-simplify]: Simplify (* 0 PI) into 0 8.683 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.683 * [backup-simplify]: Simplify (sqrt 0) into 0 8.685 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 8.685 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 8.685 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 8.685 * [taylor]: Taking taylor expansion of +nan.0 in n 8.685 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.685 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 8.685 * [taylor]: Taking taylor expansion of (sqrt 2) in n 8.685 * [taylor]: Taking taylor expansion of 2 in n 8.685 * [backup-simplify]: Simplify 2 into 2 8.685 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 8.686 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 8.686 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 8.686 * [taylor]: Taking taylor expansion of (* n PI) in n 8.686 * [taylor]: Taking taylor expansion of n in n 8.686 * [backup-simplify]: Simplify 0 into 0 8.686 * [backup-simplify]: Simplify 1 into 1 8.686 * [taylor]: Taking taylor expansion of PI in n 8.686 * [backup-simplify]: Simplify PI into PI 8.687 * [backup-simplify]: Simplify (* 0 PI) into 0 8.688 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.689 * [backup-simplify]: Simplify (sqrt 0) into 0 8.690 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 8.691 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 8.692 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 8.693 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 8.693 * [backup-simplify]: Simplify (* +nan.0 0) into 0 8.694 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 8.695 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 8.697 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 8.697 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 8.699 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0 8.699 * [backup-simplify]: Simplify (* +nan.0 0) into 0 8.699 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 8.699 * [backup-simplify]: Simplify (* +nan.0 0) into 0 8.700 * [backup-simplify]: Simplify (- 0) into 0 8.700 * [backup-simplify]: Simplify (+ 0 0) into 0 8.700 * [backup-simplify]: Simplify (- 0) into 0 8.700 * [backup-simplify]: Simplify (+ 0 0) into 0 8.701 * [backup-simplify]: Simplify (- 0) into 0 8.701 * [backup-simplify]: Simplify 0 into 0 8.701 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.702 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 8.703 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 8.704 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 8.705 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 8.707 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 8.712 * [backup-simplify]: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 8.714 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 8.717 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 8.720 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 8.725 * [backup-simplify]: Simplify (+ (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (- (* +nan.0 (* (sqrt 2) PI)))) into (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))))) 8.731 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) 8.738 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) 8.740 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.744 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 8.745 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 8.750 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 8.759 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 8.764 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 8.775 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 8.785 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) (* n k)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))) 8.785 * [backup-simplify]: Simplify (/ 1 (/ (sqrt (/ 1 k)) (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 8.785 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (k n) around 0 8.785 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 8.785 * [taylor]: Taking taylor expansion of (sqrt k) in n 8.785 * [taylor]: Taking taylor expansion of k in n 8.785 * [backup-simplify]: Simplify k into k 8.785 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 8.785 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 8.785 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 8.785 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 8.785 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 8.785 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 8.785 * [taylor]: Taking taylor expansion of 1/2 in n 8.785 * [backup-simplify]: Simplify 1/2 into 1/2 8.785 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.785 * [taylor]: Taking taylor expansion of 1/2 in n 8.786 * [backup-simplify]: Simplify 1/2 into 1/2 8.786 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.786 * [taylor]: Taking taylor expansion of k in n 8.786 * [backup-simplify]: Simplify k into k 8.786 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.786 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 8.786 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 8.786 * [taylor]: Taking taylor expansion of 2 in n 8.786 * [backup-simplify]: Simplify 2 into 2 8.786 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.786 * [taylor]: Taking taylor expansion of PI in n 8.786 * [backup-simplify]: Simplify PI into PI 8.786 * [taylor]: Taking taylor expansion of n in n 8.786 * [backup-simplify]: Simplify 0 into 0 8.786 * [backup-simplify]: Simplify 1 into 1 8.786 * [backup-simplify]: Simplify (/ PI 1) into PI 8.787 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 8.787 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.787 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.787 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 8.787 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 8.788 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 8.789 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 8.790 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 8.790 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 8.790 * [taylor]: Taking taylor expansion of (sqrt k) in k 8.790 * [taylor]: Taking taylor expansion of k in k 8.790 * [backup-simplify]: Simplify 0 into 0 8.790 * [backup-simplify]: Simplify 1 into 1 8.790 * [backup-simplify]: Simplify (sqrt 0) into 0 8.791 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.791 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 8.791 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 8.791 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 8.791 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 8.791 * [taylor]: Taking taylor expansion of 1/2 in k 8.791 * [backup-simplify]: Simplify 1/2 into 1/2 8.791 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 8.791 * [taylor]: Taking taylor expansion of 1/2 in k 8.791 * [backup-simplify]: Simplify 1/2 into 1/2 8.791 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.791 * [taylor]: Taking taylor expansion of k in k 8.791 * [backup-simplify]: Simplify 0 into 0 8.791 * [backup-simplify]: Simplify 1 into 1 8.792 * [backup-simplify]: Simplify (/ 1 1) into 1 8.792 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 8.792 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 8.792 * [taylor]: Taking taylor expansion of 2 in k 8.792 * [backup-simplify]: Simplify 2 into 2 8.792 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.792 * [taylor]: Taking taylor expansion of PI in k 8.792 * [backup-simplify]: Simplify PI into PI 8.792 * [taylor]: Taking taylor expansion of n in k 8.792 * [backup-simplify]: Simplify n into n 8.792 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.792 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 8.792 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 8.792 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 8.792 * [backup-simplify]: Simplify (- 1/2) into -1/2 8.793 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 8.793 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 8.793 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 8.793 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 8.793 * [taylor]: Taking taylor expansion of (sqrt k) in k 8.793 * [taylor]: Taking taylor expansion of k in k 8.793 * [backup-simplify]: Simplify 0 into 0 8.793 * [backup-simplify]: Simplify 1 into 1 8.793 * [backup-simplify]: Simplify (sqrt 0) into 0 8.794 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.794 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 8.794 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 8.794 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 8.794 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 8.794 * [taylor]: Taking taylor expansion of 1/2 in k 8.794 * [backup-simplify]: Simplify 1/2 into 1/2 8.794 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 8.794 * [taylor]: Taking taylor expansion of 1/2 in k 8.794 * [backup-simplify]: Simplify 1/2 into 1/2 8.794 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.794 * [taylor]: Taking taylor expansion of k in k 8.794 * [backup-simplify]: Simplify 0 into 0 8.794 * [backup-simplify]: Simplify 1 into 1 8.794 * [backup-simplify]: Simplify (/ 1 1) into 1 8.794 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 8.794 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 8.794 * [taylor]: Taking taylor expansion of 2 in k 8.794 * [backup-simplify]: Simplify 2 into 2 8.794 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.794 * [taylor]: Taking taylor expansion of PI in k 8.794 * [backup-simplify]: Simplify PI into PI 8.795 * [taylor]: Taking taylor expansion of n in k 8.795 * [backup-simplify]: Simplify n into n 8.795 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.795 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 8.795 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 8.795 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 8.795 * [backup-simplify]: Simplify (- 1/2) into -1/2 8.795 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 8.796 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 8.796 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 8.796 * [backup-simplify]: Simplify (* 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into 0 8.796 * [taylor]: Taking taylor expansion of 0 in n 8.796 * [backup-simplify]: Simplify 0 into 0 8.796 * [backup-simplify]: Simplify 0 into 0 8.796 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 8.796 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 8.796 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 8.796 * [taylor]: Taking taylor expansion of +nan.0 in n 8.796 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.796 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 8.796 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 8.796 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 8.796 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 8.796 * [taylor]: Taking taylor expansion of 1/2 in n 8.796 * [backup-simplify]: Simplify 1/2 into 1/2 8.796 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.796 * [taylor]: Taking taylor expansion of 1/2 in n 8.796 * [backup-simplify]: Simplify 1/2 into 1/2 8.796 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.796 * [taylor]: Taking taylor expansion of k in n 8.797 * [backup-simplify]: Simplify k into k 8.797 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.797 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 8.797 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 8.797 * [taylor]: Taking taylor expansion of 2 in n 8.797 * [backup-simplify]: Simplify 2 into 2 8.797 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.797 * [taylor]: Taking taylor expansion of PI in n 8.797 * [backup-simplify]: Simplify PI into PI 8.797 * [taylor]: Taking taylor expansion of n in n 8.797 * [backup-simplify]: Simplify 0 into 0 8.797 * [backup-simplify]: Simplify 1 into 1 8.797 * [backup-simplify]: Simplify (/ PI 1) into PI 8.797 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 8.798 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.798 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.798 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 8.798 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 8.799 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 8.800 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 8.801 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 8.801 * [backup-simplify]: Simplify (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 8.802 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 8.803 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 8.803 * [backup-simplify]: Simplify 0 into 0 8.805 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.805 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 8.805 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 8.805 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 8.805 * [taylor]: Taking taylor expansion of +nan.0 in n 8.805 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.805 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 8.805 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 8.805 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 8.805 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 8.805 * [taylor]: Taking taylor expansion of 1/2 in n 8.805 * [backup-simplify]: Simplify 1/2 into 1/2 8.805 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.805 * [taylor]: Taking taylor expansion of 1/2 in n 8.805 * [backup-simplify]: Simplify 1/2 into 1/2 8.805 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.805 * [taylor]: Taking taylor expansion of k in n 8.805 * [backup-simplify]: Simplify k into k 8.805 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.805 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 8.806 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 8.806 * [taylor]: Taking taylor expansion of 2 in n 8.806 * [backup-simplify]: Simplify 2 into 2 8.806 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.806 * [taylor]: Taking taylor expansion of PI in n 8.806 * [backup-simplify]: Simplify PI into PI 8.806 * [taylor]: Taking taylor expansion of n in n 8.806 * [backup-simplify]: Simplify 0 into 0 8.806 * [backup-simplify]: Simplify 1 into 1 8.806 * [backup-simplify]: Simplify (/ PI 1) into PI 8.807 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 8.808 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.808 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.808 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 8.808 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 8.810 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 8.811 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 8.812 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 8.813 * [backup-simplify]: Simplify (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 8.815 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 8.816 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 8.817 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.818 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 8.819 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 8.820 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.820 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 8.821 * [backup-simplify]: Simplify (- 0) into 0 8.821 * [backup-simplify]: Simplify (+ 0 0) into 0 8.822 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 8.823 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 8.824 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 8.825 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 8.826 * [backup-simplify]: Simplify (- 0) into 0 8.826 * [backup-simplify]: Simplify 0 into 0 8.826 * [backup-simplify]: Simplify 0 into 0 8.828 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.829 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 8.829 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 8.829 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 8.829 * [taylor]: Taking taylor expansion of +nan.0 in n 8.829 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.829 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 8.829 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 8.829 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 8.829 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 8.829 * [taylor]: Taking taylor expansion of 1/2 in n 8.829 * [backup-simplify]: Simplify 1/2 into 1/2 8.829 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.829 * [taylor]: Taking taylor expansion of 1/2 in n 8.829 * [backup-simplify]: Simplify 1/2 into 1/2 8.829 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.829 * [taylor]: Taking taylor expansion of k in n 8.829 * [backup-simplify]: Simplify k into k 8.829 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.829 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 8.829 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 8.829 * [taylor]: Taking taylor expansion of 2 in n 8.829 * [backup-simplify]: Simplify 2 into 2 8.829 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.829 * [taylor]: Taking taylor expansion of PI in n 8.829 * [backup-simplify]: Simplify PI into PI 8.829 * [taylor]: Taking taylor expansion of n in n 8.829 * [backup-simplify]: Simplify 0 into 0 8.829 * [backup-simplify]: Simplify 1 into 1 8.830 * [backup-simplify]: Simplify (/ PI 1) into PI 8.830 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 8.831 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.831 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.831 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 8.831 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 8.832 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 8.832 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 8.833 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 8.834 * [backup-simplify]: Simplify (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 8.835 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 8.836 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 8.838 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) 8.839 * [backup-simplify]: Simplify (/ 1 (/ (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 8.839 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (k n) around 0 8.839 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 8.839 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 8.839 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 8.839 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 8.839 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 8.839 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.839 * [taylor]: Taking taylor expansion of 1/2 in n 8.839 * [backup-simplify]: Simplify 1/2 into 1/2 8.839 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.839 * [taylor]: Taking taylor expansion of k in n 8.839 * [backup-simplify]: Simplify k into k 8.839 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.839 * [taylor]: Taking taylor expansion of 1/2 in n 8.839 * [backup-simplify]: Simplify 1/2 into 1/2 8.839 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 8.839 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 8.839 * [taylor]: Taking taylor expansion of -2 in n 8.839 * [backup-simplify]: Simplify -2 into -2 8.839 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.839 * [taylor]: Taking taylor expansion of PI in n 8.839 * [backup-simplify]: Simplify PI into PI 8.839 * [taylor]: Taking taylor expansion of n in n 8.839 * [backup-simplify]: Simplify 0 into 0 8.839 * [backup-simplify]: Simplify 1 into 1 8.840 * [backup-simplify]: Simplify (/ PI 1) into PI 8.840 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 8.841 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 8.841 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.841 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 8.842 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 8.842 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 8.843 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 8.843 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 8.843 * [taylor]: Taking taylor expansion of (/ -1 k) in n 8.843 * [taylor]: Taking taylor expansion of -1 in n 8.843 * [backup-simplify]: Simplify -1 into -1 8.843 * [taylor]: Taking taylor expansion of k in n 8.843 * [backup-simplify]: Simplify k into k 8.843 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 8.843 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 8.843 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 8.843 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 8.844 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) 8.844 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 8.844 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 8.844 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 8.844 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 8.844 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 8.844 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 8.844 * [taylor]: Taking taylor expansion of 1/2 in k 8.844 * [backup-simplify]: Simplify 1/2 into 1/2 8.844 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.844 * [taylor]: Taking taylor expansion of k in k 8.844 * [backup-simplify]: Simplify 0 into 0 8.844 * [backup-simplify]: Simplify 1 into 1 8.845 * [backup-simplify]: Simplify (/ 1 1) into 1 8.845 * [taylor]: Taking taylor expansion of 1/2 in k 8.845 * [backup-simplify]: Simplify 1/2 into 1/2 8.845 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 8.845 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 8.845 * [taylor]: Taking taylor expansion of -2 in k 8.845 * [backup-simplify]: Simplify -2 into -2 8.845 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.845 * [taylor]: Taking taylor expansion of PI in k 8.845 * [backup-simplify]: Simplify PI into PI 8.845 * [taylor]: Taking taylor expansion of n in k 8.845 * [backup-simplify]: Simplify n into n 8.845 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.845 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 8.845 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 8.845 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 8.845 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 8.845 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 8.846 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 8.846 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.846 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.846 * [taylor]: Taking taylor expansion of -1 in k 8.846 * [backup-simplify]: Simplify -1 into -1 8.846 * [taylor]: Taking taylor expansion of k in k 8.846 * [backup-simplify]: Simplify 0 into 0 8.846 * [backup-simplify]: Simplify 1 into 1 8.846 * [backup-simplify]: Simplify (/ -1 1) into -1 8.846 * [backup-simplify]: Simplify (sqrt 0) into 0 8.847 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.847 * [backup-simplify]: Simplify (/ (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 8.847 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 8.847 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 8.847 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 8.847 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 8.847 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 8.847 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 8.847 * [taylor]: Taking taylor expansion of 1/2 in k 8.847 * [backup-simplify]: Simplify 1/2 into 1/2 8.847 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.847 * [taylor]: Taking taylor expansion of k in k 8.847 * [backup-simplify]: Simplify 0 into 0 8.847 * [backup-simplify]: Simplify 1 into 1 8.848 * [backup-simplify]: Simplify (/ 1 1) into 1 8.848 * [taylor]: Taking taylor expansion of 1/2 in k 8.848 * [backup-simplify]: Simplify 1/2 into 1/2 8.848 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 8.848 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 8.848 * [taylor]: Taking taylor expansion of -2 in k 8.848 * [backup-simplify]: Simplify -2 into -2 8.848 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.848 * [taylor]: Taking taylor expansion of PI in k 8.848 * [backup-simplify]: Simplify PI into PI 8.848 * [taylor]: Taking taylor expansion of n in k 8.848 * [backup-simplify]: Simplify n into n 8.848 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.848 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 8.848 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 8.848 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 8.849 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 8.849 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 8.849 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 8.849 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.849 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.849 * [taylor]: Taking taylor expansion of -1 in k 8.849 * [backup-simplify]: Simplify -1 into -1 8.849 * [taylor]: Taking taylor expansion of k in k 8.849 * [backup-simplify]: Simplify 0 into 0 8.849 * [backup-simplify]: Simplify 1 into 1 8.849 * [backup-simplify]: Simplify (/ -1 1) into -1 8.849 * [backup-simplify]: Simplify (sqrt 0) into 0 8.850 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.851 * [backup-simplify]: Simplify (/ (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 8.851 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 8.851 * [taylor]: Taking taylor expansion of +nan.0 in n 8.851 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.851 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 8.851 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 8.851 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 8.851 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 8.851 * [taylor]: Taking taylor expansion of -2 in n 8.851 * [backup-simplify]: Simplify -2 into -2 8.851 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.851 * [taylor]: Taking taylor expansion of PI in n 8.851 * [backup-simplify]: Simplify PI into PI 8.851 * [taylor]: Taking taylor expansion of n in n 8.851 * [backup-simplify]: Simplify 0 into 0 8.851 * [backup-simplify]: Simplify 1 into 1 8.852 * [backup-simplify]: Simplify (/ PI 1) into PI 8.852 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 8.853 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 8.854 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 8.854 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.854 * [taylor]: Taking taylor expansion of 1/2 in n 8.854 * [backup-simplify]: Simplify 1/2 into 1/2 8.854 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.854 * [taylor]: Taking taylor expansion of k in n 8.854 * [backup-simplify]: Simplify k into k 8.854 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.854 * [taylor]: Taking taylor expansion of 1/2 in n 8.854 * [backup-simplify]: Simplify 1/2 into 1/2 8.855 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 8.855 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.855 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 8.857 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 8.858 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 8.859 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 8.860 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 8.861 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 8.864 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.865 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) 8.865 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 8.865 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 8.865 * [taylor]: Taking taylor expansion of +nan.0 in n 8.865 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.865 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 8.865 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 8.865 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 8.865 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 8.865 * [taylor]: Taking taylor expansion of -2 in n 8.866 * [backup-simplify]: Simplify -2 into -2 8.866 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.866 * [taylor]: Taking taylor expansion of PI in n 8.866 * [backup-simplify]: Simplify PI into PI 8.866 * [taylor]: Taking taylor expansion of n in n 8.866 * [backup-simplify]: Simplify 0 into 0 8.866 * [backup-simplify]: Simplify 1 into 1 8.866 * [backup-simplify]: Simplify (/ PI 1) into PI 8.866 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 8.867 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 8.867 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 8.867 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.867 * [taylor]: Taking taylor expansion of 1/2 in n 8.867 * [backup-simplify]: Simplify 1/2 into 1/2 8.867 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.867 * [taylor]: Taking taylor expansion of k in n 8.867 * [backup-simplify]: Simplify k into k 8.867 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.867 * [taylor]: Taking taylor expansion of 1/2 in n 8.867 * [backup-simplify]: Simplify 1/2 into 1/2 8.868 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 8.868 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.868 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 8.869 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 8.870 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 8.870 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 8.871 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 8.872 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 8.873 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 8.873 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.873 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 8.874 * [backup-simplify]: Simplify (+ 0 0) into 0 8.874 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.875 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 8.880 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 8.881 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 8.883 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 8.884 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into 0 8.884 * [backup-simplify]: Simplify 0 into 0 8.885 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.887 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.888 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) 8.888 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 8.888 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 8.888 * [taylor]: Taking taylor expansion of +nan.0 in n 8.888 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.888 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 8.888 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 8.888 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 8.888 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 8.888 * [taylor]: Taking taylor expansion of -2 in n 8.888 * [backup-simplify]: Simplify -2 into -2 8.888 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.888 * [taylor]: Taking taylor expansion of PI in n 8.888 * [backup-simplify]: Simplify PI into PI 8.888 * [taylor]: Taking taylor expansion of n in n 8.888 * [backup-simplify]: Simplify 0 into 0 8.888 * [backup-simplify]: Simplify 1 into 1 8.889 * [backup-simplify]: Simplify (/ PI 1) into PI 8.889 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 8.890 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 8.890 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 8.890 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 8.890 * [taylor]: Taking taylor expansion of 1/2 in n 8.890 * [backup-simplify]: Simplify 1/2 into 1/2 8.890 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.890 * [taylor]: Taking taylor expansion of k in n 8.890 * [backup-simplify]: Simplify k into k 8.890 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.890 * [taylor]: Taking taylor expansion of 1/2 in n 8.890 * [backup-simplify]: Simplify 1/2 into 1/2 8.891 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 8.891 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 8.891 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 8.892 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 8.892 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 8.894 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 8.896 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 8.897 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 8.902 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 8.902 * * * [progress]: simplifying candidates 8.902 * * * * [progress]: [ 1 / 1611 ] simplifiying candidate # 8.902 * * * * [progress]: [ 2 / 1611 ] simplifiying candidate # 8.902 * * * * [progress]: [ 3 / 1611 ] simplifiying candidate # 8.902 * * * * [progress]: [ 4 / 1611 ] simplifiying candidate # 8.902 * * * * [progress]: [ 5 / 1611 ] simplifiying candidate # 8.903 * * * * [progress]: [ 6 / 1611 ] simplifiying candidate # 8.903 * * * * [progress]: [ 7 / 1611 ] simplifiying candidate # 8.903 * * * * [progress]: [ 8 / 1611 ] simplifiying candidate # 8.903 * * * * [progress]: [ 9 / 1611 ] simplifiying candidate # 8.903 * * * * [progress]: [ 10 / 1611 ] simplifiying candidate # 8.903 * * * * [progress]: [ 11 / 1611 ] simplifiying 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8.907 * * * * [progress]: [ 58 / 1611 ] simplifiying candidate # 8.907 * * * * [progress]: [ 59 / 1611 ] simplifiying candidate # 8.907 * * * * [progress]: [ 60 / 1611 ] simplifiying candidate # 8.907 * * * * [progress]: [ 61 / 1611 ] simplifiying candidate # 8.908 * * * * [progress]: [ 62 / 1611 ] simplifiying candidate # 8.908 * * * * [progress]: [ 63 / 1611 ] simplifiying candidate # 8.908 * * * * [progress]: [ 64 / 1611 ] simplifiying candidate # 8.908 * * * * [progress]: [ 65 / 1611 ] simplifiying candidate # 8.908 * * * * [progress]: [ 66 / 1611 ] simplifiying candidate # 8.908 * * * * [progress]: [ 67 / 1611 ] simplifiying candidate #real (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))> 8.908 * * * * [progress]: [ 68 / 1611 ] simplifiying candidate # 8.908 * * * * [progress]: [ 69 / 1611 ] simplifiying candidate # 8.908 * * * * [progress]: [ 70 / 1611 ] simplifiying candidate # 8.908 * * * * [progress]: [ 71 / 1611 ] simplifiying candidate # 8.908 * * * * [progress]: [ 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candidate #real (real->posit16 (* n (* 2 PI)))) (- 1/2 (/ k 2))))))> 8.909 * * * * [progress]: [ 88 / 1611 ] simplifiying candidate # 8.909 * * * * [progress]: [ 89 / 1611 ] simplifiying candidate # 8.909 * * * * [progress]: [ 90 / 1611 ] simplifiying candidate # 8.910 * * * * [progress]: [ 91 / 1611 ] simplifiying candidate # 8.910 * * * * [progress]: [ 92 / 1611 ] simplifiying candidate # 8.910 * * * * [progress]: [ 93 / 1611 ] simplifiying candidate # 8.910 * * * * [progress]: [ 94 / 1611 ] simplifiying candidate # 8.910 * * * * [progress]: [ 95 / 1611 ] simplifiying candidate # 8.910 * * * * [progress]: [ 96 / 1611 ] simplifiying candidate # 8.910 * * * * [progress]: [ 97 / 1611 ] simplifiying candidate # 8.910 * * * * [progress]: [ 98 / 1611 ] simplifiying candidate # 8.910 * * * * [progress]: [ 99 / 1611 ] simplifiying candidate # 8.910 * * * * [progress]: [ 100 / 1611 ] simplifiying candidate # 8.910 * * * * [progress]: [ 101 / 1611 ] simplifiying candidate # 8.910 * * * * 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[progress]: [ 1596 / 1611 ] simplifiying candidate # 9.018 * * * * [progress]: [ 1597 / 1611 ] simplifiying candidate # 9.018 * * * * [progress]: [ 1598 / 1611 ] simplifiying candidate # 9.018 * * * * [progress]: [ 1599 / 1611 ] simplifiying candidate #real (real->posit16 (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))> 9.018 * * * * [progress]: [ 1600 / 1611 ] simplifiying candidate # 9.018 * * * * [progress]: [ 1601 / 1611 ] simplifiying candidate # 9.018 * * * * [progress]: [ 1602 / 1611 ] simplifiying candidate # 9.018 * * * * [progress]: [ 1603 / 1611 ] simplifiying candidate # 9.018 * * * * [progress]: [ 1604 / 1611 ] simplifiying candidate # 9.019 * * * * [progress]: [ 1605 / 1611 ] simplifiying candidate # 9.019 * * * * [progress]: [ 1606 / 1611 ] simplifiying candidate # 9.019 * * * * [progress]: [ 1607 / 1611 ] simplifiying candidate # 9.019 * * * * [progress]: [ 1608 / 1611 ] simplifiying candidate # 9.019 * * * * [progress]: [ 1609 / 1611 ] simplifiying candidate # 9.019 * * * * [progress]: [ 1610 / 1611 ] simplifiying candidate # 9.019 * * * * [progress]: [ 1611 / 1611 ] simplifiying candidate # 9.085 * [simplify]: Simplifying: (expm1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (log1p (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))) (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2))) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (/ k 2)) (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) 1) (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2)))) (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (pow (* n (* 2 PI)) 1) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* 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(- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 9.167 * * [simplify]: iteration 0: 1728 enodes 9.998 * * [simplify]: iteration 1: 2002 enodes 10.560 * * [simplify]: iteration complete: 2002 enodes 10.563 * * [simplify]: Extracting #0: cost 1206 inf + 0 10.568 * * [simplify]: Extracting #1: cost 1366 inf + 42 10.576 * * [simplify]: Extracting #2: cost 1480 inf + 1030 10.584 * * [simplify]: Extracting #3: cost 1478 inf + 4950 10.605 * * [simplify]: Extracting #4: cost 1363 inf + 55431 10.652 * * [simplify]: Extracting #5: cost 1062 inf + 220654 10.727 * * [simplify]: Extracting #6: cost 798 inf + 382302 10.814 * * [simplify]: Extracting #7: cost 548 inf + 555326 10.922 * * [simplify]: Extracting #8: cost 311 inf + 744460 11.032 * * [simplify]: Extracting #9: cost 149 inf + 884289 11.131 * * [simplify]: Extracting #10: cost 72 inf + 952676 11.251 * * [simplify]: Extracting #11: cost 37 inf + 980879 11.364 * * [simplify]: Extracting #12: cost 21 inf + 989015 11.505 * * [simplify]: Extracting #13: cost 17 inf + 990253 11.620 * * [simplify]: Extracting #14: cost 11 inf + 994390 11.774 * * [simplify]: Extracting #15: cost 6 inf + 999751 11.869 * * [simplify]: Extracting #16: cost 4 inf + 1001443 12.032 * * [simplify]: Extracting #17: cost 1 inf + 1004851 12.212 * * [simplify]: Extracting #18: cost 0 inf + 1006257 12.383 * [simplify]: Simplified to: (expm1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (log1p (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (- 1/2 (/ k 2)) (- 1/2 (/ k 2)) (- 1/2 (/ k 2)) (sqrt (* n (* 2 PI))) (pow (* n (* 2 PI)) (/ k 2)) (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2)))) (* n (* 2 PI)) (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2)))) (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (* n (* 2 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PI)) (- 1/2 (/ k 2))))))) (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ 1 (sqrt (sqrt k))) (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (/ k 2)))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) 2) (* (cbrt k) (cbrt k)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) 2) (sqrt k))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (/ k 2)))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (/ k 2)))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ 1 2) k)))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (/ k 2)))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) 2) (* (cbrt k) (cbrt k)))))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) 2) (sqrt k))))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (/ k 2)))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (/ k 2)))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ 1 2) k)))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (/ k 2)))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (cbrt k) (cbrt 2)) (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (cbrt k) 2) (* (cbrt k) (cbrt k)))))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (sqrt k) 2) (sqrt k))))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (/ k 2)))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (/ k 2)))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ 1 2) k)))) (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI))) (pow n (- 1/2 (/ k 2))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1 (/ 1 (sqrt k)) (/ 1 (/ (sqrt k) (sqrt (* n (* 2 PI))))) (/ (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt 1)) (/ (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt 1)) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ 1 (sqrt k)) (real->posit16 (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (- (fma 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (log (* n (* 2 PI))))) (* (log n) (* k k)))) (fma 1/8 (* (exp (* 1/2 (log (* n (* 2 PI))))) (* (* (log n) (log n)) (* k k))) (+ (exp (* 1/2 (log (* n (* 2 PI))))) (* 1/8 (* (* (log (* 2 PI)) (log (* 2 PI))) (* (exp (* 1/2 (log (* n (* 2 PI))))) (* k k))))))) (fma 1/2 (* (exp (* 1/2 (log (* n (* 2 PI))))) (* (log n) k)) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (log (* n (* 2 PI))))) k))))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* 2 (* n PI)) (* 2 (* n PI)) (* 2 (* n PI)) (- (fma +nan.0 (/ (* (sqrt 2) (* (* k k) (* (* (sqrt 1/2) (sqrt 1/2)) (log (* 2 PI))))) PI) (- (fma +nan.0 (/ (* (sqrt 1/2) (* k k)) PI) (- (fma +nan.0 (/ (* n (* (sqrt 1/2) k)) (* PI PI)) (- (fma +nan.0 (/ (* (log n) (* (sqrt 2) (* (* (sqrt 1/2) (sqrt 1/2)) (* k k)))) PI) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI))))))))))) (- (fma +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) k)) (- (fma +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) (* k k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n)))))))))))) (- (fma +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* k k))) (- (fma +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (* +nan.0 (exp (- (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) (- (fma +nan.0 (* (sqrt 2) (* n (* PI k))) (- (fma +nan.0 (* (sqrt 2) (* n PI)) (- (fma +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k)))) (- (fma +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k)))) (- (* +nan.0 (* (sqrt 2) (* (* n n) (* PI PI))))))))))))) (- (fma +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) (* k (* k k))) (- (fma +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) k) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) (* k k)))))))) (- (fma +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k) (- (fma +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* k k)) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 12.802 * * * [progress]: adding candidates to table 24.866 * * [progress]: iteration 3 / 4 24.866 * * * [progress]: picking best candidate 24.902 * * * * [pick]: Picked # 24.902 * * * [progress]: localizing error 24.930 * * * [progress]: generating rewritten candidates 24.930 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1 2) 24.955 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1) 24.971 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 2 1) 24.985 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1 1) 25.002 * * * [progress]: generating series expansions 25.002 * * * * [progress]: [ 1 / 4 ] generating series at (2 1 2) 25.004 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) 25.004 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in (n k) around 0 25.004 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in k 25.004 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in k 25.004 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in k 25.004 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in k 25.004 * [taylor]: Taking taylor expansion of 1/2 in k 25.004 * [backup-simplify]: Simplify 1/2 into 1/2 25.004 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 25.004 * [taylor]: Taking taylor expansion of 1/2 in k 25.004 * [backup-simplify]: Simplify 1/2 into 1/2 25.004 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 25.004 * [taylor]: Taking taylor expansion of 1/2 in k 25.004 * [backup-simplify]: Simplify 1/2 into 1/2 25.004 * [taylor]: Taking taylor expansion of k in k 25.004 * [backup-simplify]: Simplify 0 into 0 25.004 * [backup-simplify]: Simplify 1 into 1 25.004 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 25.004 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 25.004 * [taylor]: Taking taylor expansion of 2 in k 25.004 * [backup-simplify]: Simplify 2 into 2 25.004 * [taylor]: Taking taylor expansion of (* n PI) in k 25.004 * [taylor]: Taking taylor expansion of n in k 25.004 * [backup-simplify]: Simplify n into n 25.004 * [taylor]: Taking taylor expansion of PI in k 25.004 * [backup-simplify]: Simplify PI into PI 25.004 * [backup-simplify]: Simplify (* n PI) into (* n PI) 25.004 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 25.004 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 25.005 * [backup-simplify]: Simplify (* 1/2 0) into 0 25.006 * [backup-simplify]: Simplify (- 0) into 0 25.006 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 25.006 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4 25.007 * [backup-simplify]: Simplify (* 1/4 (log (* 2 (* n PI)))) into (* 1/4 (log (* 2 (* n PI)))) 25.007 * [backup-simplify]: Simplify (exp (* 1/4 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/4) 25.007 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n 25.007 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n 25.007 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n 25.007 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n 25.007 * [taylor]: Taking taylor expansion of 1/2 in n 25.007 * [backup-simplify]: Simplify 1/2 into 1/2 25.007 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 25.007 * [taylor]: Taking taylor expansion of 1/2 in n 25.007 * [backup-simplify]: Simplify 1/2 into 1/2 25.007 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 25.007 * [taylor]: Taking taylor expansion of 1/2 in n 25.007 * [backup-simplify]: Simplify 1/2 into 1/2 25.007 * [taylor]: Taking taylor expansion of k in n 25.007 * [backup-simplify]: Simplify k into k 25.007 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 25.007 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 25.007 * [taylor]: Taking taylor expansion of 2 in n 25.007 * [backup-simplify]: Simplify 2 into 2 25.007 * [taylor]: Taking taylor expansion of (* n PI) in n 25.007 * [taylor]: Taking taylor expansion of n in n 25.007 * [backup-simplify]: Simplify 0 into 0 25.007 * [backup-simplify]: Simplify 1 into 1 25.007 * [taylor]: Taking taylor expansion of PI in n 25.007 * [backup-simplify]: Simplify PI into PI 25.008 * [backup-simplify]: Simplify (* 0 PI) into 0 25.008 * [backup-simplify]: Simplify (* 2 0) into 0 25.010 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 25.012 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 25.013 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 25.013 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 25.013 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 25.013 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 25.013 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k))) 25.015 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 25.016 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 25.017 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 25.017 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n 25.017 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n 25.017 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n 25.017 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n 25.017 * [taylor]: Taking taylor expansion of 1/2 in n 25.017 * [backup-simplify]: Simplify 1/2 into 1/2 25.017 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 25.017 * [taylor]: Taking taylor expansion of 1/2 in n 25.017 * [backup-simplify]: Simplify 1/2 into 1/2 25.017 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 25.017 * [taylor]: Taking taylor expansion of 1/2 in n 25.017 * [backup-simplify]: Simplify 1/2 into 1/2 25.017 * [taylor]: Taking taylor expansion of k in n 25.017 * [backup-simplify]: Simplify k into k 25.017 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 25.017 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 25.017 * [taylor]: Taking taylor expansion of 2 in n 25.017 * [backup-simplify]: Simplify 2 into 2 25.017 * [taylor]: Taking taylor expansion of (* n PI) in n 25.017 * [taylor]: Taking taylor expansion of n in n 25.017 * [backup-simplify]: Simplify 0 into 0 25.017 * [backup-simplify]: Simplify 1 into 1 25.018 * [taylor]: Taking taylor expansion of PI in n 25.018 * [backup-simplify]: Simplify PI into PI 25.018 * [backup-simplify]: Simplify (* 0 PI) into 0 25.018 * [backup-simplify]: Simplify (* 2 0) into 0 25.020 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 25.022 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 25.023 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 25.023 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 25.023 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 25.023 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 25.023 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k))) 25.025 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 25.026 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 25.027 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 25.027 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) in k 25.027 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 25.027 * [taylor]: Taking taylor expansion of 1/2 in k 25.027 * [backup-simplify]: Simplify 1/2 into 1/2 25.027 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 25.027 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 25.028 * [taylor]: Taking taylor expansion of 1/2 in k 25.028 * [backup-simplify]: Simplify 1/2 into 1/2 25.028 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 25.028 * [taylor]: Taking taylor expansion of 1/2 in k 25.028 * [backup-simplify]: Simplify 1/2 into 1/2 25.028 * [taylor]: Taking taylor expansion of k in k 25.028 * [backup-simplify]: Simplify 0 into 0 25.028 * [backup-simplify]: Simplify 1 into 1 25.028 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 25.028 * [taylor]: Taking taylor expansion of (log n) in k 25.028 * [taylor]: Taking taylor expansion of n in k 25.028 * [backup-simplify]: Simplify n into n 25.028 * [backup-simplify]: Simplify (log n) into (log n) 25.028 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 25.028 * [taylor]: Taking taylor expansion of (* 2 PI) in k 25.028 * [taylor]: Taking taylor expansion of 2 in k 25.028 * [backup-simplify]: Simplify 2 into 2 25.028 * [taylor]: Taking taylor expansion of PI in k 25.028 * [backup-simplify]: Simplify PI into PI 25.028 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 25.029 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 25.030 * [backup-simplify]: Simplify (* 1/2 0) into 0 25.030 * [backup-simplify]: Simplify (- 0) into 0 25.031 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 25.032 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 25.033 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 25.034 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (+ (log n) (log (* 2 PI))))) into (* 1/4 (+ (log n) (log (* 2 PI)))) 25.040 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 25.041 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 25.042 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 25.044 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 25.045 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 25.046 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 25.046 * [backup-simplify]: Simplify (- 0) into 0 25.047 * [backup-simplify]: Simplify (+ 0 0) into 0 25.047 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 k)))) into 0 25.049 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 25.050 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 25.052 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0 25.052 * [taylor]: Taking taylor expansion of 0 in k 25.052 * [backup-simplify]: Simplify 0 into 0 25.052 * [backup-simplify]: Simplify 0 into 0 25.053 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 25.054 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 25.055 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 25.056 * [backup-simplify]: Simplify (+ 0 0) into 0 25.057 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 25.057 * [backup-simplify]: Simplify (- 1/2) into -1/2 25.057 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 25.059 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 25.062 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* 0 (* 1/2 (+ (log n) (log (* 2 PI)))))) into (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 25.064 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) 25.066 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) 25.066 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 25.067 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 25.069 * [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 25.069 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 25.070 * [backup-simplify]: Simplify (- 0) into 0 25.070 * [backup-simplify]: Simplify (+ 0 0) into 0 25.070 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 k))))) into 0 25.072 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 25.073 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 25.074 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 25.074 * [taylor]: Taking taylor expansion of 0 in k 25.074 * [backup-simplify]: Simplify 0 into 0 25.074 * [backup-simplify]: Simplify 0 into 0 25.074 * [backup-simplify]: Simplify 0 into 0 25.075 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 25.076 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 25.078 * [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 25.078 * [backup-simplify]: Simplify (+ 0 0) into 0 25.078 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 25.079 * [backup-simplify]: Simplify (- 0) into 0 25.079 * [backup-simplify]: Simplify (+ 0 0) into 0 25.080 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 25.082 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* 0 (* 1/2 (+ (log n) (log (* 2 PI))))))) into 0 25.085 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) 25.088 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) 25.096 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))))) 25.097 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (/ (- 1/2 (/ (/ 1 k) 2)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) 25.097 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 25.097 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in k 25.097 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in k 25.097 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in k 25.097 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in k 25.097 * [taylor]: Taking taylor expansion of 1/2 in k 25.097 * [backup-simplify]: Simplify 1/2 into 1/2 25.097 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 25.097 * [taylor]: Taking taylor expansion of 1/2 in k 25.097 * [backup-simplify]: Simplify 1/2 into 1/2 25.097 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 25.097 * [taylor]: Taking taylor expansion of 1/2 in k 25.097 * [backup-simplify]: Simplify 1/2 into 1/2 25.097 * [taylor]: Taking taylor expansion of (/ 1 k) in k 25.097 * [taylor]: Taking taylor expansion of k in k 25.097 * [backup-simplify]: Simplify 0 into 0 25.097 * [backup-simplify]: Simplify 1 into 1 25.098 * [backup-simplify]: Simplify (/ 1 1) into 1 25.098 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 25.098 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 25.098 * [taylor]: Taking taylor expansion of 2 in k 25.098 * [backup-simplify]: Simplify 2 into 2 25.098 * [taylor]: Taking taylor expansion of (/ PI n) in k 25.098 * [taylor]: Taking taylor expansion of PI in k 25.098 * [backup-simplify]: Simplify PI into PI 25.098 * [taylor]: Taking taylor expansion of n in k 25.098 * [backup-simplify]: Simplify n into n 25.098 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 25.098 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 25.098 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 25.099 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 25.099 * [backup-simplify]: Simplify (- 1/2) into -1/2 25.099 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 25.100 * [backup-simplify]: Simplify (* 1/2 -1/2) into -1/4 25.100 * [backup-simplify]: Simplify (* -1/4 (log (* 2 (/ PI n)))) into (* -1/4 (log (* 2 (/ PI n)))) 25.100 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))))) 25.100 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n 25.100 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n 25.100 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n 25.100 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n 25.100 * [taylor]: Taking taylor expansion of 1/2 in n 25.100 * [backup-simplify]: Simplify 1/2 into 1/2 25.100 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 25.100 * [taylor]: Taking taylor expansion of 1/2 in n 25.100 * [backup-simplify]: Simplify 1/2 into 1/2 25.100 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 25.100 * [taylor]: Taking taylor expansion of 1/2 in n 25.100 * [backup-simplify]: Simplify 1/2 into 1/2 25.100 * [taylor]: Taking taylor expansion of (/ 1 k) in n 25.101 * [taylor]: Taking taylor expansion of k in n 25.101 * [backup-simplify]: Simplify k into k 25.101 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 25.101 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 25.101 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 25.101 * [taylor]: Taking taylor expansion of 2 in n 25.101 * [backup-simplify]: Simplify 2 into 2 25.101 * [taylor]: Taking taylor expansion of (/ PI n) in n 25.101 * [taylor]: Taking taylor expansion of PI in n 25.101 * [backup-simplify]: Simplify PI into PI 25.101 * [taylor]: Taking taylor expansion of n in n 25.101 * [backup-simplify]: Simplify 0 into 0 25.101 * [backup-simplify]: Simplify 1 into 1 25.101 * [backup-simplify]: Simplify (/ PI 1) into PI 25.102 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 25.103 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 25.103 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 25.103 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 25.103 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 25.103 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 25.105 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 25.106 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 25.107 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 25.107 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n 25.107 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n 25.107 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n 25.107 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n 25.107 * [taylor]: Taking taylor expansion of 1/2 in n 25.107 * [backup-simplify]: Simplify 1/2 into 1/2 25.107 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 25.107 * [taylor]: Taking taylor expansion of 1/2 in n 25.107 * [backup-simplify]: Simplify 1/2 into 1/2 25.107 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 25.107 * [taylor]: Taking taylor expansion of 1/2 in n 25.107 * [backup-simplify]: Simplify 1/2 into 1/2 25.107 * [taylor]: Taking taylor expansion of (/ 1 k) in n 25.107 * [taylor]: Taking taylor expansion of k in n 25.108 * [backup-simplify]: Simplify k into k 25.108 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 25.108 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 25.108 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 25.108 * [taylor]: Taking taylor expansion of 2 in n 25.108 * [backup-simplify]: Simplify 2 into 2 25.108 * [taylor]: Taking taylor expansion of (/ PI n) in n 25.108 * [taylor]: Taking taylor expansion of PI in n 25.108 * [backup-simplify]: Simplify PI into PI 25.108 * [taylor]: Taking taylor expansion of n in n 25.108 * [backup-simplify]: Simplify 0 into 0 25.108 * [backup-simplify]: Simplify 1 into 1 25.108 * [backup-simplify]: Simplify (/ PI 1) into PI 25.109 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 25.110 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 25.110 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 25.110 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 25.110 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 25.110 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 25.112 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 25.113 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 25.114 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 25.114 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) in k 25.114 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 25.115 * [taylor]: Taking taylor expansion of 1/2 in k 25.115 * [backup-simplify]: Simplify 1/2 into 1/2 25.115 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 25.115 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 25.115 * [taylor]: Taking taylor expansion of 1/2 in k 25.115 * [backup-simplify]: Simplify 1/2 into 1/2 25.115 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 25.115 * [taylor]: Taking taylor expansion of 1/2 in k 25.115 * [backup-simplify]: Simplify 1/2 into 1/2 25.115 * [taylor]: Taking taylor expansion of (/ 1 k) in k 25.115 * [taylor]: Taking taylor expansion of k in k 25.115 * [backup-simplify]: Simplify 0 into 0 25.115 * [backup-simplify]: Simplify 1 into 1 25.115 * [backup-simplify]: Simplify (/ 1 1) into 1 25.115 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 25.115 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 25.115 * [taylor]: Taking taylor expansion of (* 2 PI) in k 25.115 * [taylor]: Taking taylor expansion of 2 in k 25.115 * [backup-simplify]: Simplify 2 into 2 25.115 * [taylor]: Taking taylor expansion of PI in k 25.115 * [backup-simplify]: Simplify PI into PI 25.116 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 25.117 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 25.117 * [taylor]: Taking taylor expansion of (log n) in k 25.117 * [taylor]: Taking taylor expansion of n in k 25.117 * [backup-simplify]: Simplify n into n 25.117 * [backup-simplify]: Simplify (log n) into (log n) 25.118 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 25.118 * [backup-simplify]: Simplify (- 1/2) into -1/2 25.119 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 25.119 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 25.120 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 25.121 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 25.123 * [backup-simplify]: Simplify (* 1/2 (* -1/2 (- (log (* 2 PI)) (log n)))) into (* -1/4 (- (log (* 2 PI)) (log n))) 25.124 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 25.125 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 25.126 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 25.127 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 25.128 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 25.129 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 25.129 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 25.130 * [backup-simplify]: Simplify (- 0) into 0 25.130 * [backup-simplify]: Simplify (+ 0 0) into 0 25.131 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0 25.132 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 25.133 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 25.135 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 25.135 * [taylor]: Taking taylor expansion of 0 in k 25.135 * [backup-simplify]: Simplify 0 into 0 25.136 * [backup-simplify]: Simplify 0 into 0 25.136 * [backup-simplify]: Simplify 0 into 0 25.137 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.138 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 25.141 * [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 25.141 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 25.142 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 25.143 * [backup-simplify]: Simplify (- 0) into 0 25.143 * [backup-simplify]: Simplify (+ 0 0) into 0 25.144 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k)))))) into 0 25.145 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 25.147 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 25.149 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 25.149 * [taylor]: Taking taylor expansion of 0 in k 25.149 * [backup-simplify]: Simplify 0 into 0 25.149 * [backup-simplify]: Simplify 0 into 0 25.149 * [backup-simplify]: Simplify 0 into 0 25.149 * [backup-simplify]: Simplify 0 into 0 25.151 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.152 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 25.159 * [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 25.159 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 25.161 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 25.161 * [backup-simplify]: Simplify (- 0) into 0 25.168 * [backup-simplify]: Simplify (+ 0 0) into 0 25.170 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))))) into 0 25.172 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 25.174 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 25.176 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 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 25.176 * [taylor]: Taking taylor expansion of 0 in k 25.176 * [backup-simplify]: Simplify 0 into 0 25.177 * [backup-simplify]: Simplify 0 into 0 25.178 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) 25.179 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (/ (- 1/2 (/ (/ 1 (- k)) 2)) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) 25.179 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in (n k) around 0 25.179 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in k 25.179 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in k 25.179 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in k 25.179 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in k 25.179 * [taylor]: Taking taylor expansion of 1/2 in k 25.179 * [backup-simplify]: Simplify 1/2 into 1/2 25.179 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 25.179 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 25.179 * [taylor]: Taking taylor expansion of 1/2 in k 25.179 * [backup-simplify]: Simplify 1/2 into 1/2 25.179 * [taylor]: Taking taylor expansion of (/ 1 k) in k 25.179 * [taylor]: Taking taylor expansion of k in k 25.179 * [backup-simplify]: Simplify 0 into 0 25.179 * [backup-simplify]: Simplify 1 into 1 25.179 * [backup-simplify]: Simplify (/ 1 1) into 1 25.179 * [taylor]: Taking taylor expansion of 1/2 in k 25.180 * [backup-simplify]: Simplify 1/2 into 1/2 25.180 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 25.180 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 25.180 * [taylor]: Taking taylor expansion of -2 in k 25.180 * [backup-simplify]: Simplify -2 into -2 25.180 * [taylor]: Taking taylor expansion of (/ PI n) in k 25.180 * [taylor]: Taking taylor expansion of PI in k 25.180 * [backup-simplify]: Simplify PI into PI 25.180 * [taylor]: Taking taylor expansion of n in k 25.180 * [backup-simplify]: Simplify n into n 25.180 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 25.180 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 25.180 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 25.180 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 25.181 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 25.181 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4 25.181 * [backup-simplify]: Simplify (* 1/4 (log (* -2 (/ PI n)))) into (* 1/4 (log (* -2 (/ PI n)))) 25.182 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 25.182 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n 25.182 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n 25.182 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n 25.182 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n 25.182 * [taylor]: Taking taylor expansion of 1/2 in n 25.182 * [backup-simplify]: Simplify 1/2 into 1/2 25.182 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 25.182 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 25.182 * [taylor]: Taking taylor expansion of 1/2 in n 25.182 * [backup-simplify]: Simplify 1/2 into 1/2 25.183 * [taylor]: Taking taylor expansion of (/ 1 k) in n 25.183 * [taylor]: Taking taylor expansion of k in n 25.183 * [backup-simplify]: Simplify k into k 25.183 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 25.183 * [taylor]: Taking taylor expansion of 1/2 in n 25.183 * [backup-simplify]: Simplify 1/2 into 1/2 25.183 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 25.183 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 25.183 * [taylor]: Taking taylor expansion of -2 in n 25.183 * [backup-simplify]: Simplify -2 into -2 25.183 * [taylor]: Taking taylor expansion of (/ PI n) in n 25.183 * [taylor]: Taking taylor expansion of PI in n 25.183 * [backup-simplify]: Simplify PI into PI 25.183 * [taylor]: Taking taylor expansion of n in n 25.183 * [backup-simplify]: Simplify 0 into 0 25.183 * [backup-simplify]: Simplify 1 into 1 25.184 * [backup-simplify]: Simplify (/ PI 1) into PI 25.184 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 25.185 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 25.185 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 25.185 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 25.185 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 25.187 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 25.188 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 25.190 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 25.190 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n 25.190 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n 25.190 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n 25.190 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n 25.190 * [taylor]: Taking taylor expansion of 1/2 in n 25.190 * [backup-simplify]: Simplify 1/2 into 1/2 25.190 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 25.190 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 25.190 * [taylor]: Taking taylor expansion of 1/2 in n 25.190 * [backup-simplify]: Simplify 1/2 into 1/2 25.190 * [taylor]: Taking taylor expansion of (/ 1 k) in n 25.190 * [taylor]: Taking taylor expansion of k in n 25.190 * [backup-simplify]: Simplify k into k 25.190 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 25.190 * [taylor]: Taking taylor expansion of 1/2 in n 25.190 * [backup-simplify]: Simplify 1/2 into 1/2 25.190 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 25.190 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 25.190 * [taylor]: Taking taylor expansion of -2 in n 25.190 * [backup-simplify]: Simplify -2 into -2 25.190 * [taylor]: Taking taylor expansion of (/ PI n) in n 25.190 * [taylor]: Taking taylor expansion of PI in n 25.190 * [backup-simplify]: Simplify PI into PI 25.190 * [taylor]: Taking taylor expansion of n in n 25.190 * [backup-simplify]: Simplify 0 into 0 25.190 * [backup-simplify]: Simplify 1 into 1 25.191 * [backup-simplify]: Simplify (/ PI 1) into PI 25.191 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 25.193 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 25.193 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 25.193 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 25.193 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 25.195 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 25.196 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 25.197 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 25.197 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) in k 25.197 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 25.197 * [taylor]: Taking taylor expansion of 1/2 in k 25.197 * [backup-simplify]: Simplify 1/2 into 1/2 25.197 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 25.197 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 25.197 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 25.198 * [taylor]: Taking taylor expansion of 1/2 in k 25.198 * [backup-simplify]: Simplify 1/2 into 1/2 25.198 * [taylor]: Taking taylor expansion of (/ 1 k) in k 25.198 * [taylor]: Taking taylor expansion of k in k 25.198 * [backup-simplify]: Simplify 0 into 0 25.198 * [backup-simplify]: Simplify 1 into 1 25.198 * [backup-simplify]: Simplify (/ 1 1) into 1 25.198 * [taylor]: Taking taylor expansion of 1/2 in k 25.198 * [backup-simplify]: Simplify 1/2 into 1/2 25.198 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 25.198 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 25.198 * [taylor]: Taking taylor expansion of (* -2 PI) in k 25.198 * [taylor]: Taking taylor expansion of -2 in k 25.198 * [backup-simplify]: Simplify -2 into -2 25.198 * [taylor]: Taking taylor expansion of PI in k 25.198 * [backup-simplify]: Simplify PI into PI 25.199 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 25.200 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 25.200 * [taylor]: Taking taylor expansion of (log n) in k 25.200 * [taylor]: Taking taylor expansion of n in k 25.200 * [backup-simplify]: Simplify n into n 25.200 * [backup-simplify]: Simplify (log n) into (log n) 25.201 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 25.201 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 25.201 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 25.202 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 25.203 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 25.205 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (- (log (* -2 PI)) (log n)))) into (* 1/4 (- (log (* -2 PI)) (log n))) 25.206 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 25.207 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 25.209 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 25.209 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 25.211 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 25.211 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 25.212 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 25.212 * [backup-simplify]: Simplify (+ 0 0) into 0 25.213 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 25.214 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 25.216 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 25.218 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 25.218 * [taylor]: Taking taylor expansion of 0 in k 25.218 * [backup-simplify]: Simplify 0 into 0 25.218 * [backup-simplify]: Simplify 0 into 0 25.218 * [backup-simplify]: Simplify 0 into 0 25.219 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.220 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 25.224 * [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 25.224 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 25.225 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 25.225 * [backup-simplify]: Simplify (+ 0 0) into 0 25.226 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 25.228 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 25.229 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 25.232 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 25.232 * [taylor]: Taking taylor expansion of 0 in k 25.232 * [backup-simplify]: Simplify 0 into 0 25.232 * [backup-simplify]: Simplify 0 into 0 25.232 * [backup-simplify]: Simplify 0 into 0 25.232 * [backup-simplify]: Simplify 0 into 0 25.233 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.235 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 25.241 * [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 25.241 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 25.242 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 25.243 * [backup-simplify]: Simplify (+ 0 0) into 0 25.244 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 25.244 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 25.246 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 25.247 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 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 25.247 * [taylor]: Taking taylor expansion of 0 in k 25.247 * [backup-simplify]: Simplify 0 into 0 25.247 * [backup-simplify]: Simplify 0 into 0 25.248 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) 25.248 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1) 25.249 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) 25.249 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in (n k) around 0 25.249 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in k 25.249 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in k 25.249 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in k 25.249 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in k 25.249 * [taylor]: Taking taylor expansion of 1/2 in k 25.249 * [backup-simplify]: Simplify 1/2 into 1/2 25.249 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 25.249 * [taylor]: Taking taylor expansion of 1/2 in k 25.249 * [backup-simplify]: Simplify 1/2 into 1/2 25.249 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 25.249 * [taylor]: Taking taylor expansion of 1/2 in k 25.249 * [backup-simplify]: Simplify 1/2 into 1/2 25.249 * [taylor]: Taking taylor expansion of k in k 25.249 * [backup-simplify]: Simplify 0 into 0 25.249 * [backup-simplify]: Simplify 1 into 1 25.249 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 25.249 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 25.249 * [taylor]: Taking taylor expansion of 2 in k 25.249 * [backup-simplify]: Simplify 2 into 2 25.249 * [taylor]: Taking taylor expansion of (* n PI) in k 25.249 * [taylor]: Taking taylor expansion of n in k 25.249 * [backup-simplify]: Simplify n into n 25.249 * [taylor]: Taking taylor expansion of PI in k 25.249 * [backup-simplify]: Simplify PI into PI 25.249 * [backup-simplify]: Simplify (* n PI) into (* n PI) 25.249 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 25.249 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 25.249 * [backup-simplify]: Simplify (* 1/2 0) into 0 25.250 * [backup-simplify]: Simplify (- 0) into 0 25.250 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 25.250 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4 25.250 * [backup-simplify]: Simplify (* 1/4 (log (* 2 (* n PI)))) into (* 1/4 (log (* 2 (* n PI)))) 25.250 * [backup-simplify]: Simplify (exp (* 1/4 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/4) 25.250 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n 25.250 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n 25.250 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n 25.250 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n 25.250 * [taylor]: Taking taylor expansion of 1/2 in n 25.250 * [backup-simplify]: Simplify 1/2 into 1/2 25.250 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 25.250 * [taylor]: Taking taylor expansion of 1/2 in n 25.250 * [backup-simplify]: Simplify 1/2 into 1/2 25.250 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 25.250 * [taylor]: Taking taylor expansion of 1/2 in n 25.250 * [backup-simplify]: Simplify 1/2 into 1/2 25.250 * [taylor]: Taking taylor expansion of k in n 25.251 * [backup-simplify]: Simplify k into k 25.251 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 25.251 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 25.251 * [taylor]: Taking taylor expansion of 2 in n 25.251 * [backup-simplify]: Simplify 2 into 2 25.251 * [taylor]: Taking taylor expansion of (* n PI) in n 25.251 * [taylor]: Taking taylor expansion of n in n 25.251 * [backup-simplify]: Simplify 0 into 0 25.251 * [backup-simplify]: Simplify 1 into 1 25.251 * [taylor]: Taking taylor expansion of PI in n 25.251 * [backup-simplify]: Simplify PI into PI 25.251 * [backup-simplify]: Simplify (* 0 PI) into 0 25.251 * [backup-simplify]: Simplify (* 2 0) into 0 25.252 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 25.253 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 25.254 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 25.254 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 25.254 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 25.254 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 25.254 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k))) 25.255 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 25.256 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 25.256 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 25.256 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n 25.256 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n 25.256 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n 25.256 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n 25.257 * [taylor]: Taking taylor expansion of 1/2 in n 25.257 * [backup-simplify]: Simplify 1/2 into 1/2 25.257 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 25.257 * [taylor]: Taking taylor expansion of 1/2 in n 25.257 * [backup-simplify]: Simplify 1/2 into 1/2 25.257 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 25.257 * [taylor]: Taking taylor expansion of 1/2 in n 25.257 * [backup-simplify]: Simplify 1/2 into 1/2 25.257 * [taylor]: Taking taylor expansion of k in n 25.257 * [backup-simplify]: Simplify k into k 25.257 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 25.257 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 25.257 * [taylor]: Taking taylor expansion of 2 in n 25.257 * [backup-simplify]: Simplify 2 into 2 25.257 * [taylor]: Taking taylor expansion of (* n PI) in n 25.257 * [taylor]: Taking taylor expansion of n in n 25.257 * [backup-simplify]: Simplify 0 into 0 25.257 * [backup-simplify]: Simplify 1 into 1 25.257 * [taylor]: Taking taylor expansion of PI in n 25.257 * [backup-simplify]: Simplify PI into PI 25.257 * [backup-simplify]: Simplify (* 0 PI) into 0 25.257 * [backup-simplify]: Simplify (* 2 0) into 0 25.258 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 25.259 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 25.260 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 25.260 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 25.260 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 25.260 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 25.260 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k))) 25.261 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 25.262 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 25.262 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 25.263 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) in k 25.263 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 25.263 * [taylor]: Taking taylor expansion of 1/2 in k 25.263 * [backup-simplify]: Simplify 1/2 into 1/2 25.263 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 25.263 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 25.263 * [taylor]: Taking taylor expansion of 1/2 in k 25.263 * [backup-simplify]: Simplify 1/2 into 1/2 25.263 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 25.263 * [taylor]: Taking taylor expansion of 1/2 in k 25.263 * [backup-simplify]: Simplify 1/2 into 1/2 25.263 * [taylor]: Taking taylor expansion of k in k 25.263 * [backup-simplify]: Simplify 0 into 0 25.263 * [backup-simplify]: Simplify 1 into 1 25.263 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 25.263 * [taylor]: Taking taylor expansion of (log n) in k 25.263 * [taylor]: Taking taylor expansion of n in k 25.263 * [backup-simplify]: Simplify n into n 25.263 * [backup-simplify]: Simplify (log n) into (log n) 25.263 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 25.263 * [taylor]: Taking taylor expansion of (* 2 PI) in k 25.263 * [taylor]: Taking taylor expansion of 2 in k 25.263 * [backup-simplify]: Simplify 2 into 2 25.263 * [taylor]: Taking taylor expansion of PI in k 25.263 * [backup-simplify]: Simplify PI into PI 25.263 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 25.264 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 25.264 * [backup-simplify]: Simplify (* 1/2 0) into 0 25.264 * [backup-simplify]: Simplify (- 0) into 0 25.265 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 25.265 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 25.266 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 25.267 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (+ (log n) (log (* 2 PI))))) into (* 1/4 (+ (log n) (log (* 2 PI)))) 25.267 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 25.268 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 25.269 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 25.269 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 25.271 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 25.271 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 25.272 * [backup-simplify]: Simplify (- 0) into 0 25.272 * [backup-simplify]: Simplify (+ 0 0) into 0 25.273 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 k)))) into 0 25.274 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 25.276 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 25.278 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0 25.278 * [taylor]: Taking taylor expansion of 0 in k 25.278 * [backup-simplify]: Simplify 0 into 0 25.278 * [backup-simplify]: Simplify 0 into 0 25.279 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 25.279 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 25.281 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 25.282 * [backup-simplify]: Simplify (+ 0 0) into 0 25.282 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 25.283 * [backup-simplify]: Simplify (- 1/2) into -1/2 25.283 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 25.285 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 25.288 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* 0 (* 1/2 (+ (log n) (log (* 2 PI)))))) into (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 25.291 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) 25.294 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) 25.296 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 25.303 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 25.307 * [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 25.308 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 25.309 * [backup-simplify]: Simplify (- 0) into 0 25.309 * [backup-simplify]: Simplify (+ 0 0) into 0 25.310 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 k))))) into 0 25.311 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 25.313 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 25.315 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 25.315 * [taylor]: Taking taylor expansion of 0 in k 25.315 * [backup-simplify]: Simplify 0 into 0 25.315 * [backup-simplify]: Simplify 0 into 0 25.315 * [backup-simplify]: Simplify 0 into 0 25.316 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 25.317 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 25.319 * [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 25.319 * [backup-simplify]: Simplify (+ 0 0) into 0 25.319 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 25.320 * [backup-simplify]: Simplify (- 0) into 0 25.320 * [backup-simplify]: Simplify (+ 0 0) into 0 25.321 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 25.323 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* 0 (* 1/2 (+ (log n) (log (* 2 PI))))))) into 0 25.326 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) 25.329 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) 25.335 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))))) 25.336 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (/ (- 1/2 (/ (/ 1 k) 2)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) 25.336 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 25.336 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in k 25.336 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in k 25.336 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in k 25.336 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in k 25.336 * [taylor]: Taking taylor expansion of 1/2 in k 25.336 * [backup-simplify]: Simplify 1/2 into 1/2 25.336 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 25.336 * [taylor]: Taking taylor expansion of 1/2 in k 25.336 * [backup-simplify]: Simplify 1/2 into 1/2 25.336 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 25.336 * [taylor]: Taking taylor expansion of 1/2 in k 25.336 * [backup-simplify]: Simplify 1/2 into 1/2 25.336 * [taylor]: Taking taylor expansion of (/ 1 k) in k 25.336 * [taylor]: Taking taylor expansion of k in k 25.336 * [backup-simplify]: Simplify 0 into 0 25.336 * [backup-simplify]: Simplify 1 into 1 25.336 * [backup-simplify]: Simplify (/ 1 1) into 1 25.336 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 25.336 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 25.336 * [taylor]: Taking taylor expansion of 2 in k 25.336 * [backup-simplify]: Simplify 2 into 2 25.336 * [taylor]: Taking taylor expansion of (/ PI n) in k 25.337 * [taylor]: Taking taylor expansion of PI in k 25.337 * [backup-simplify]: Simplify PI into PI 25.337 * [taylor]: Taking taylor expansion of n in k 25.337 * [backup-simplify]: Simplify n into n 25.337 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 25.337 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 25.337 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 25.337 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 25.337 * [backup-simplify]: Simplify (- 1/2) into -1/2 25.338 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 25.338 * [backup-simplify]: Simplify (* 1/2 -1/2) into -1/4 25.338 * [backup-simplify]: Simplify (* -1/4 (log (* 2 (/ PI n)))) into (* -1/4 (log (* 2 (/ PI n)))) 25.338 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))))) 25.338 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n 25.338 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n 25.338 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n 25.338 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n 25.338 * [taylor]: Taking taylor expansion of 1/2 in n 25.338 * [backup-simplify]: Simplify 1/2 into 1/2 25.338 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 25.338 * [taylor]: Taking taylor expansion of 1/2 in n 25.338 * [backup-simplify]: Simplify 1/2 into 1/2 25.338 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 25.338 * [taylor]: Taking taylor expansion of 1/2 in n 25.338 * [backup-simplify]: Simplify 1/2 into 1/2 25.338 * [taylor]: Taking taylor expansion of (/ 1 k) in n 25.338 * [taylor]: Taking taylor expansion of k in n 25.338 * [backup-simplify]: Simplify k into k 25.338 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 25.338 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 25.338 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 25.338 * [taylor]: Taking taylor expansion of 2 in n 25.338 * [backup-simplify]: Simplify 2 into 2 25.338 * [taylor]: Taking taylor expansion of (/ PI n) in n 25.338 * [taylor]: Taking taylor expansion of PI in n 25.338 * [backup-simplify]: Simplify PI into PI 25.338 * [taylor]: Taking taylor expansion of n in n 25.338 * [backup-simplify]: Simplify 0 into 0 25.338 * [backup-simplify]: Simplify 1 into 1 25.339 * [backup-simplify]: Simplify (/ PI 1) into PI 25.339 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 25.340 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 25.340 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 25.340 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 25.340 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 25.340 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 25.341 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 25.342 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 25.344 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 25.344 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n 25.344 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n 25.344 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n 25.344 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n 25.344 * [taylor]: Taking taylor expansion of 1/2 in n 25.344 * [backup-simplify]: Simplify 1/2 into 1/2 25.344 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 25.344 * [taylor]: Taking taylor expansion of 1/2 in n 25.344 * [backup-simplify]: Simplify 1/2 into 1/2 25.344 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 25.344 * [taylor]: Taking taylor expansion of 1/2 in n 25.344 * [backup-simplify]: Simplify 1/2 into 1/2 25.344 * [taylor]: Taking taylor expansion of (/ 1 k) in n 25.344 * [taylor]: Taking taylor expansion of k in n 25.344 * [backup-simplify]: Simplify k into k 25.344 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 25.344 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 25.344 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 25.344 * [taylor]: Taking taylor expansion of 2 in n 25.344 * [backup-simplify]: Simplify 2 into 2 25.344 * [taylor]: Taking taylor expansion of (/ PI n) in n 25.344 * [taylor]: Taking taylor expansion of PI in n 25.344 * [backup-simplify]: Simplify PI into PI 25.344 * [taylor]: Taking taylor expansion of n in n 25.344 * [backup-simplify]: Simplify 0 into 0 25.344 * [backup-simplify]: Simplify 1 into 1 25.345 * [backup-simplify]: Simplify (/ PI 1) into PI 25.346 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 25.347 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 25.347 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 25.347 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 25.347 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 25.347 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 25.349 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 25.351 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 25.353 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 25.353 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) in k 25.353 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 25.353 * [taylor]: Taking taylor expansion of 1/2 in k 25.353 * [backup-simplify]: Simplify 1/2 into 1/2 25.353 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 25.353 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 25.353 * [taylor]: Taking taylor expansion of 1/2 in k 25.353 * [backup-simplify]: Simplify 1/2 into 1/2 25.353 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 25.353 * [taylor]: Taking taylor expansion of 1/2 in k 25.353 * [backup-simplify]: Simplify 1/2 into 1/2 25.353 * [taylor]: Taking taylor expansion of (/ 1 k) in k 25.353 * [taylor]: Taking taylor expansion of k in k 25.353 * [backup-simplify]: Simplify 0 into 0 25.353 * [backup-simplify]: Simplify 1 into 1 25.354 * [backup-simplify]: Simplify (/ 1 1) into 1 25.354 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 25.354 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 25.354 * [taylor]: Taking taylor expansion of (* 2 PI) in k 25.354 * [taylor]: Taking taylor expansion of 2 in k 25.354 * [backup-simplify]: Simplify 2 into 2 25.354 * [taylor]: Taking taylor expansion of PI in k 25.354 * [backup-simplify]: Simplify PI into PI 25.355 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 25.356 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 25.356 * [taylor]: Taking taylor expansion of (log n) in k 25.356 * [taylor]: Taking taylor expansion of n in k 25.356 * [backup-simplify]: Simplify n into n 25.356 * [backup-simplify]: Simplify (log n) into (log n) 25.356 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 25.357 * [backup-simplify]: Simplify (- 1/2) into -1/2 25.357 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 25.357 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 25.358 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 25.359 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 25.361 * [backup-simplify]: Simplify (* 1/2 (* -1/2 (- (log (* 2 PI)) (log n)))) into (* -1/4 (- (log (* 2 PI)) (log n))) 25.362 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 25.363 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 25.364 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 25.365 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 25.367 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 25.367 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 25.368 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 25.368 * [backup-simplify]: Simplify (- 0) into 0 25.369 * [backup-simplify]: Simplify (+ 0 0) into 0 25.369 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0 25.371 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 25.373 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 25.375 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 25.375 * [taylor]: Taking taylor expansion of 0 in k 25.375 * [backup-simplify]: Simplify 0 into 0 25.375 * [backup-simplify]: Simplify 0 into 0 25.375 * [backup-simplify]: Simplify 0 into 0 25.376 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.377 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 25.380 * [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 25.381 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 25.382 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 25.382 * [backup-simplify]: Simplify (- 0) into 0 25.382 * [backup-simplify]: Simplify (+ 0 0) into 0 25.383 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k)))))) into 0 25.385 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 25.386 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 25.389 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 25.389 * [taylor]: Taking taylor expansion of 0 in k 25.389 * [backup-simplify]: Simplify 0 into 0 25.389 * [backup-simplify]: Simplify 0 into 0 25.389 * [backup-simplify]: Simplify 0 into 0 25.389 * [backup-simplify]: Simplify 0 into 0 25.391 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.392 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 25.398 * [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 25.398 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 25.400 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 25.400 * [backup-simplify]: Simplify (- 0) into 0 25.401 * [backup-simplify]: Simplify (+ 0 0) into 0 25.402 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))))) into 0 25.404 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 25.406 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 25.409 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 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 25.409 * [taylor]: Taking taylor expansion of 0 in k 25.409 * [backup-simplify]: Simplify 0 into 0 25.409 * [backup-simplify]: Simplify 0 into 0 25.410 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) 25.411 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (/ (- 1/2 (/ (/ 1 (- k)) 2)) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) 25.411 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in (n k) around 0 25.411 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in k 25.411 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in k 25.411 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in k 25.411 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in k 25.411 * [taylor]: Taking taylor expansion of 1/2 in k 25.411 * [backup-simplify]: Simplify 1/2 into 1/2 25.411 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 25.411 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 25.411 * [taylor]: Taking taylor expansion of 1/2 in k 25.411 * [backup-simplify]: Simplify 1/2 into 1/2 25.411 * [taylor]: Taking taylor expansion of (/ 1 k) in k 25.411 * [taylor]: Taking taylor expansion of k in k 25.411 * [backup-simplify]: Simplify 0 into 0 25.411 * [backup-simplify]: Simplify 1 into 1 25.412 * [backup-simplify]: Simplify (/ 1 1) into 1 25.412 * [taylor]: Taking taylor expansion of 1/2 in k 25.412 * [backup-simplify]: Simplify 1/2 into 1/2 25.412 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 25.412 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 25.412 * [taylor]: Taking taylor expansion of -2 in k 25.412 * [backup-simplify]: Simplify -2 into -2 25.412 * [taylor]: Taking taylor expansion of (/ PI n) in k 25.412 * [taylor]: Taking taylor expansion of PI in k 25.412 * [backup-simplify]: Simplify PI into PI 25.412 * [taylor]: Taking taylor expansion of n in k 25.412 * [backup-simplify]: Simplify n into n 25.412 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 25.412 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 25.412 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 25.413 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 25.413 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 25.413 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4 25.414 * [backup-simplify]: Simplify (* 1/4 (log (* -2 (/ PI n)))) into (* 1/4 (log (* -2 (/ PI n)))) 25.414 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 25.414 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n 25.414 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n 25.414 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n 25.414 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n 25.414 * [taylor]: Taking taylor expansion of 1/2 in n 25.414 * [backup-simplify]: Simplify 1/2 into 1/2 25.414 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 25.414 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 25.414 * [taylor]: Taking taylor expansion of 1/2 in n 25.414 * [backup-simplify]: Simplify 1/2 into 1/2 25.414 * [taylor]: Taking taylor expansion of (/ 1 k) in n 25.414 * [taylor]: Taking taylor expansion of k in n 25.414 * [backup-simplify]: Simplify k into k 25.414 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 25.414 * [taylor]: Taking taylor expansion of 1/2 in n 25.414 * [backup-simplify]: Simplify 1/2 into 1/2 25.414 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 25.414 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 25.414 * [taylor]: Taking taylor expansion of -2 in n 25.414 * [backup-simplify]: Simplify -2 into -2 25.414 * [taylor]: Taking taylor expansion of (/ PI n) in n 25.414 * [taylor]: Taking taylor expansion of PI in n 25.414 * [backup-simplify]: Simplify PI into PI 25.415 * [taylor]: Taking taylor expansion of n in n 25.415 * [backup-simplify]: Simplify 0 into 0 25.415 * [backup-simplify]: Simplify 1 into 1 25.415 * [backup-simplify]: Simplify (/ PI 1) into PI 25.416 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 25.417 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 25.417 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 25.417 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 25.417 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 25.419 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 25.420 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 25.422 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 25.422 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n 25.422 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n 25.422 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n 25.422 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n 25.422 * [taylor]: Taking taylor expansion of 1/2 in n 25.422 * [backup-simplify]: Simplify 1/2 into 1/2 25.422 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 25.422 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 25.422 * [taylor]: Taking taylor expansion of 1/2 in n 25.422 * [backup-simplify]: Simplify 1/2 into 1/2 25.422 * [taylor]: Taking taylor expansion of (/ 1 k) in n 25.422 * [taylor]: Taking taylor expansion of k in n 25.422 * [backup-simplify]: Simplify k into k 25.422 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 25.422 * [taylor]: Taking taylor expansion of 1/2 in n 25.422 * [backup-simplify]: Simplify 1/2 into 1/2 25.422 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 25.422 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 25.422 * [taylor]: Taking taylor expansion of -2 in n 25.422 * [backup-simplify]: Simplify -2 into -2 25.422 * [taylor]: Taking taylor expansion of (/ PI n) in n 25.422 * [taylor]: Taking taylor expansion of PI in n 25.423 * [backup-simplify]: Simplify PI into PI 25.423 * [taylor]: Taking taylor expansion of n in n 25.423 * [backup-simplify]: Simplify 0 into 0 25.423 * [backup-simplify]: Simplify 1 into 1 25.423 * [backup-simplify]: Simplify (/ PI 1) into PI 25.424 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 25.425 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 25.425 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 25.425 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 25.425 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 25.427 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 25.428 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 25.429 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 25.429 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) in k 25.429 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 25.429 * [taylor]: Taking taylor expansion of 1/2 in k 25.429 * [backup-simplify]: Simplify 1/2 into 1/2 25.429 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 25.429 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 25.429 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 25.429 * [taylor]: Taking taylor expansion of 1/2 in k 25.429 * [backup-simplify]: Simplify 1/2 into 1/2 25.429 * [taylor]: Taking taylor expansion of (/ 1 k) in k 25.429 * [taylor]: Taking taylor expansion of k in k 25.429 * [backup-simplify]: Simplify 0 into 0 25.429 * [backup-simplify]: Simplify 1 into 1 25.430 * [backup-simplify]: Simplify (/ 1 1) into 1 25.430 * [taylor]: Taking taylor expansion of 1/2 in k 25.430 * [backup-simplify]: Simplify 1/2 into 1/2 25.430 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 25.430 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 25.430 * [taylor]: Taking taylor expansion of (* -2 PI) in k 25.430 * [taylor]: Taking taylor expansion of -2 in k 25.430 * [backup-simplify]: Simplify -2 into -2 25.430 * [taylor]: Taking taylor expansion of PI in k 25.430 * [backup-simplify]: Simplify PI into PI 25.431 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 25.432 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 25.432 * [taylor]: Taking taylor expansion of (log n) in k 25.432 * [taylor]: Taking taylor expansion of n in k 25.432 * [backup-simplify]: Simplify n into n 25.432 * [backup-simplify]: Simplify (log n) into (log n) 25.432 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 25.433 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 25.433 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 25.434 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 25.441 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 25.443 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (- (log (* -2 PI)) (log n)))) into (* 1/4 (- (log (* -2 PI)) (log n))) 25.444 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 25.445 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 25.446 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 25.447 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 25.448 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 25.448 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 25.448 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 25.448 * [backup-simplify]: Simplify (+ 0 0) into 0 25.449 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 25.450 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 25.450 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 25.452 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 25.452 * [taylor]: Taking taylor expansion of 0 in k 25.452 * [backup-simplify]: Simplify 0 into 0 25.452 * [backup-simplify]: Simplify 0 into 0 25.452 * [backup-simplify]: Simplify 0 into 0 25.452 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.453 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 25.455 * [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 25.455 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 25.456 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 25.456 * [backup-simplify]: Simplify (+ 0 0) into 0 25.457 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 25.457 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 25.458 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 25.460 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 25.460 * [taylor]: Taking taylor expansion of 0 in k 25.460 * [backup-simplify]: Simplify 0 into 0 25.460 * [backup-simplify]: Simplify 0 into 0 25.460 * [backup-simplify]: Simplify 0 into 0 25.460 * [backup-simplify]: Simplify 0 into 0 25.461 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.461 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 25.465 * [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 25.465 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 25.466 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 25.466 * [backup-simplify]: Simplify (+ 0 0) into 0 25.467 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 25.468 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 25.469 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 25.471 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 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 25.471 * [taylor]: Taking taylor expansion of 0 in k 25.471 * [backup-simplify]: Simplify 0 into 0 25.471 * [backup-simplify]: Simplify 0 into 0 25.472 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) 25.472 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 2 1) 25.473 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) 25.473 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 25.473 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 25.473 * [taylor]: Taking taylor expansion of 2 in n 25.473 * [backup-simplify]: Simplify 2 into 2 25.473 * [taylor]: Taking taylor expansion of (* n PI) in n 25.473 * [taylor]: Taking taylor expansion of n in n 25.473 * [backup-simplify]: Simplify 0 into 0 25.473 * [backup-simplify]: Simplify 1 into 1 25.473 * [taylor]: Taking taylor expansion of PI in n 25.473 * [backup-simplify]: Simplify PI into PI 25.473 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 25.473 * [taylor]: Taking taylor expansion of 2 in n 25.473 * [backup-simplify]: Simplify 2 into 2 25.473 * [taylor]: Taking taylor expansion of (* n PI) in n 25.473 * [taylor]: Taking taylor expansion of n in n 25.473 * [backup-simplify]: Simplify 0 into 0 25.473 * [backup-simplify]: Simplify 1 into 1 25.473 * [taylor]: Taking taylor expansion of PI in n 25.473 * [backup-simplify]: Simplify PI into PI 25.473 * [backup-simplify]: Simplify (* 0 PI) into 0 25.473 * [backup-simplify]: Simplify (* 2 0) into 0 25.474 * [backup-simplify]: Simplify 0 into 0 25.475 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 25.476 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 25.476 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 25.476 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 25.477 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 25.477 * [backup-simplify]: Simplify 0 into 0 25.478 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 25.479 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 25.479 * [backup-simplify]: Simplify 0 into 0 25.481 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 25.482 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 25.482 * [backup-simplify]: Simplify 0 into 0 25.484 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 25.486 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 25.486 * [backup-simplify]: Simplify 0 into 0 25.488 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 25.490 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 25.490 * [backup-simplify]: Simplify 0 into 0 25.492 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 25.494 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 25.495 * [backup-simplify]: Simplify 0 into 0 25.495 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 25.496 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) 25.496 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 25.496 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 25.496 * [taylor]: Taking taylor expansion of 2 in n 25.496 * [backup-simplify]: Simplify 2 into 2 25.496 * [taylor]: Taking taylor expansion of (/ PI n) in n 25.496 * [taylor]: Taking taylor expansion of PI in n 25.496 * [backup-simplify]: Simplify PI into PI 25.496 * [taylor]: Taking taylor expansion of n in n 25.496 * [backup-simplify]: Simplify 0 into 0 25.496 * [backup-simplify]: Simplify 1 into 1 25.497 * [backup-simplify]: Simplify (/ PI 1) into PI 25.497 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 25.497 * [taylor]: Taking taylor expansion of 2 in n 25.497 * [backup-simplify]: Simplify 2 into 2 25.497 * [taylor]: Taking taylor expansion of (/ PI n) in n 25.497 * [taylor]: Taking taylor expansion of PI in n 25.497 * [backup-simplify]: Simplify PI into PI 25.497 * [taylor]: Taking taylor expansion of n in n 25.497 * [backup-simplify]: Simplify 0 into 0 25.497 * [backup-simplify]: Simplify 1 into 1 25.497 * [backup-simplify]: Simplify (/ PI 1) into PI 25.498 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 25.498 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 25.499 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 25.500 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 25.500 * [backup-simplify]: Simplify 0 into 0 25.501 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.502 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 25.502 * [backup-simplify]: Simplify 0 into 0 25.504 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.505 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 25.505 * [backup-simplify]: Simplify 0 into 0 25.506 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.508 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 25.508 * [backup-simplify]: Simplify 0 into 0 25.509 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.510 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 25.511 * [backup-simplify]: Simplify 0 into 0 25.512 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.514 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 25.514 * [backup-simplify]: Simplify 0 into 0 25.514 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 25.515 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n)) 25.515 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 25.515 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 25.515 * [taylor]: Taking taylor expansion of -2 in n 25.515 * [backup-simplify]: Simplify -2 into -2 25.515 * [taylor]: Taking taylor expansion of (/ PI n) in n 25.515 * [taylor]: Taking taylor expansion of PI in n 25.515 * [backup-simplify]: Simplify PI into PI 25.515 * [taylor]: Taking taylor expansion of n in n 25.515 * [backup-simplify]: Simplify 0 into 0 25.515 * [backup-simplify]: Simplify 1 into 1 25.516 * [backup-simplify]: Simplify (/ PI 1) into PI 25.516 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 25.516 * [taylor]: Taking taylor expansion of -2 in n 25.516 * [backup-simplify]: Simplify -2 into -2 25.516 * [taylor]: Taking taylor expansion of (/ PI n) in n 25.516 * [taylor]: Taking taylor expansion of PI in n 25.516 * [backup-simplify]: Simplify PI into PI 25.516 * [taylor]: Taking taylor expansion of n in n 25.516 * [backup-simplify]: Simplify 0 into 0 25.516 * [backup-simplify]: Simplify 1 into 1 25.517 * [backup-simplify]: Simplify (/ PI 1) into PI 25.517 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 25.518 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 25.519 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 25.520 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 25.520 * [backup-simplify]: Simplify 0 into 0 25.521 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.522 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 25.522 * [backup-simplify]: Simplify 0 into 0 25.523 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.523 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 25.523 * [backup-simplify]: Simplify 0 into 0 25.524 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.525 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 25.525 * [backup-simplify]: Simplify 0 into 0 25.525 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.526 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 25.526 * [backup-simplify]: Simplify 0 into 0 25.527 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.528 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 25.528 * [backup-simplify]: Simplify 0 into 0 25.528 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 25.529 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1 1) 25.529 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) 25.529 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 25.529 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 25.529 * [taylor]: Taking taylor expansion of 2 in n 25.529 * [backup-simplify]: Simplify 2 into 2 25.529 * [taylor]: Taking taylor expansion of (* n PI) in n 25.529 * [taylor]: Taking taylor expansion of n in n 25.529 * [backup-simplify]: Simplify 0 into 0 25.529 * [backup-simplify]: Simplify 1 into 1 25.529 * [taylor]: Taking taylor expansion of PI in n 25.529 * [backup-simplify]: Simplify PI into PI 25.529 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 25.529 * [taylor]: Taking taylor expansion of 2 in n 25.529 * [backup-simplify]: Simplify 2 into 2 25.529 * [taylor]: Taking taylor expansion of (* n PI) in n 25.529 * [taylor]: Taking taylor expansion of n in n 25.529 * [backup-simplify]: Simplify 0 into 0 25.529 * [backup-simplify]: Simplify 1 into 1 25.529 * [taylor]: Taking taylor expansion of PI in n 25.529 * [backup-simplify]: Simplify PI into PI 25.529 * [backup-simplify]: Simplify (* 0 PI) into 0 25.530 * [backup-simplify]: Simplify (* 2 0) into 0 25.530 * [backup-simplify]: Simplify 0 into 0 25.531 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 25.532 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 25.532 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 25.533 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 25.533 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 25.533 * [backup-simplify]: Simplify 0 into 0 25.534 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 25.535 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 25.535 * [backup-simplify]: Simplify 0 into 0 25.536 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 25.536 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 25.537 * [backup-simplify]: Simplify 0 into 0 25.537 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 25.538 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 25.538 * [backup-simplify]: Simplify 0 into 0 25.539 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 25.540 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 25.540 * [backup-simplify]: Simplify 0 into 0 25.541 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 25.543 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 25.543 * [backup-simplify]: Simplify 0 into 0 25.543 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 25.543 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) 25.543 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 25.543 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 25.543 * [taylor]: Taking taylor expansion of 2 in n 25.543 * [backup-simplify]: Simplify 2 into 2 25.543 * [taylor]: Taking taylor expansion of (/ PI n) in n 25.543 * [taylor]: Taking taylor expansion of PI in n 25.543 * [backup-simplify]: Simplify PI into PI 25.543 * [taylor]: Taking taylor expansion of n in n 25.543 * [backup-simplify]: Simplify 0 into 0 25.543 * [backup-simplify]: Simplify 1 into 1 25.544 * [backup-simplify]: Simplify (/ PI 1) into PI 25.544 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 25.544 * [taylor]: Taking taylor expansion of 2 in n 25.544 * [backup-simplify]: Simplify 2 into 2 25.544 * [taylor]: Taking taylor expansion of (/ PI n) in n 25.544 * [taylor]: Taking taylor expansion of PI in n 25.544 * [backup-simplify]: Simplify PI into PI 25.544 * [taylor]: Taking taylor expansion of n in n 25.544 * [backup-simplify]: Simplify 0 into 0 25.544 * [backup-simplify]: Simplify 1 into 1 25.544 * [backup-simplify]: Simplify (/ PI 1) into PI 25.545 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 25.545 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 25.546 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 25.546 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 25.546 * [backup-simplify]: Simplify 0 into 0 25.547 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.547 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 25.547 * [backup-simplify]: Simplify 0 into 0 25.548 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.549 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 25.549 * [backup-simplify]: Simplify 0 into 0 25.549 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.555 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 25.555 * [backup-simplify]: Simplify 0 into 0 25.556 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.557 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 25.557 * [backup-simplify]: Simplify 0 into 0 25.558 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.559 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 25.559 * [backup-simplify]: Simplify 0 into 0 25.559 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 25.560 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n)) 25.560 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 25.560 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 25.560 * [taylor]: Taking taylor expansion of -2 in n 25.560 * [backup-simplify]: Simplify -2 into -2 25.560 * [taylor]: Taking taylor expansion of (/ PI n) in n 25.560 * [taylor]: Taking taylor expansion of PI in n 25.560 * [backup-simplify]: Simplify PI into PI 25.560 * [taylor]: Taking taylor expansion of n in n 25.560 * [backup-simplify]: Simplify 0 into 0 25.560 * [backup-simplify]: Simplify 1 into 1 25.560 * [backup-simplify]: Simplify (/ PI 1) into PI 25.560 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 25.560 * [taylor]: Taking taylor expansion of -2 in n 25.560 * [backup-simplify]: Simplify -2 into -2 25.560 * [taylor]: Taking taylor expansion of (/ PI n) in n 25.560 * [taylor]: Taking taylor expansion of PI in n 25.560 * [backup-simplify]: Simplify PI into PI 25.560 * [taylor]: Taking taylor expansion of n in n 25.560 * [backup-simplify]: Simplify 0 into 0 25.560 * [backup-simplify]: Simplify 1 into 1 25.561 * [backup-simplify]: Simplify (/ PI 1) into PI 25.561 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 25.561 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 25.562 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 25.563 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 25.563 * [backup-simplify]: Simplify 0 into 0 25.563 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.564 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 25.564 * [backup-simplify]: Simplify 0 into 0 25.565 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.565 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 25.565 * [backup-simplify]: Simplify 0 into 0 25.566 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.567 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 25.567 * [backup-simplify]: Simplify 0 into 0 25.568 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.569 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 25.569 * [backup-simplify]: Simplify 0 into 0 25.570 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 25.571 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 25.571 * [backup-simplify]: Simplify 0 into 0 25.571 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 25.571 * * * [progress]: simplifying candidates 25.571 * * * * [progress]: [ 1 / 138 ] simplifiying candidate # 25.571 * * * * [progress]: [ 2 / 138 ] simplifiying candidate # 25.571 * * * * [progress]: [ 3 / 138 ] simplifiying candidate # 25.571 * * * * [progress]: [ 4 / 138 ] simplifiying candidate # 25.571 * * * * [progress]: [ 5 / 138 ] simplifiying candidate # 25.571 * * * * [progress]: [ 6 / 138 ] simplifiying candidate # 25.572 * * * * [progress]: [ 7 / 138 ] simplifiying candidate # 25.572 * * * * [progress]: [ 8 / 138 ] simplifiying candidate # 25.572 * * * * [progress]: [ 9 / 138 ] simplifiying candidate # 25.572 * * * * [progress]: [ 10 / 138 ] simplifiying candidate # 25.572 * * * * [progress]: [ 11 / 138 ] simplifiying candidate # 25.572 * * * * [progress]: [ 12 / 138 ] simplifiying candidate # 25.572 * * * * [progress]: [ 13 / 138 ] simplifiying candidate # 25.572 * * * * [progress]: [ 14 / 138 ] simplifiying candidate # 25.572 * * * * [progress]: [ 15 / 138 ] simplifiying candidate # 25.572 * * * * [progress]: [ 16 / 138 ] simplifiying candidate # 25.572 * * * * [progress]: [ 17 / 138 ] simplifiying candidate # 25.572 * * * * [progress]: [ 18 / 138 ] simplifiying candidate # 25.572 * * * * [progress]: [ 19 / 138 ] simplifiying candidate # 25.572 * * * * [progress]: [ 20 / 138 ] simplifiying candidate # 25.572 * * * * [progress]: [ 21 / 138 ] simplifiying candidate # 25.572 * * * * [progress]: [ 22 / 138 ] simplifiying candidate # 25.572 * * * * [progress]: [ 23 / 138 ] simplifiying candidate # 25.572 * * * * [progress]: [ 24 / 138 ] simplifiying candidate # 25.572 * * * * [progress]: [ 25 / 138 ] simplifiying candidate # 25.572 * * * * [progress]: [ 26 / 138 ] simplifiying candidate # 25.572 * * * * [progress]: [ 27 / 138 ] simplifiying candidate # 25.572 * * * * [progress]: [ 28 / 138 ] simplifiying candidate # 25.573 * * * * [progress]: [ 29 / 138 ] simplifiying candidate # 25.573 * * * * [progress]: [ 30 / 138 ] simplifiying candidate # 25.573 * * * * [progress]: [ 31 / 138 ] simplifiying candidate # 25.573 * * * * [progress]: [ 32 / 138 ] simplifiying candidate # 25.573 * * * * [progress]: [ 33 / 138 ] simplifiying candidate # 25.573 * * * * [progress]: [ 34 / 138 ] simplifiying candidate # 25.573 * * * * [progress]: [ 35 / 138 ] simplifiying candidate # 25.573 * * * * [progress]: [ 36 / 138 ] simplifiying candidate # 25.573 * * * * [progress]: [ 37 / 138 ] simplifiying candidate # 25.573 * * * * [progress]: [ 38 / 138 ] simplifiying candidate # 25.573 * * * * [progress]: [ 39 / 138 ] simplifiying candidate # 25.573 * * * * [progress]: [ 40 / 138 ] simplifiying candidate # 25.573 * * * * [progress]: [ 41 / 138 ] simplifiying candidate # 25.573 * * * * [progress]: [ 42 / 138 ] simplifiying candidate #real (real->posit16 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))) (sqrt k)))> 25.573 * * * * [progress]: [ 43 / 138 ] simplifiying candidate # 25.573 * * * * [progress]: [ 44 / 138 ] simplifiying candidate # 25.573 * * * * [progress]: [ 45 / 138 ] simplifiying candidate # 25.573 * * * * [progress]: [ 46 / 138 ] simplifiying candidate # 25.573 * * * * [progress]: [ 47 / 138 ] simplifiying candidate # 25.573 * * * * [progress]: [ 48 / 138 ] simplifiying candidate # 25.573 * * * * [progress]: [ 49 / 138 ] simplifiying candidate # 25.573 * * * * [progress]: [ 50 / 138 ] simplifiying candidate # 25.573 * * * * [progress]: [ 51 / 138 ] simplifiying candidate # 25.573 * * * * [progress]: [ 52 / 138 ] simplifiying candidate # 25.574 * * * * [progress]: [ 53 / 138 ] simplifiying candidate # 25.574 * * * * [progress]: [ 54 / 138 ] simplifiying candidate # 25.574 * * * * [progress]: [ 55 / 138 ] simplifiying candidate # 25.574 * * * * [progress]: [ 56 / 138 ] simplifiying candidate # 25.574 * * * * [progress]: [ 57 / 138 ] simplifiying candidate # 25.574 * * * * [progress]: [ 58 / 138 ] simplifiying candidate # 25.574 * * * * [progress]: [ 59 / 138 ] simplifiying candidate # 25.574 * * * * [progress]: [ 60 / 138 ] simplifiying candidate # 25.574 * * * * [progress]: [ 61 / 138 ] simplifiying candidate # 25.574 * * * * [progress]: [ 62 / 138 ] simplifiying candidate # 25.574 * * * * [progress]: [ 63 / 138 ] simplifiying candidate # 25.574 * * * * [progress]: [ 64 / 138 ] simplifiying candidate # 25.574 * * * * [progress]: [ 65 / 138 ] simplifiying candidate # 25.574 * * * * [progress]: [ 66 / 138 ] simplifiying candidate # 25.574 * * * * [progress]: [ 67 / 138 ] simplifiying candidate # 25.574 * * * * [progress]: [ 68 / 138 ] simplifiying candidate # 25.574 * * * * [progress]: [ 69 / 138 ] simplifiying candidate # 25.574 * * * * [progress]: [ 70 / 138 ] simplifiying candidate # 25.574 * * * * [progress]: [ 71 / 138 ] simplifiying candidate # 25.574 * * * * [progress]: [ 72 / 138 ] simplifiying candidate # 25.574 * * * * [progress]: [ 73 / 138 ] simplifiying candidate # 25.574 * * * * [progress]: [ 74 / 138 ] simplifiying candidate # 25.575 * * * * [progress]: [ 75 / 138 ] simplifiying candidate # 25.575 * * * * [progress]: [ 76 / 138 ] simplifiying candidate # 25.575 * * * * [progress]: [ 77 / 138 ] simplifiying candidate # 25.575 * * * * [progress]: [ 78 / 138 ] simplifiying candidate # 25.575 * * * * [progress]: [ 79 / 138 ] simplifiying candidate # 25.575 * * * * [progress]: [ 80 / 138 ] simplifiying candidate # 25.575 * * * * [progress]: [ 81 / 138 ] simplifiying candidate # 25.575 * * * * [progress]: [ 82 / 138 ] simplifiying candidate # 25.575 * * * * [progress]: [ 83 / 138 ] simplifiying candidate # 25.575 * * * * [progress]: [ 84 / 138 ] simplifiying candidate #real (real->posit16 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))> 25.575 * * * * [progress]: [ 85 / 138 ] simplifiying candidate # 25.575 * * * * [progress]: [ 86 / 138 ] simplifiying candidate # 25.575 * * * * [progress]: [ 87 / 138 ] simplifiying candidate # 25.575 * * * * [progress]: [ 88 / 138 ] simplifiying candidate # 25.575 * * * * [progress]: [ 89 / 138 ] simplifiying candidate # 25.575 * * * * [progress]: [ 90 / 138 ] simplifiying candidate # 25.575 * * * * [progress]: [ 91 / 138 ] simplifiying candidate # 25.575 * * * * [progress]: [ 92 / 138 ] simplifiying candidate # 25.575 * * * * [progress]: [ 93 / 138 ] simplifiying candidate # 25.575 * * * * [progress]: [ 94 / 138 ] simplifiying candidate # 25.575 * * 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[progress]: [ 124 / 138 ] simplifiying candidate # 25.577 * * * * [progress]: [ 125 / 138 ] simplifiying candidate #real (real->posit16 (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))> 25.577 * * * * [progress]: [ 126 / 138 ] simplifiying candidate # 25.577 * * * * [progress]: [ 127 / 138 ] simplifiying candidate # 25.577 * * * * [progress]: [ 128 / 138 ] simplifiying candidate # 25.577 * * * * [progress]: [ 129 / 138 ] simplifiying candidate # 25.577 * * * * [progress]: [ 130 / 138 ] simplifiying candidate # 25.577 * * * * [progress]: [ 131 / 138 ] simplifiying candidate # 25.577 * * * * [progress]: [ 132 / 138 ] simplifiying candidate # 25.577 * * * * [progress]: [ 133 / 138 ] simplifiying candidate # 25.577 * * * * [progress]: [ 134 / 138 ] simplifiying candidate # 25.577 * * * * [progress]: [ 135 / 138 ] simplifiying candidate # 25.577 * * * * [progress]: [ 136 / 138 ] simplifiying candidate # 25.577 * * * * [progress]: [ 137 / 138 ] simplifiying candidate # 25.577 * * * * [progress]: [ 138 / 138 ] simplifiying candidate # 25.579 * [simplify]: Simplifying: (expm1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log1p (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (* 1 (/ (- 1/2 (/ k 2)) 2)) (* 1 (/ (- 1/2 (/ k 2)) 2)) (* 1 (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ 1/2 2)) (pow (* n (* 2 PI)) (/ (/ k 2) 2)) (pow (* n (* 2 PI)) (* (cbrt (/ (- 1/2 (/ k 2)) 2)) (cbrt (/ (- 1/2 (/ k 2)) 2)))) (pow (* n (* 2 PI)) (sqrt (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (sqrt 2))) (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) 1)) (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))) (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) 1)) (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (pow (* n (* 2 PI)) (/ 1 1)) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2))) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) 1)) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) 1)) (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (pow (* n (* 2 PI)) (/ 1 1)) (pow (* n (* 2 PI)) 1) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (exp (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (* (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (real->posit16 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (expm1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log1p (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (* 1 (/ (- 1/2 (/ k 2)) 2)) (* 1 (/ (- 1/2 (/ k 2)) 2)) (* 1 (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ 1/2 2)) (pow (* n (* 2 PI)) (/ (/ k 2) 2)) (pow (* n (* 2 PI)) (* (cbrt (/ (- 1/2 (/ k 2)) 2)) (cbrt (/ (- 1/2 (/ k 2)) 2)))) (pow (* n (* 2 PI)) (sqrt (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (sqrt 2))) (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) 1)) (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))) (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) 1)) (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (pow (* n (* 2 PI)) (/ 1 1)) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2))) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) 1)) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) 1)) (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (pow (* n (* 2 PI)) (/ 1 1)) (pow (* n (* 2 PI)) 1) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (exp (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (* (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (real->posit16 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (expm1 (* n (* 2 PI))) (log1p (* n (* 2 PI))) (* n (* 2 PI)) (* n (* 2 PI)) (+ (log n) (+ (log 2) (log PI))) (+ (log n) (log (* 2 PI))) (log (* n (* 2 PI))) (exp (* n (* 2 PI))) (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI))) (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI))) (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI))) (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI))) (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI))) (* n 2) (* (cbrt n) (* 2 PI)) (* (sqrt n) (* 2 PI)) (* n (* 2 PI)) (real->posit16 (* n (* 2 PI))) (expm1 (* n (* 2 PI))) (log1p (* n (* 2 PI))) (* n (* 2 PI)) (* n (* 2 PI)) (+ (log n) (+ (log 2) (log PI))) (+ (log n) (log (* 2 PI))) (log (* n (* 2 PI))) (exp (* n (* 2 PI))) (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI))) (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI))) (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI))) (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI))) (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI))) (* n 2) (* (cbrt n) (* 2 PI)) (* (sqrt n) (* 2 PI)) (* n (* 2 PI)) (real->posit16 (* n (* 2 PI))) (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) (* 2 (* n PI)) (* 2 (* n PI)) (* 2 (* n PI)) (* 2 (* n PI)) (* 2 (* n PI)) (* 2 (* n PI)) 25.582 * * [simplify]: iteration 0: 165 enodes 25.629 * * [simplify]: iteration 1: 455 enodes 25.892 * * [simplify]: iteration 2: 1480 enodes 26.290 * * [simplify]: iteration 3: 2012 enodes 26.626 * * [simplify]: iteration complete: 2012 enodes 26.626 * * [simplify]: Extracting #0: cost 49 inf + 0 26.627 * * [simplify]: Extracting #1: cost 326 inf + 0 26.631 * * [simplify]: Extracting #2: cost 577 inf + 3783 26.641 * * [simplify]: Extracting #3: cost 401 inf + 49768 26.670 * * [simplify]: Extracting #4: cost 154 inf + 125993 26.731 * * [simplify]: Extracting #5: cost 51 inf + 172238 26.780 * * [simplify]: Extracting #6: cost 23 inf + 183455 26.864 * * [simplify]: Extracting #7: cost 2 inf + 190999 26.928 * * [simplify]: Extracting #8: cost 0 inf + 190629 27.004 * * [simplify]: Extracting #9: cost 0 inf + 190559 27.078 * [simplify]: Simplified to: (expm1 (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (log1p (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (* (- 1/4 (/ k 4)) (log (* (* PI 2) n))) (* (- 1/4 (/ k 4)) (log (* (* PI 2) n))) (* (- 1/4 (/ k 4)) (log (* (* PI 2) n))) (* (- 1/4 (/ k 4)) (log (* (* PI 2) n))) (- 1/4 (/ k 4)) (- 1/4 (/ k 4)) (- 1/4 (/ k 4)) (exp (* (log (* (* PI 2) n)) 1/4)) (pow (* (* PI 2) n) (/ k 4)) (pow (* (* PI 2) n) (* (cbrt (- 1/4 (/ k 4))) (cbrt (- 1/4 (/ k 4))))) (pow (* (* PI 2) n) (sqrt (- 1/4 (/ k 4)))) (pow (* (* PI 2) n) (* (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2)) (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2)))) (pow (* (* PI 2) n) (* (/ (cbrt (- 1/2 (/ k 2))) (sqrt 2)) (cbrt (- 1/2 (/ k 2))))) (pow (* (* PI 2) n) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (pow (* (* PI 2) n) (/ (sqrt (- 1/2 (/ k 2))) (* (cbrt 2) (cbrt 2)))) (pow (* (* PI 2) n) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))) (pow (* (* PI 2) n) (sqrt (- 1/2 (/ k 2)))) (pow (* (* PI 2) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* PI 2) n) (/ 1 (sqrt 2))) (* (* PI 2) n) (pow (* (* PI 2) n) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (* (cbrt 2) (cbrt 2)))) (pow (* (* PI 2) n) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2))) (pow (* (* PI 2) n) (+ (sqrt 1/2) (sqrt (/ k 2)))) (pow (* (* PI 2) n) (/ (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (cbrt 2)) (cbrt 2))) (pow (* (* PI 2) n) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))) (pow (* (* PI 2) n) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (pow (* (* PI 2) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* PI 2) n) (/ 1 (sqrt 2))) (* (* PI 2) n) (* (* PI 2) n) (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (pow n (- 1/4 (/ k 4))) (pow (* PI 2) (- 1/4 (/ k 4))) (* (- 1/4 (/ k 4)) (log (* (* PI 2) n))) (exp (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (* (cbrt (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (cbrt (pow (* (* PI 2) n) (- 1/4 (/ k 4))))) (cbrt (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (pow (pow (* (* PI 2) n) (- 1/4 (/ k 4))) 3) (sqrt (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (sqrt (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (pow (* (* PI 2) n) (- 1/8 (/ k 8))) (pow (* (* PI 2) n) (- 1/8 (/ k 8))) (real->posit16 (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (expm1 (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (log1p (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (* (- 1/4 (/ k 4)) (log (* (* PI 2) n))) (* (- 1/4 (/ k 4)) (log (* (* PI 2) n))) (* (- 1/4 (/ k 4)) (log (* (* PI 2) n))) (* (- 1/4 (/ k 4)) (log (* (* PI 2) n))) (- 1/4 (/ k 4)) (- 1/4 (/ k 4)) (- 1/4 (/ k 4)) (exp (* (log (* (* PI 2) n)) 1/4)) (pow (* (* PI 2) n) (/ k 4)) (pow (* (* PI 2) n) (* (cbrt (- 1/4 (/ k 4))) (cbrt (- 1/4 (/ k 4))))) (pow (* (* PI 2) n) (sqrt (- 1/4 (/ k 4)))) (pow (* (* PI 2) n) (* (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2)) (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2)))) (pow (* (* PI 2) n) (* (/ (cbrt (- 1/2 (/ k 2))) (sqrt 2)) (cbrt (- 1/2 (/ k 2))))) (pow (* (* PI 2) n) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (pow (* (* PI 2) n) (/ (sqrt (- 1/2 (/ k 2))) (* (cbrt 2) (cbrt 2)))) (pow (* (* PI 2) n) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))) (pow (* (* PI 2) n) (sqrt (- 1/2 (/ k 2)))) (pow (* (* PI 2) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* PI 2) n) (/ 1 (sqrt 2))) (* (* PI 2) n) (pow (* (* PI 2) n) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (* (cbrt 2) (cbrt 2)))) (pow (* (* PI 2) n) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2))) (pow (* (* PI 2) n) (+ (sqrt 1/2) (sqrt (/ k 2)))) (pow (* (* PI 2) n) (/ (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (cbrt 2)) (cbrt 2))) (pow (* (* PI 2) n) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))) (pow (* (* PI 2) n) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (pow (* (* PI 2) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* PI 2) n) (/ 1 (sqrt 2))) (* (* PI 2) n) (* (* PI 2) n) (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (pow n (- 1/4 (/ k 4))) (pow (* PI 2) (- 1/4 (/ k 4))) (* (- 1/4 (/ k 4)) (log (* (* PI 2) n))) (exp (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (* (cbrt (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (cbrt (pow (* (* PI 2) n) (- 1/4 (/ k 4))))) (cbrt (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (pow (pow (* (* PI 2) n) (- 1/4 (/ k 4))) 3) (sqrt (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (sqrt (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (pow (* (* PI 2) n) (- 1/8 (/ k 8))) (pow (* (* PI 2) n) (- 1/8 (/ k 8))) (real->posit16 (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (expm1 (* (* PI 2) n)) (log1p (* (* PI 2) n)) (* (* PI 2) n) (* (* PI 2) n) (log (* (* PI 2) n)) (log (* (* PI 2) n)) (log (* (* PI 2) n)) (* (exp (* n PI)) (exp (* n PI))) (* (* (* 8 (* (* PI PI) PI)) (* n n)) n) (* (* (* (* PI 2) n) (* (* PI 2) n)) (* (* PI 2) n)) (* (cbrt (* (* PI 2) n)) (cbrt (* (* PI 2) n))) (cbrt (* (* PI 2) n)) (* (* (* (* PI 2) n) (* (* PI 2) n)) (* (* PI 2) n)) (sqrt (* (* PI 2) n)) (sqrt (* (* PI 2) n)) (* n 2) (* (cbrt n) (* PI 2)) (* PI (* 2 (sqrt n))) (* (* PI 2) n) (real->posit16 (* (* PI 2) n)) (expm1 (* (* PI 2) n)) (log1p (* (* PI 2) n)) (* (* PI 2) n) (* (* PI 2) n) (log (* (* PI 2) n)) (log (* (* PI 2) n)) (log (* (* PI 2) n)) (* (exp (* n PI)) (exp (* n PI))) (* (* (* 8 (* (* PI PI) PI)) (* n n)) n) (* (* (* (* PI 2) n) (* (* PI 2) n)) (* (* PI 2) n)) (* (cbrt (* (* PI 2) n)) (cbrt (* (* PI 2) n))) (cbrt (* (* PI 2) n)) (* (* (* (* PI 2) n) (* (* PI 2) n)) (* (* PI 2) n)) (sqrt (* (* PI 2) n)) (sqrt (* (* PI 2) n)) (* n 2) (* (cbrt n) (* PI 2)) (* PI (* 2 (sqrt n))) (* (* PI 2) n) (real->posit16 (* (* PI 2) n)) (fma -1/4 (* k (fma (exp (* (log (* (* PI 2) n)) 1/4)) (log n) (* (log (* PI 2)) (exp (* (log (* (* PI 2) n)) 1/4))))) (fma (fma (* (* k k) (exp (* (log (* (* PI 2) n)) 1/4))) (* (log n) (log n)) (* (* (* k k) (exp (* (log (* (* PI 2) n)) 1/4))) (* (log (* PI 2)) (log (* PI 2))))) 1/32 (fma (* 1/16 (* (log (* PI 2)) (exp (* (log (* (* PI 2) n)) 1/4)))) (* k (* k (log n))) (exp (* (log (* (* PI 2) n)) 1/4))))) (exp (* (log (* (* PI 2) n)) (* (fma k -1/2 1/2) 1/2))) (exp (* 1/2 (* (fma k -1/2 1/2) (- (log (* PI -2)) (log (/ -1 n)))))) (fma -1/4 (* k (fma (exp (* (log (* (* PI 2) n)) 1/4)) (log n) (* (log (* PI 2)) (exp (* (log (* (* PI 2) n)) 1/4))))) (fma (fma (* (* k k) (exp (* (log (* (* PI 2) n)) 1/4))) (* (log n) (log n)) (* (* (* k k) (exp (* (log (* (* PI 2) n)) 1/4))) (* (log (* PI 2)) (log (* PI 2))))) 1/32 (fma (* 1/16 (* (log (* PI 2)) (exp (* (log (* (* PI 2) n)) 1/4)))) (* k (* k (log n))) (exp (* (log (* (* PI 2) n)) 1/4))))) (exp (* (log (* (* PI 2) n)) (* (fma k -1/2 1/2) 1/2))) (exp (* 1/2 (* (fma k -1/2 1/2) (- (log (* PI -2)) (log (/ -1 n)))))) (* (* PI 2) n) (* (* PI 2) n) (* (* PI 2) n) (* (* PI 2) n) (* (* PI 2) n) (* (* PI 2) n) 27.089 * * * [progress]: adding candidates to table 27.904 * * [progress]: iteration 4 / 4 27.904 * * * [progress]: picking best candidate 27.944 * * * * [pick]: Picked # 27.944 * * * [progress]: localizing error 28.006 * * * [progress]: generating rewritten candidates 28.006 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 1) 28.040 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 1) 28.068 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1 1) 28.085 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1 1 1) 28.113 * * * [progress]: generating series expansions 28.114 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 1) 28.115 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 28.115 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 28.115 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 28.115 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 28.115 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 28.115 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 28.115 * [taylor]: Taking taylor expansion of 1/2 in k 28.115 * [backup-simplify]: Simplify 1/2 into 1/2 28.115 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 28.115 * [taylor]: Taking taylor expansion of 1/2 in k 28.115 * [backup-simplify]: Simplify 1/2 into 1/2 28.115 * [taylor]: Taking taylor expansion of k in k 28.115 * [backup-simplify]: Simplify 0 into 0 28.115 * [backup-simplify]: Simplify 1 into 1 28.115 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 28.115 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 28.115 * [taylor]: Taking taylor expansion of 2 in k 28.115 * [backup-simplify]: Simplify 2 into 2 28.115 * [taylor]: Taking taylor expansion of (* n PI) in k 28.115 * [taylor]: Taking taylor expansion of n in k 28.115 * [backup-simplify]: Simplify n into n 28.115 * [taylor]: Taking taylor expansion of PI in k 28.115 * [backup-simplify]: Simplify PI into PI 28.115 * [backup-simplify]: Simplify (* n PI) into (* n PI) 28.115 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 28.116 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 28.116 * [backup-simplify]: Simplify (* 1/2 0) into 0 28.116 * [backup-simplify]: Simplify (- 0) into 0 28.117 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 28.117 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 28.117 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 28.117 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 28.117 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 28.117 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 28.117 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 28.117 * [taylor]: Taking taylor expansion of 1/2 in n 28.117 * [backup-simplify]: Simplify 1/2 into 1/2 28.117 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 28.117 * [taylor]: Taking taylor expansion of 1/2 in n 28.117 * [backup-simplify]: Simplify 1/2 into 1/2 28.117 * [taylor]: Taking taylor expansion of k in n 28.117 * [backup-simplify]: Simplify k into k 28.117 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 28.118 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 28.118 * [taylor]: Taking taylor expansion of 2 in n 28.118 * [backup-simplify]: Simplify 2 into 2 28.118 * [taylor]: Taking taylor expansion of (* n PI) in n 28.118 * [taylor]: Taking taylor expansion of n in n 28.118 * [backup-simplify]: Simplify 0 into 0 28.118 * [backup-simplify]: Simplify 1 into 1 28.118 * [taylor]: Taking taylor expansion of PI in n 28.118 * [backup-simplify]: Simplify PI into PI 28.118 * [backup-simplify]: Simplify (* 0 PI) into 0 28.119 * [backup-simplify]: Simplify (* 2 0) into 0 28.120 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 28.122 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 28.123 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 28.123 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 28.123 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 28.123 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 28.125 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 28.126 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 28.127 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 28.127 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 28.127 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 28.127 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 28.127 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 28.127 * [taylor]: Taking taylor expansion of 1/2 in n 28.127 * [backup-simplify]: Simplify 1/2 into 1/2 28.127 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 28.127 * [taylor]: Taking taylor expansion of 1/2 in n 28.127 * [backup-simplify]: Simplify 1/2 into 1/2 28.127 * [taylor]: Taking taylor expansion of k in n 28.127 * [backup-simplify]: Simplify k into k 28.127 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 28.127 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 28.127 * [taylor]: Taking taylor expansion of 2 in n 28.127 * [backup-simplify]: Simplify 2 into 2 28.127 * [taylor]: Taking taylor expansion of (* n PI) in n 28.127 * [taylor]: Taking taylor expansion of n in n 28.128 * [backup-simplify]: Simplify 0 into 0 28.128 * [backup-simplify]: Simplify 1 into 1 28.128 * [taylor]: Taking taylor expansion of PI in n 28.128 * [backup-simplify]: Simplify PI into PI 28.128 * [backup-simplify]: Simplify (* 0 PI) into 0 28.128 * [backup-simplify]: Simplify (* 2 0) into 0 28.130 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 28.132 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 28.133 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 28.133 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 28.133 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 28.133 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 28.134 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 28.135 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 28.137 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 28.137 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 28.137 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 28.137 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 28.137 * [taylor]: Taking taylor expansion of 1/2 in k 28.137 * [backup-simplify]: Simplify 1/2 into 1/2 28.137 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 28.137 * [taylor]: Taking taylor expansion of 1/2 in k 28.137 * [backup-simplify]: Simplify 1/2 into 1/2 28.137 * [taylor]: Taking taylor expansion of k in k 28.137 * [backup-simplify]: Simplify 0 into 0 28.137 * [backup-simplify]: Simplify 1 into 1 28.137 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 28.137 * [taylor]: Taking taylor expansion of (log n) in k 28.137 * [taylor]: Taking taylor expansion of n in k 28.137 * [backup-simplify]: Simplify n into n 28.137 * [backup-simplify]: Simplify (log n) into (log n) 28.137 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 28.137 * [taylor]: Taking taylor expansion of (* 2 PI) in k 28.137 * [taylor]: Taking taylor expansion of 2 in k 28.137 * [backup-simplify]: Simplify 2 into 2 28.137 * [taylor]: Taking taylor expansion of PI in k 28.137 * [backup-simplify]: Simplify PI into PI 28.138 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 28.138 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 28.139 * [backup-simplify]: Simplify (* 1/2 0) into 0 28.139 * [backup-simplify]: Simplify (- 0) into 0 28.139 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 28.140 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 28.141 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 28.141 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 28.142 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 28.143 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 28.143 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 28.144 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 28.144 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 28.145 * [backup-simplify]: Simplify (- 0) into 0 28.145 * [backup-simplify]: Simplify (+ 0 0) into 0 28.146 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 28.147 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 28.148 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 28.148 * [taylor]: Taking taylor expansion of 0 in k 28.148 * [backup-simplify]: Simplify 0 into 0 28.148 * [backup-simplify]: Simplify 0 into 0 28.148 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 28.149 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 28.150 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 28.150 * [backup-simplify]: Simplify (+ 0 0) into 0 28.151 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 28.151 * [backup-simplify]: Simplify (- 1/2) into -1/2 28.151 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 28.152 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 28.154 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 28.156 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 28.157 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 28.157 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 28.159 * [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 28.160 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 28.160 * [backup-simplify]: Simplify (- 0) into 0 28.160 * [backup-simplify]: Simplify (+ 0 0) into 0 28.161 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 28.162 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 28.163 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 28.163 * [taylor]: Taking taylor expansion of 0 in k 28.163 * [backup-simplify]: Simplify 0 into 0 28.163 * [backup-simplify]: Simplify 0 into 0 28.163 * [backup-simplify]: Simplify 0 into 0 28.164 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 28.165 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 28.168 * [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 28.168 * [backup-simplify]: Simplify (+ 0 0) into 0 28.169 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 28.170 * [backup-simplify]: Simplify (- 0) into 0 28.170 * [backup-simplify]: Simplify (+ 0 0) into 0 28.172 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 28.176 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 28.188 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 28.198 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 28.199 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 28.199 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 28.199 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 28.199 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 28.199 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 28.199 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 28.199 * [taylor]: Taking taylor expansion of 1/2 in k 28.199 * [backup-simplify]: Simplify 1/2 into 1/2 28.199 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 28.199 * [taylor]: Taking taylor expansion of 1/2 in k 28.199 * [backup-simplify]: Simplify 1/2 into 1/2 28.199 * [taylor]: Taking taylor expansion of (/ 1 k) in k 28.199 * [taylor]: Taking taylor expansion of k in k 28.199 * [backup-simplify]: Simplify 0 into 0 28.199 * [backup-simplify]: Simplify 1 into 1 28.200 * [backup-simplify]: Simplify (/ 1 1) into 1 28.200 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 28.200 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 28.200 * [taylor]: Taking taylor expansion of 2 in k 28.200 * [backup-simplify]: Simplify 2 into 2 28.200 * [taylor]: Taking taylor expansion of (/ PI n) in k 28.200 * [taylor]: Taking taylor expansion of PI in k 28.200 * [backup-simplify]: Simplify PI into PI 28.200 * [taylor]: Taking taylor expansion of n in k 28.200 * [backup-simplify]: Simplify n into n 28.200 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 28.200 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 28.200 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 28.201 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 28.201 * [backup-simplify]: Simplify (- 1/2) into -1/2 28.202 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 28.202 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 28.202 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 28.202 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 28.202 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 28.202 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 28.202 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 28.202 * [taylor]: Taking taylor expansion of 1/2 in n 28.202 * [backup-simplify]: Simplify 1/2 into 1/2 28.202 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 28.202 * [taylor]: Taking taylor expansion of 1/2 in n 28.202 * [backup-simplify]: Simplify 1/2 into 1/2 28.202 * [taylor]: Taking taylor expansion of (/ 1 k) in n 28.202 * [taylor]: Taking taylor expansion of k in n 28.202 * [backup-simplify]: Simplify k into k 28.202 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 28.202 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 28.202 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 28.202 * [taylor]: Taking taylor expansion of 2 in n 28.203 * [backup-simplify]: Simplify 2 into 2 28.203 * [taylor]: Taking taylor expansion of (/ PI n) in n 28.203 * [taylor]: Taking taylor expansion of PI in n 28.203 * [backup-simplify]: Simplify PI into PI 28.203 * [taylor]: Taking taylor expansion of n in n 28.203 * [backup-simplify]: Simplify 0 into 0 28.203 * [backup-simplify]: Simplify 1 into 1 28.203 * [backup-simplify]: Simplify (/ PI 1) into PI 28.204 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 28.205 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 28.205 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 28.205 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 28.205 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 28.206 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 28.208 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 28.209 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 28.209 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 28.209 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 28.209 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 28.209 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 28.209 * [taylor]: Taking taylor expansion of 1/2 in n 28.209 * [backup-simplify]: Simplify 1/2 into 1/2 28.209 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 28.209 * [taylor]: Taking taylor expansion of 1/2 in n 28.209 * [backup-simplify]: Simplify 1/2 into 1/2 28.209 * [taylor]: Taking taylor expansion of (/ 1 k) in n 28.209 * [taylor]: Taking taylor expansion of k in n 28.209 * [backup-simplify]: Simplify k into k 28.209 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 28.209 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 28.209 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 28.209 * [taylor]: Taking taylor expansion of 2 in n 28.209 * [backup-simplify]: Simplify 2 into 2 28.209 * [taylor]: Taking taylor expansion of (/ PI n) in n 28.209 * [taylor]: Taking taylor expansion of PI in n 28.210 * [backup-simplify]: Simplify PI into PI 28.210 * [taylor]: Taking taylor expansion of n in n 28.210 * [backup-simplify]: Simplify 0 into 0 28.210 * [backup-simplify]: Simplify 1 into 1 28.210 * [backup-simplify]: Simplify (/ PI 1) into PI 28.211 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 28.212 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 28.212 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 28.212 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 28.212 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 28.213 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 28.215 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 28.216 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 28.216 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 28.216 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 28.216 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 28.216 * [taylor]: Taking taylor expansion of 1/2 in k 28.216 * [backup-simplify]: Simplify 1/2 into 1/2 28.216 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 28.216 * [taylor]: Taking taylor expansion of 1/2 in k 28.216 * [backup-simplify]: Simplify 1/2 into 1/2 28.216 * [taylor]: Taking taylor expansion of (/ 1 k) in k 28.216 * [taylor]: Taking taylor expansion of k in k 28.216 * [backup-simplify]: Simplify 0 into 0 28.216 * [backup-simplify]: Simplify 1 into 1 28.217 * [backup-simplify]: Simplify (/ 1 1) into 1 28.217 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 28.217 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 28.217 * [taylor]: Taking taylor expansion of (* 2 PI) in k 28.217 * [taylor]: Taking taylor expansion of 2 in k 28.217 * [backup-simplify]: Simplify 2 into 2 28.217 * [taylor]: Taking taylor expansion of PI in k 28.217 * [backup-simplify]: Simplify PI into PI 28.217 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 28.218 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 28.218 * [taylor]: Taking taylor expansion of (log n) in k 28.218 * [taylor]: Taking taylor expansion of n in k 28.218 * [backup-simplify]: Simplify n into n 28.218 * [backup-simplify]: Simplify (log n) into (log n) 28.219 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 28.219 * [backup-simplify]: Simplify (- 1/2) into -1/2 28.220 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 28.220 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 28.221 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 28.222 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 28.223 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 28.224 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 28.225 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 28.226 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 28.228 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 28.228 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 28.229 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 28.229 * [backup-simplify]: Simplify (- 0) into 0 28.229 * [backup-simplify]: Simplify (+ 0 0) into 0 28.231 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 28.232 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 28.234 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 28.234 * [taylor]: Taking taylor expansion of 0 in k 28.234 * [backup-simplify]: Simplify 0 into 0 28.234 * [backup-simplify]: Simplify 0 into 0 28.234 * [backup-simplify]: Simplify 0 into 0 28.235 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 28.236 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 28.239 * [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 28.240 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 28.241 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 28.241 * [backup-simplify]: Simplify (- 0) into 0 28.241 * [backup-simplify]: Simplify (+ 0 0) into 0 28.243 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 28.244 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 28.247 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 28.247 * [taylor]: Taking taylor expansion of 0 in k 28.247 * [backup-simplify]: Simplify 0 into 0 28.247 * [backup-simplify]: Simplify 0 into 0 28.247 * [backup-simplify]: Simplify 0 into 0 28.247 * [backup-simplify]: Simplify 0 into 0 28.248 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 28.249 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 28.255 * [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 28.256 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 28.257 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 28.257 * [backup-simplify]: Simplify (- 0) into 0 28.258 * [backup-simplify]: Simplify (+ 0 0) into 0 28.259 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 28.261 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 28.264 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 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 28.264 * [taylor]: Taking taylor expansion of 0 in k 28.264 * [backup-simplify]: Simplify 0 into 0 28.264 * [backup-simplify]: Simplify 0 into 0 28.265 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 28.266 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 28.266 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 28.266 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 28.266 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 28.266 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 28.266 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 28.266 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 28.266 * [taylor]: Taking taylor expansion of 1/2 in k 28.266 * [backup-simplify]: Simplify 1/2 into 1/2 28.266 * [taylor]: Taking taylor expansion of (/ 1 k) in k 28.266 * [taylor]: Taking taylor expansion of k in k 28.266 * [backup-simplify]: Simplify 0 into 0 28.266 * [backup-simplify]: Simplify 1 into 1 28.267 * [backup-simplify]: Simplify (/ 1 1) into 1 28.267 * [taylor]: Taking taylor expansion of 1/2 in k 28.267 * [backup-simplify]: Simplify 1/2 into 1/2 28.267 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 28.267 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 28.267 * [taylor]: Taking taylor expansion of -2 in k 28.267 * [backup-simplify]: Simplify -2 into -2 28.267 * [taylor]: Taking taylor expansion of (/ PI n) in k 28.267 * [taylor]: Taking taylor expansion of PI in k 28.267 * [backup-simplify]: Simplify PI into PI 28.267 * [taylor]: Taking taylor expansion of n in k 28.267 * [backup-simplify]: Simplify n into n 28.267 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 28.267 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 28.267 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 28.268 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 28.268 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 28.268 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 28.269 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 28.269 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 28.269 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 28.269 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 28.269 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 28.269 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 28.269 * [taylor]: Taking taylor expansion of 1/2 in n 28.269 * [backup-simplify]: Simplify 1/2 into 1/2 28.269 * [taylor]: Taking taylor expansion of (/ 1 k) in n 28.269 * [taylor]: Taking taylor expansion of k in n 28.269 * [backup-simplify]: Simplify k into k 28.269 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 28.269 * [taylor]: Taking taylor expansion of 1/2 in n 28.269 * [backup-simplify]: Simplify 1/2 into 1/2 28.269 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 28.269 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 28.269 * [taylor]: Taking taylor expansion of -2 in n 28.269 * [backup-simplify]: Simplify -2 into -2 28.269 * [taylor]: Taking taylor expansion of (/ PI n) in n 28.269 * [taylor]: Taking taylor expansion of PI in n 28.269 * [backup-simplify]: Simplify PI into PI 28.269 * [taylor]: Taking taylor expansion of n in n 28.269 * [backup-simplify]: Simplify 0 into 0 28.269 * [backup-simplify]: Simplify 1 into 1 28.270 * [backup-simplify]: Simplify (/ PI 1) into PI 28.270 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 28.271 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 28.271 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 28.272 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 28.273 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 28.274 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 28.275 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 28.275 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 28.276 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 28.276 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 28.276 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 28.276 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 28.276 * [taylor]: Taking taylor expansion of 1/2 in n 28.276 * [backup-simplify]: Simplify 1/2 into 1/2 28.276 * [taylor]: Taking taylor expansion of (/ 1 k) in n 28.276 * [taylor]: Taking taylor expansion of k in n 28.276 * [backup-simplify]: Simplify k into k 28.276 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 28.276 * [taylor]: Taking taylor expansion of 1/2 in n 28.276 * [backup-simplify]: Simplify 1/2 into 1/2 28.276 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 28.276 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 28.276 * [taylor]: Taking taylor expansion of -2 in n 28.276 * [backup-simplify]: Simplify -2 into -2 28.276 * [taylor]: Taking taylor expansion of (/ PI n) in n 28.276 * [taylor]: Taking taylor expansion of PI in n 28.276 * [backup-simplify]: Simplify PI into PI 28.276 * [taylor]: Taking taylor expansion of n in n 28.276 * [backup-simplify]: Simplify 0 into 0 28.276 * [backup-simplify]: Simplify 1 into 1 28.277 * [backup-simplify]: Simplify (/ PI 1) into PI 28.277 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 28.278 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 28.278 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 28.278 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 28.280 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 28.281 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 28.282 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 28.282 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 28.282 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 28.282 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 28.282 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 28.282 * [taylor]: Taking taylor expansion of 1/2 in k 28.282 * [backup-simplify]: Simplify 1/2 into 1/2 28.282 * [taylor]: Taking taylor expansion of (/ 1 k) in k 28.282 * [taylor]: Taking taylor expansion of k in k 28.283 * [backup-simplify]: Simplify 0 into 0 28.283 * [backup-simplify]: Simplify 1 into 1 28.283 * [backup-simplify]: Simplify (/ 1 1) into 1 28.283 * [taylor]: Taking taylor expansion of 1/2 in k 28.283 * [backup-simplify]: Simplify 1/2 into 1/2 28.283 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 28.283 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 28.283 * [taylor]: Taking taylor expansion of (* -2 PI) in k 28.283 * [taylor]: Taking taylor expansion of -2 in k 28.283 * [backup-simplify]: Simplify -2 into -2 28.283 * [taylor]: Taking taylor expansion of PI in k 28.283 * [backup-simplify]: Simplify PI into PI 28.284 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 28.285 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 28.285 * [taylor]: Taking taylor expansion of (log n) in k 28.285 * [taylor]: Taking taylor expansion of n in k 28.285 * [backup-simplify]: Simplify n into n 28.285 * [backup-simplify]: Simplify (log n) into (log n) 28.285 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 28.286 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 28.286 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 28.287 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 28.288 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 28.289 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 28.290 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 28.291 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 28.291 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 28.292 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 28.292 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 28.293 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 28.293 * [backup-simplify]: Simplify (+ 0 0) into 0 28.294 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 28.294 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 28.296 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 28.296 * [taylor]: Taking taylor expansion of 0 in k 28.296 * [backup-simplify]: Simplify 0 into 0 28.296 * [backup-simplify]: Simplify 0 into 0 28.296 * [backup-simplify]: Simplify 0 into 0 28.296 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 28.297 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 28.299 * [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 28.299 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 28.300 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 28.300 * [backup-simplify]: Simplify (+ 0 0) into 0 28.301 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 28.302 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 28.303 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 28.303 * [taylor]: Taking taylor expansion of 0 in k 28.303 * [backup-simplify]: Simplify 0 into 0 28.303 * [backup-simplify]: Simplify 0 into 0 28.303 * [backup-simplify]: Simplify 0 into 0 28.303 * [backup-simplify]: Simplify 0 into 0 28.306 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 28.307 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 28.310 * [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 28.310 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 28.311 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 28.311 * [backup-simplify]: Simplify (+ 0 0) into 0 28.312 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 28.319 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 28.321 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 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 28.321 * [taylor]: Taking taylor expansion of 0 in k 28.321 * [backup-simplify]: Simplify 0 into 0 28.321 * [backup-simplify]: Simplify 0 into 0 28.322 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 28.322 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 1) 28.322 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 28.322 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 28.322 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 28.322 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 28.322 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 28.322 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 28.322 * [taylor]: Taking taylor expansion of 1/2 in k 28.322 * [backup-simplify]: Simplify 1/2 into 1/2 28.322 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 28.322 * [taylor]: Taking taylor expansion of 1/2 in k 28.322 * [backup-simplify]: Simplify 1/2 into 1/2 28.322 * [taylor]: Taking taylor expansion of k in k 28.322 * [backup-simplify]: Simplify 0 into 0 28.322 * [backup-simplify]: Simplify 1 into 1 28.322 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 28.322 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 28.322 * [taylor]: Taking taylor expansion of 2 in k 28.323 * [backup-simplify]: Simplify 2 into 2 28.323 * [taylor]: Taking taylor expansion of (* n PI) in k 28.323 * [taylor]: Taking taylor expansion of n in k 28.323 * [backup-simplify]: Simplify n into n 28.323 * [taylor]: Taking taylor expansion of PI in k 28.323 * [backup-simplify]: Simplify PI into PI 28.323 * [backup-simplify]: Simplify (* n PI) into (* n PI) 28.323 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 28.323 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 28.323 * [backup-simplify]: Simplify (* 1/2 0) into 0 28.323 * [backup-simplify]: Simplify (- 0) into 0 28.324 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 28.324 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 28.324 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 28.324 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 28.324 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 28.324 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 28.324 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 28.324 * [taylor]: Taking taylor expansion of 1/2 in n 28.324 * [backup-simplify]: Simplify 1/2 into 1/2 28.324 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 28.324 * [taylor]: Taking taylor expansion of 1/2 in n 28.324 * [backup-simplify]: Simplify 1/2 into 1/2 28.324 * [taylor]: Taking taylor expansion of k in n 28.324 * [backup-simplify]: Simplify k into k 28.324 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 28.324 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 28.324 * [taylor]: Taking taylor expansion of 2 in n 28.324 * [backup-simplify]: Simplify 2 into 2 28.324 * [taylor]: Taking taylor expansion of (* n PI) in n 28.324 * [taylor]: Taking taylor expansion of n in n 28.324 * [backup-simplify]: Simplify 0 into 0 28.324 * [backup-simplify]: Simplify 1 into 1 28.324 * [taylor]: Taking taylor expansion of PI in n 28.324 * [backup-simplify]: Simplify PI into PI 28.324 * [backup-simplify]: Simplify (* 0 PI) into 0 28.325 * [backup-simplify]: Simplify (* 2 0) into 0 28.326 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 28.327 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 28.327 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 28.327 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 28.327 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 28.327 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 28.328 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 28.329 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 28.330 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 28.330 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 28.330 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 28.330 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 28.330 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 28.330 * [taylor]: Taking taylor expansion of 1/2 in n 28.330 * [backup-simplify]: Simplify 1/2 into 1/2 28.330 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 28.330 * [taylor]: Taking taylor expansion of 1/2 in n 28.330 * [backup-simplify]: Simplify 1/2 into 1/2 28.330 * [taylor]: Taking taylor expansion of k in n 28.330 * [backup-simplify]: Simplify k into k 28.330 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 28.330 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 28.330 * [taylor]: Taking taylor expansion of 2 in n 28.330 * [backup-simplify]: Simplify 2 into 2 28.330 * [taylor]: Taking taylor expansion of (* n PI) in n 28.330 * [taylor]: Taking taylor expansion of n in n 28.330 * [backup-simplify]: Simplify 0 into 0 28.330 * [backup-simplify]: Simplify 1 into 1 28.330 * [taylor]: Taking taylor expansion of PI in n 28.330 * [backup-simplify]: Simplify PI into PI 28.330 * [backup-simplify]: Simplify (* 0 PI) into 0 28.331 * [backup-simplify]: Simplify (* 2 0) into 0 28.332 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 28.333 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 28.333 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 28.334 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 28.334 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 28.334 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 28.335 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 28.335 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 28.336 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 28.336 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 28.336 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 28.336 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 28.336 * [taylor]: Taking taylor expansion of 1/2 in k 28.336 * [backup-simplify]: Simplify 1/2 into 1/2 28.336 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 28.336 * [taylor]: Taking taylor expansion of 1/2 in k 28.336 * [backup-simplify]: Simplify 1/2 into 1/2 28.336 * [taylor]: Taking taylor expansion of k in k 28.336 * [backup-simplify]: Simplify 0 into 0 28.336 * [backup-simplify]: Simplify 1 into 1 28.336 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 28.336 * [taylor]: Taking taylor expansion of (log n) in k 28.336 * [taylor]: Taking taylor expansion of n in k 28.336 * [backup-simplify]: Simplify n into n 28.336 * [backup-simplify]: Simplify (log n) into (log n) 28.336 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 28.336 * [taylor]: Taking taylor expansion of (* 2 PI) in k 28.336 * [taylor]: Taking taylor expansion of 2 in k 28.336 * [backup-simplify]: Simplify 2 into 2 28.336 * [taylor]: Taking taylor expansion of PI in k 28.336 * [backup-simplify]: Simplify PI into PI 28.337 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 28.337 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 28.338 * [backup-simplify]: Simplify (* 1/2 0) into 0 28.338 * [backup-simplify]: Simplify (- 0) into 0 28.338 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 28.339 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 28.339 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 28.340 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 28.341 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 28.342 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 28.343 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 28.344 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 28.345 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 28.345 * [backup-simplify]: Simplify (- 0) into 0 28.346 * [backup-simplify]: Simplify (+ 0 0) into 0 28.347 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 28.348 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 28.350 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 28.350 * [taylor]: Taking taylor expansion of 0 in k 28.350 * [backup-simplify]: Simplify 0 into 0 28.350 * [backup-simplify]: Simplify 0 into 0 28.351 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 28.352 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 28.354 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 28.354 * [backup-simplify]: Simplify (+ 0 0) into 0 28.355 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 28.355 * [backup-simplify]: Simplify (- 1/2) into -1/2 28.355 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 28.356 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 28.358 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 28.360 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 28.361 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 28.361 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 28.363 * [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 28.364 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 28.364 * [backup-simplify]: Simplify (- 0) into 0 28.364 * [backup-simplify]: Simplify (+ 0 0) into 0 28.365 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 28.366 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 28.368 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 28.368 * [taylor]: Taking taylor expansion of 0 in k 28.368 * [backup-simplify]: Simplify 0 into 0 28.368 * [backup-simplify]: Simplify 0 into 0 28.368 * [backup-simplify]: Simplify 0 into 0 28.369 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 28.369 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 28.371 * [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 28.371 * [backup-simplify]: Simplify (+ 0 0) into 0 28.372 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 28.372 * [backup-simplify]: Simplify (- 0) into 0 28.372 * [backup-simplify]: Simplify (+ 0 0) into 0 28.374 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 28.376 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 28.379 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 28.385 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 28.385 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 28.385 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 28.385 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 28.385 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 28.385 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 28.385 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 28.385 * [taylor]: Taking taylor expansion of 1/2 in k 28.385 * [backup-simplify]: Simplify 1/2 into 1/2 28.385 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 28.386 * [taylor]: Taking taylor expansion of 1/2 in k 28.386 * [backup-simplify]: Simplify 1/2 into 1/2 28.386 * [taylor]: Taking taylor expansion of (/ 1 k) in k 28.386 * [taylor]: Taking taylor expansion of k in k 28.386 * [backup-simplify]: Simplify 0 into 0 28.386 * [backup-simplify]: Simplify 1 into 1 28.386 * [backup-simplify]: Simplify (/ 1 1) into 1 28.386 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 28.386 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 28.386 * [taylor]: Taking taylor expansion of 2 in k 28.386 * [backup-simplify]: Simplify 2 into 2 28.386 * [taylor]: Taking taylor expansion of (/ PI n) in k 28.386 * [taylor]: Taking taylor expansion of PI in k 28.386 * [backup-simplify]: Simplify PI into PI 28.386 * [taylor]: Taking taylor expansion of n in k 28.386 * [backup-simplify]: Simplify n into n 28.386 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 28.386 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 28.386 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 28.387 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 28.387 * [backup-simplify]: Simplify (- 1/2) into -1/2 28.388 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 28.388 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 28.388 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 28.388 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 28.388 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 28.388 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 28.388 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 28.388 * [taylor]: Taking taylor expansion of 1/2 in n 28.388 * [backup-simplify]: Simplify 1/2 into 1/2 28.388 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 28.388 * [taylor]: Taking taylor expansion of 1/2 in n 28.388 * [backup-simplify]: Simplify 1/2 into 1/2 28.388 * [taylor]: Taking taylor expansion of (/ 1 k) in n 28.388 * [taylor]: Taking taylor expansion of k in n 28.388 * [backup-simplify]: Simplify k into k 28.388 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 28.388 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 28.388 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 28.389 * [taylor]: Taking taylor expansion of 2 in n 28.389 * [backup-simplify]: Simplify 2 into 2 28.389 * [taylor]: Taking taylor expansion of (/ PI n) in n 28.389 * [taylor]: Taking taylor expansion of PI in n 28.389 * [backup-simplify]: Simplify PI into PI 28.389 * [taylor]: Taking taylor expansion of n in n 28.389 * [backup-simplify]: Simplify 0 into 0 28.389 * [backup-simplify]: Simplify 1 into 1 28.389 * [backup-simplify]: Simplify (/ PI 1) into PI 28.390 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 28.391 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 28.391 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 28.391 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 28.391 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 28.393 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 28.394 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 28.395 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 28.395 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 28.395 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 28.395 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 28.395 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 28.395 * [taylor]: Taking taylor expansion of 1/2 in n 28.395 * [backup-simplify]: Simplify 1/2 into 1/2 28.395 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 28.395 * [taylor]: Taking taylor expansion of 1/2 in n 28.395 * [backup-simplify]: Simplify 1/2 into 1/2 28.395 * [taylor]: Taking taylor expansion of (/ 1 k) in n 28.395 * [taylor]: Taking taylor expansion of k in n 28.395 * [backup-simplify]: Simplify k into k 28.395 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 28.395 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 28.395 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 28.395 * [taylor]: Taking taylor expansion of 2 in n 28.395 * [backup-simplify]: Simplify 2 into 2 28.395 * [taylor]: Taking taylor expansion of (/ PI n) in n 28.395 * [taylor]: Taking taylor expansion of PI in n 28.395 * [backup-simplify]: Simplify PI into PI 28.395 * [taylor]: Taking taylor expansion of n in n 28.395 * [backup-simplify]: Simplify 0 into 0 28.395 * [backup-simplify]: Simplify 1 into 1 28.395 * [backup-simplify]: Simplify (/ PI 1) into PI 28.396 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 28.396 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 28.396 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 28.396 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 28.396 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 28.397 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 28.398 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 28.399 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 28.399 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 28.399 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 28.399 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 28.399 * [taylor]: Taking taylor expansion of 1/2 in k 28.399 * [backup-simplify]: Simplify 1/2 into 1/2 28.399 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 28.399 * [taylor]: Taking taylor expansion of 1/2 in k 28.399 * [backup-simplify]: Simplify 1/2 into 1/2 28.399 * [taylor]: Taking taylor expansion of (/ 1 k) in k 28.399 * [taylor]: Taking taylor expansion of k in k 28.399 * [backup-simplify]: Simplify 0 into 0 28.399 * [backup-simplify]: Simplify 1 into 1 28.399 * [backup-simplify]: Simplify (/ 1 1) into 1 28.399 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 28.399 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 28.399 * [taylor]: Taking taylor expansion of (* 2 PI) in k 28.399 * [taylor]: Taking taylor expansion of 2 in k 28.399 * [backup-simplify]: Simplify 2 into 2 28.399 * [taylor]: Taking taylor expansion of PI in k 28.399 * [backup-simplify]: Simplify PI into PI 28.400 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 28.400 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 28.400 * [taylor]: Taking taylor expansion of (log n) in k 28.400 * [taylor]: Taking taylor expansion of n in k 28.400 * [backup-simplify]: Simplify n into n 28.400 * [backup-simplify]: Simplify (log n) into (log n) 28.401 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 28.401 * [backup-simplify]: Simplify (- 1/2) into -1/2 28.401 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 28.401 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 28.402 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 28.403 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 28.403 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 28.404 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 28.405 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 28.405 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 28.406 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 28.406 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 28.407 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 28.407 * [backup-simplify]: Simplify (- 0) into 0 28.407 * [backup-simplify]: Simplify (+ 0 0) into 0 28.408 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 28.409 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 28.410 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 28.410 * [taylor]: Taking taylor expansion of 0 in k 28.410 * [backup-simplify]: Simplify 0 into 0 28.410 * [backup-simplify]: Simplify 0 into 0 28.410 * [backup-simplify]: Simplify 0 into 0 28.411 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 28.412 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 28.418 * [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 28.419 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 28.419 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 28.420 * [backup-simplify]: Simplify (- 0) into 0 28.420 * [backup-simplify]: Simplify (+ 0 0) into 0 28.421 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 28.422 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 28.425 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 28.425 * [taylor]: Taking taylor expansion of 0 in k 28.425 * [backup-simplify]: Simplify 0 into 0 28.425 * [backup-simplify]: Simplify 0 into 0 28.425 * [backup-simplify]: Simplify 0 into 0 28.425 * [backup-simplify]: Simplify 0 into 0 28.426 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 28.427 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 28.434 * [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 28.434 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 28.435 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 28.436 * [backup-simplify]: Simplify (- 0) into 0 28.436 * [backup-simplify]: Simplify (+ 0 0) into 0 28.438 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 28.440 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 28.443 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 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 28.443 * [taylor]: Taking taylor expansion of 0 in k 28.443 * [backup-simplify]: Simplify 0 into 0 28.443 * [backup-simplify]: Simplify 0 into 0 28.444 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 28.445 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 28.445 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 28.445 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 28.445 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 28.445 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 28.445 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 28.445 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 28.445 * [taylor]: Taking taylor expansion of 1/2 in k 28.445 * [backup-simplify]: Simplify 1/2 into 1/2 28.445 * [taylor]: Taking taylor expansion of (/ 1 k) in k 28.445 * [taylor]: Taking taylor expansion of k in k 28.445 * [backup-simplify]: Simplify 0 into 0 28.445 * [backup-simplify]: Simplify 1 into 1 28.446 * [backup-simplify]: Simplify (/ 1 1) into 1 28.446 * [taylor]: Taking taylor expansion of 1/2 in k 28.446 * [backup-simplify]: Simplify 1/2 into 1/2 28.446 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 28.446 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 28.446 * [taylor]: Taking taylor expansion of -2 in k 28.446 * [backup-simplify]: Simplify -2 into -2 28.446 * [taylor]: Taking taylor expansion of (/ PI n) in k 28.446 * [taylor]: Taking taylor expansion of PI in k 28.446 * [backup-simplify]: Simplify PI into PI 28.446 * [taylor]: Taking taylor expansion of n in k 28.446 * [backup-simplify]: Simplify n into n 28.446 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 28.446 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 28.446 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 28.447 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 28.447 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 28.447 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 28.447 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 28.447 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 28.447 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 28.447 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 28.447 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 28.447 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 28.447 * [taylor]: Taking taylor expansion of 1/2 in n 28.447 * [backup-simplify]: Simplify 1/2 into 1/2 28.447 * [taylor]: Taking taylor expansion of (/ 1 k) in n 28.447 * [taylor]: Taking taylor expansion of k in n 28.447 * [backup-simplify]: Simplify k into k 28.447 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 28.447 * [taylor]: Taking taylor expansion of 1/2 in n 28.447 * [backup-simplify]: Simplify 1/2 into 1/2 28.447 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 28.447 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 28.447 * [taylor]: Taking taylor expansion of -2 in n 28.447 * [backup-simplify]: Simplify -2 into -2 28.447 * [taylor]: Taking taylor expansion of (/ PI n) in n 28.447 * [taylor]: Taking taylor expansion of PI in n 28.447 * [backup-simplify]: Simplify PI into PI 28.447 * [taylor]: Taking taylor expansion of n in n 28.447 * [backup-simplify]: Simplify 0 into 0 28.447 * [backup-simplify]: Simplify 1 into 1 28.448 * [backup-simplify]: Simplify (/ PI 1) into PI 28.448 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 28.449 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 28.449 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 28.449 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 28.450 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 28.451 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 28.451 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 28.451 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 28.451 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 28.451 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 28.452 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 28.452 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 28.452 * [taylor]: Taking taylor expansion of 1/2 in n 28.452 * [backup-simplify]: Simplify 1/2 into 1/2 28.452 * [taylor]: Taking taylor expansion of (/ 1 k) in n 28.452 * [taylor]: Taking taylor expansion of k in n 28.452 * [backup-simplify]: Simplify k into k 28.452 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 28.452 * [taylor]: Taking taylor expansion of 1/2 in n 28.452 * [backup-simplify]: Simplify 1/2 into 1/2 28.452 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 28.452 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 28.452 * [taylor]: Taking taylor expansion of -2 in n 28.452 * [backup-simplify]: Simplify -2 into -2 28.452 * [taylor]: Taking taylor expansion of (/ PI n) in n 28.452 * [taylor]: Taking taylor expansion of PI in n 28.452 * [backup-simplify]: Simplify PI into PI 28.452 * [taylor]: Taking taylor expansion of n in n 28.452 * [backup-simplify]: Simplify 0 into 0 28.452 * [backup-simplify]: Simplify 1 into 1 28.452 * [backup-simplify]: Simplify (/ PI 1) into PI 28.452 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 28.453 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 28.453 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 28.453 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 28.454 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 28.455 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 28.456 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 28.456 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 28.456 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 28.456 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 28.456 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 28.456 * [taylor]: Taking taylor expansion of 1/2 in k 28.456 * [backup-simplify]: Simplify 1/2 into 1/2 28.456 * [taylor]: Taking taylor expansion of (/ 1 k) in k 28.456 * [taylor]: Taking taylor expansion of k in k 28.456 * [backup-simplify]: Simplify 0 into 0 28.456 * [backup-simplify]: Simplify 1 into 1 28.456 * [backup-simplify]: Simplify (/ 1 1) into 1 28.456 * [taylor]: Taking taylor expansion of 1/2 in k 28.456 * [backup-simplify]: Simplify 1/2 into 1/2 28.456 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 28.456 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 28.456 * [taylor]: Taking taylor expansion of (* -2 PI) in k 28.456 * [taylor]: Taking taylor expansion of -2 in k 28.456 * [backup-simplify]: Simplify -2 into -2 28.456 * [taylor]: Taking taylor expansion of PI in k 28.456 * [backup-simplify]: Simplify PI into PI 28.457 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 28.457 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 28.457 * [taylor]: Taking taylor expansion of (log n) in k 28.457 * [taylor]: Taking taylor expansion of n in k 28.457 * [backup-simplify]: Simplify n into n 28.457 * [backup-simplify]: Simplify (log n) into (log n) 28.458 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 28.458 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 28.458 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 28.459 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 28.459 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 28.461 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 28.462 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 28.462 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 28.463 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 28.464 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 28.464 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 28.464 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 28.464 * [backup-simplify]: Simplify (+ 0 0) into 0 28.465 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 28.466 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 28.467 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 28.467 * [taylor]: Taking taylor expansion of 0 in k 28.467 * [backup-simplify]: Simplify 0 into 0 28.467 * [backup-simplify]: Simplify 0 into 0 28.468 * [backup-simplify]: Simplify 0 into 0 28.468 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 28.469 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 28.471 * [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 28.471 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 28.471 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 28.472 * [backup-simplify]: Simplify (+ 0 0) into 0 28.473 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 28.474 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 28.475 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 28.475 * [taylor]: Taking taylor expansion of 0 in k 28.475 * [backup-simplify]: Simplify 0 into 0 28.475 * [backup-simplify]: Simplify 0 into 0 28.475 * [backup-simplify]: Simplify 0 into 0 28.475 * [backup-simplify]: Simplify 0 into 0 28.476 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 28.476 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 28.480 * [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 28.480 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 28.481 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 28.481 * [backup-simplify]: Simplify (+ 0 0) into 0 28.482 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 28.483 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 28.485 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 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 28.485 * [taylor]: Taking taylor expansion of 0 in k 28.485 * [backup-simplify]: Simplify 0 into 0 28.485 * [backup-simplify]: Simplify 0 into 0 28.486 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 28.486 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1 1) 28.486 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) 28.486 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 28.486 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 28.486 * [taylor]: Taking taylor expansion of 2 in n 28.486 * [backup-simplify]: Simplify 2 into 2 28.486 * [taylor]: Taking taylor expansion of (* n PI) in n 28.486 * [taylor]: Taking taylor expansion of n in n 28.486 * [backup-simplify]: Simplify 0 into 0 28.486 * [backup-simplify]: Simplify 1 into 1 28.486 * [taylor]: Taking taylor expansion of PI in n 28.486 * [backup-simplify]: Simplify PI into PI 28.486 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 28.486 * [taylor]: Taking taylor expansion of 2 in n 28.486 * [backup-simplify]: Simplify 2 into 2 28.486 * [taylor]: Taking taylor expansion of (* n PI) in n 28.486 * [taylor]: Taking taylor expansion of n in n 28.486 * [backup-simplify]: Simplify 0 into 0 28.486 * [backup-simplify]: Simplify 1 into 1 28.486 * [taylor]: Taking taylor expansion of PI in n 28.486 * [backup-simplify]: Simplify PI into PI 28.487 * [backup-simplify]: Simplify (* 0 PI) into 0 28.487 * [backup-simplify]: Simplify (* 2 0) into 0 28.487 * [backup-simplify]: Simplify 0 into 0 28.488 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 28.489 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 28.489 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 28.490 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 28.490 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 28.490 * [backup-simplify]: Simplify 0 into 0 28.491 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 28.492 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 28.492 * [backup-simplify]: Simplify 0 into 0 28.493 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 28.493 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 28.493 * [backup-simplify]: Simplify 0 into 0 28.494 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 28.495 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 28.495 * [backup-simplify]: Simplify 0 into 0 28.496 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 28.497 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 28.497 * [backup-simplify]: Simplify 0 into 0 28.498 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 28.499 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 28.499 * [backup-simplify]: Simplify 0 into 0 28.500 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 28.500 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) 28.500 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 28.500 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 28.500 * [taylor]: Taking taylor expansion of 2 in n 28.500 * [backup-simplify]: Simplify 2 into 2 28.500 * [taylor]: Taking taylor expansion of (/ PI n) in n 28.500 * [taylor]: Taking taylor expansion of PI in n 28.500 * [backup-simplify]: Simplify PI into PI 28.500 * [taylor]: Taking taylor expansion of n in n 28.500 * [backup-simplify]: Simplify 0 into 0 28.500 * [backup-simplify]: Simplify 1 into 1 28.501 * [backup-simplify]: Simplify (/ PI 1) into PI 28.501 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 28.501 * [taylor]: Taking taylor expansion of 2 in n 28.501 * [backup-simplify]: Simplify 2 into 2 28.501 * [taylor]: Taking taylor expansion of (/ PI n) in n 28.501 * [taylor]: Taking taylor expansion of PI in n 28.501 * [backup-simplify]: Simplify PI into PI 28.501 * [taylor]: Taking taylor expansion of n in n 28.501 * [backup-simplify]: Simplify 0 into 0 28.501 * [backup-simplify]: Simplify 1 into 1 28.501 * [backup-simplify]: Simplify (/ PI 1) into PI 28.501 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 28.502 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 28.502 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 28.503 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 28.503 * [backup-simplify]: Simplify 0 into 0 28.503 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 28.504 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 28.504 * [backup-simplify]: Simplify 0 into 0 28.505 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 28.505 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 28.505 * [backup-simplify]: Simplify 0 into 0 28.506 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 28.508 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 28.508 * [backup-simplify]: Simplify 0 into 0 28.509 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 28.510 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 28.510 * [backup-simplify]: Simplify 0 into 0 28.512 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 28.514 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 28.514 * [backup-simplify]: Simplify 0 into 0 28.514 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 28.515 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n)) 28.515 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 28.515 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 28.515 * [taylor]: Taking taylor expansion of -2 in n 28.515 * [backup-simplify]: Simplify -2 into -2 28.515 * [taylor]: Taking taylor expansion of (/ PI n) in n 28.515 * [taylor]: Taking taylor expansion of PI in n 28.515 * [backup-simplify]: Simplify PI into PI 28.515 * [taylor]: Taking taylor expansion of n in n 28.515 * [backup-simplify]: Simplify 0 into 0 28.515 * [backup-simplify]: Simplify 1 into 1 28.516 * [backup-simplify]: Simplify (/ PI 1) into PI 28.516 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 28.516 * [taylor]: Taking taylor expansion of -2 in n 28.516 * [backup-simplify]: Simplify -2 into -2 28.516 * [taylor]: Taking taylor expansion of (/ PI n) in n 28.516 * [taylor]: Taking taylor expansion of PI in n 28.516 * [backup-simplify]: Simplify PI into PI 28.516 * [taylor]: Taking taylor expansion of n in n 28.516 * [backup-simplify]: Simplify 0 into 0 28.516 * [backup-simplify]: Simplify 1 into 1 28.516 * [backup-simplify]: Simplify (/ PI 1) into PI 28.517 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 28.517 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 28.518 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 28.519 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 28.519 * [backup-simplify]: Simplify 0 into 0 28.520 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 28.521 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 28.521 * [backup-simplify]: Simplify 0 into 0 28.522 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 28.523 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 28.523 * [backup-simplify]: Simplify 0 into 0 28.525 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 28.533 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 28.533 * [backup-simplify]: Simplify 0 into 0 28.534 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 28.535 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 28.535 * [backup-simplify]: Simplify 0 into 0 28.536 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 28.537 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 28.537 * [backup-simplify]: Simplify 0 into 0 28.537 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 28.538 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1 1 1) 28.538 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) 28.538 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 28.538 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 28.538 * [taylor]: Taking taylor expansion of 2 in n 28.538 * [backup-simplify]: Simplify 2 into 2 28.538 * [taylor]: Taking taylor expansion of (* n PI) in n 28.538 * [taylor]: Taking taylor expansion of n in n 28.538 * [backup-simplify]: Simplify 0 into 0 28.538 * [backup-simplify]: Simplify 1 into 1 28.538 * [taylor]: Taking taylor expansion of PI in n 28.538 * [backup-simplify]: Simplify PI into PI 28.538 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 28.538 * [taylor]: Taking taylor expansion of 2 in n 28.538 * [backup-simplify]: Simplify 2 into 2 28.538 * [taylor]: Taking taylor expansion of (* n PI) in n 28.538 * [taylor]: Taking taylor expansion of n in n 28.538 * [backup-simplify]: Simplify 0 into 0 28.538 * [backup-simplify]: Simplify 1 into 1 28.538 * [taylor]: Taking taylor expansion of PI in n 28.538 * [backup-simplify]: Simplify PI into PI 28.539 * [backup-simplify]: Simplify (* 0 PI) into 0 28.539 * [backup-simplify]: Simplify (* 2 0) into 0 28.539 * [backup-simplify]: Simplify 0 into 0 28.540 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 28.541 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 28.541 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 28.542 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 28.543 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 28.543 * [backup-simplify]: Simplify 0 into 0 28.543 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 28.544 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 28.544 * [backup-simplify]: Simplify 0 into 0 28.545 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 28.546 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 28.546 * [backup-simplify]: Simplify 0 into 0 28.547 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 28.548 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 28.548 * [backup-simplify]: Simplify 0 into 0 28.549 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 28.550 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 28.550 * [backup-simplify]: Simplify 0 into 0 28.551 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 28.552 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 28.552 * [backup-simplify]: Simplify 0 into 0 28.552 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 28.553 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) 28.553 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 28.553 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 28.553 * [taylor]: Taking taylor expansion of 2 in n 28.553 * [backup-simplify]: Simplify 2 into 2 28.553 * [taylor]: Taking taylor expansion of (/ PI n) in n 28.553 * [taylor]: Taking taylor expansion of PI in n 28.553 * [backup-simplify]: Simplify PI into PI 28.553 * [taylor]: Taking taylor expansion of n in n 28.553 * [backup-simplify]: Simplify 0 into 0 28.553 * [backup-simplify]: Simplify 1 into 1 28.553 * [backup-simplify]: Simplify (/ PI 1) into PI 28.553 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 28.553 * [taylor]: Taking taylor expansion of 2 in n 28.553 * [backup-simplify]: Simplify 2 into 2 28.553 * [taylor]: Taking taylor expansion of (/ PI n) in n 28.553 * [taylor]: Taking taylor expansion of PI in n 28.553 * [backup-simplify]: Simplify PI into PI 28.553 * [taylor]: Taking taylor expansion of n in n 28.553 * [backup-simplify]: Simplify 0 into 0 28.553 * [backup-simplify]: Simplify 1 into 1 28.554 * [backup-simplify]: Simplify (/ PI 1) into PI 28.554 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 28.554 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 28.555 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 28.555 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 28.556 * [backup-simplify]: Simplify 0 into 0 28.556 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 28.557 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 28.557 * [backup-simplify]: Simplify 0 into 0 28.557 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 28.558 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 28.558 * [backup-simplify]: Simplify 0 into 0 28.559 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 28.560 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 28.560 * [backup-simplify]: Simplify 0 into 0 28.560 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 28.561 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 28.561 * [backup-simplify]: Simplify 0 into 0 28.562 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 28.563 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 28.563 * [backup-simplify]: Simplify 0 into 0 28.564 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 28.564 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n)) 28.564 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 28.564 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 28.564 * [taylor]: Taking taylor expansion of -2 in n 28.564 * [backup-simplify]: Simplify -2 into -2 28.564 * [taylor]: Taking taylor expansion of (/ PI n) in n 28.564 * [taylor]: Taking taylor expansion of PI in n 28.564 * [backup-simplify]: Simplify PI into PI 28.564 * [taylor]: Taking taylor expansion of n in n 28.564 * [backup-simplify]: Simplify 0 into 0 28.564 * [backup-simplify]: Simplify 1 into 1 28.565 * [backup-simplify]: Simplify (/ PI 1) into PI 28.565 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 28.565 * [taylor]: Taking taylor expansion of -2 in n 28.565 * [backup-simplify]: Simplify -2 into -2 28.565 * [taylor]: Taking taylor expansion of (/ PI n) in n 28.565 * [taylor]: Taking taylor expansion of PI in n 28.565 * [backup-simplify]: Simplify PI into PI 28.565 * [taylor]: Taking taylor expansion of n in n 28.565 * [backup-simplify]: Simplify 0 into 0 28.565 * [backup-simplify]: Simplify 1 into 1 28.565 * [backup-simplify]: Simplify (/ PI 1) into PI 28.565 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 28.566 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 28.566 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 28.567 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 28.567 * [backup-simplify]: Simplify 0 into 0 28.567 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 28.568 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 28.568 * [backup-simplify]: Simplify 0 into 0 28.569 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 28.569 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 28.569 * [backup-simplify]: Simplify 0 into 0 28.570 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 28.571 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 28.571 * [backup-simplify]: Simplify 0 into 0 28.572 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 28.573 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 28.573 * [backup-simplify]: Simplify 0 into 0 28.574 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 28.574 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 28.575 * [backup-simplify]: Simplify 0 into 0 28.575 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 28.575 * * * [progress]: simplifying candidates 28.575 * * * * [progress]: [ 1 / 188 ] simplifiying candidate # 28.575 * * * * [progress]: [ 2 / 188 ] simplifiying candidate # 28.575 * * * * [progress]: [ 3 / 188 ] simplifiying candidate # 28.575 * * * * [progress]: [ 4 / 188 ] simplifiying candidate # 28.575 * * * * [progress]: [ 5 / 188 ] simplifiying candidate # 28.575 * * * * [progress]: [ 6 / 188 ] simplifiying candidate # 28.575 * * * * [progress]: [ 7 / 188 ] simplifiying candidate # 28.575 * * * * [progress]: [ 8 / 188 ] simplifiying candidate # 28.575 * * * * [progress]: [ 9 / 188 ] simplifiying candidate # 28.576 * * * * [progress]: [ 10 / 188 ] simplifiying candidate # 28.576 * * * * [progress]: [ 11 / 188 ] simplifiying candidate # 28.576 * * * * [progress]: [ 12 / 188 ] simplifiying candidate # 28.576 * * * * [progress]: [ 13 / 188 ] simplifiying candidate # 28.576 * * * * [progress]: [ 14 / 188 ] simplifiying candidate # 28.576 * 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* [progress]: [ 61 / 188 ] simplifiying candidate # 28.579 * * * * [progress]: [ 62 / 188 ] simplifiying candidate # 28.579 * * * * [progress]: [ 63 / 188 ] simplifiying candidate # 28.579 * * * * [progress]: [ 64 / 188 ] simplifiying candidate # 28.579 * * * * [progress]: [ 65 / 188 ] simplifiying candidate # 28.579 * * * * [progress]: [ 66 / 188 ] simplifiying candidate # 28.579 * * * * [progress]: [ 67 / 188 ] simplifiying candidate #real (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))))> 28.579 * * * * [progress]: [ 68 / 188 ] simplifiying candidate # 28.579 * * * * [progress]: [ 69 / 188 ] simplifiying candidate # 28.579 * * * * [progress]: [ 70 / 188 ] simplifiying candidate # 28.579 * * * * [progress]: [ 71 / 188 ] simplifiying candidate # 28.580 * * * * [progress]: [ 72 / 188 ] simplifiying candidate # 28.580 * * * * [progress]: [ 73 / 188 ] simplifiying candidate # 28.580 * * * * [progress]: [ 74 / 188 ] simplifiying candidate # 28.580 * * * * [progress]: [ 75 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* * * * [progress]: [ 106 / 188 ] simplifiying candidate # 28.582 * * * * [progress]: [ 107 / 188 ] simplifiying candidate # 28.582 * * * * [progress]: [ 108 / 188 ] simplifiying candidate # 28.582 * * * * [progress]: [ 109 / 188 ] simplifiying candidate # 28.582 * * * * [progress]: [ 110 / 188 ] simplifiying candidate # 28.583 * * * * [progress]: [ 111 / 188 ] simplifiying candidate # 28.583 * * * * [progress]: [ 112 / 188 ] simplifiying candidate # 28.583 * * * * [progress]: [ 113 / 188 ] simplifiying candidate # 28.583 * * * * [progress]: [ 114 / 188 ] simplifiying candidate # 28.583 * * * * [progress]: [ 115 / 188 ] simplifiying candidate # 28.583 * * * * [progress]: [ 116 / 188 ] simplifiying candidate # 28.583 * * * * [progress]: [ 117 / 188 ] simplifiying candidate # 28.583 * * * * [progress]: [ 118 / 188 ] simplifiying candidate # 28.583 * * * * [progress]: [ 119 / 188 ] simplifiying candidate # 28.583 * * * * [progress]: [ 120 / 188 ] simplifiying candidate # 28.583 * * * * [progress]: [ 121 / 188 ] simplifiying candidate # 28.583 * * * * [progress]: [ 122 / 188 ] simplifiying candidate # 28.583 * * * * [progress]: [ 123 / 188 ] simplifiying candidate # 28.584 * * * * [progress]: [ 124 / 188 ] simplifiying candidate # 28.584 * * * * [progress]: [ 125 / 188 ] simplifiying candidate # 28.584 * * * * [progress]: [ 126 / 188 ] simplifiying candidate # 28.584 * * * * [progress]: [ 127 / 188 ] simplifiying candidate # 28.584 * * * * [progress]: [ 128 / 188 ] simplifiying candidate # 28.584 * * * * [progress]: [ 129 / 188 ] simplifiying candidate # 28.584 * * * * [progress]: [ 130 / 188 ] simplifiying candidate # 28.584 * * * * [progress]: [ 131 / 188 ] simplifiying candidate # 28.584 * * * * [progress]: [ 132 / 188 ] simplifiying candidate # 28.584 * * * * [progress]: [ 133 / 188 ] simplifiying candidate # 28.584 * * * * [progress]: [ 134 / 188 ] simplifiying candidate #real (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))> 28.584 * * * * [progress]: [ 135 / 188 ] simplifiying candidate # 28.584 * * * * [progress]: [ 136 / 188 ] simplifiying candidate # 28.584 * * * * [progress]: [ 137 / 188 ] simplifiying candidate # 28.584 * * * * [progress]: [ 138 / 188 ] simplifiying candidate # 28.585 * * * * [progress]: [ 139 / 188 ] simplifiying candidate # 28.585 * * * * [progress]: [ 140 / 188 ] simplifiying candidate # 28.585 * * * * [progress]: [ 141 / 188 ] simplifiying candidate # 28.585 * * * * [progress]: [ 142 / 188 ] simplifiying candidate # 28.585 * * * * [progress]: [ 143 / 188 ] simplifiying candidate # 28.585 * * * * [progress]: [ 144 / 188 ] simplifiying candidate # 28.585 * * * * [progress]: [ 145 / 188 ] simplifiying candidate # 28.585 * * * * [progress]: [ 146 / 188 ] simplifiying candidate # 28.585 * * * * [progress]: [ 147 / 188 ] simplifiying candidate # 28.585 * * * * [progress]: [ 148 / 188 ] simplifiying candidate # 28.585 * * * * [progress]: [ 149 / 188 ] simplifiying candidate # 28.585 * * * * [progress]: [ 150 / 188 ] simplifiying candidate # 28.585 * * * * [progress]: [ 151 / 188 ] simplifiying candidate # 28.585 * * * * [progress]: [ 152 / 188 ] simplifiying candidate # 28.585 * * * * [progress]: [ 153 / 188 ] simplifiying candidate # 28.585 * * * * [progress]: [ 154 / 188 ] simplifiying candidate #real (real->posit16 (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))))> 28.586 * * * * [progress]: [ 155 / 188 ] simplifiying candidate # 28.586 * * * * [progress]: [ 156 / 188 ] simplifiying candidate # 28.586 * * * * [progress]: [ 157 / 188 ] simplifiying candidate # 28.586 * * * * [progress]: [ 158 / 188 ] simplifiying candidate # 28.586 * * * * [progress]: [ 159 / 188 ] simplifiying candidate # 28.586 * * * * [progress]: [ 160 / 188 ] simplifiying candidate # 28.586 * * * * [progress]: [ 161 / 188 ] simplifiying candidate # 28.586 * * * * [progress]: [ 162 / 188 ] simplifiying candidate # 28.586 * * * * [progress]: [ 163 / 188 ] 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candidate # 28.587 * * * * [progress]: [ 177 / 188 ] simplifiying candidate # 28.587 * * * * [progress]: [ 178 / 188 ] simplifiying candidate # 28.587 * * * * [progress]: [ 179 / 188 ] simplifiying candidate # 28.587 * * * * [progress]: [ 180 / 188 ] simplifiying candidate # 28.587 * * * * [progress]: [ 181 / 188 ] simplifiying candidate # 28.587 * * * * [progress]: [ 182 / 188 ] simplifiying candidate # 28.587 * * * * [progress]: [ 183 / 188 ] simplifiying candidate # 28.587 * * * * [progress]: [ 184 / 188 ] simplifiying candidate # 28.587 * * * * [progress]: [ 185 / 188 ] simplifiying candidate # 28.588 * * * * [progress]: [ 186 / 188 ] simplifiying candidate # 28.588 * * * * [progress]: [ 187 / 188 ] simplifiying candidate # 28.588 * * * * [progress]: [ 188 / 188 ] simplifiying candidate # 28.592 * [simplify]: Simplifying: (expm1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (log1p (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))) (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2))) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (/ k 2)) (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) 1) (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2)))) (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (pow (* n (* 2 PI)) 1) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) (/ 1 1))))) (pow (* n (* 2 PI)) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1)))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) 1)))) (pow (* n (* 2 PI)) (fma (- (/ k 2)) 1 (* (/ k 2) 1))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ 1 2) k)))) (pow (* n (* 2 PI)) (fma (- (/ 1 2)) k (* (/ 1 2) k))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) 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2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* 2 (* n PI)) (* 2 (* n PI)) (* 2 (* n PI)) (* 2 (* n PI)) (* 2 (* n PI)) (* 2 (* n PI)) 28.600 * * [simplify]: iteration 0: 292 enodes 28.723 * * [simplify]: iteration 1: 900 enodes 29.044 * * [simplify]: iteration 2: 2000 enodes 29.407 * * [simplify]: iteration complete: 2000 enodes 29.407 * * [simplify]: Extracting #0: cost 62 inf + 0 29.408 * * [simplify]: Extracting #1: cost 332 inf + 0 29.415 * * [simplify]: Extracting #2: cost 681 inf + 1768 29.422 * * [simplify]: Extracting #3: cost 785 inf + 15150 29.436 * * [simplify]: Extracting #4: cost 618 inf + 54519 29.466 * * [simplify]: Extracting #5: cost 287 inf + 164102 29.517 * * [simplify]: Extracting #6: cost 108 inf + 250766 29.559 * * [simplify]: Extracting #7: cost 34 inf + 291936 29.612 * * [simplify]: Extracting #8: cost 4 inf + 308847 29.682 * * [simplify]: Extracting #9: cost 0 inf + 311182 29.754 * [simplify]: Simplified to: (expm1 (pow (* (* PI 2) n) (- 1/2 (* 1/2 k)))) (log1p (pow (* (* PI 2) n) (- 1/2 (* 1/2 k)))) (* (log (* (* PI 2) n)) (- 1/2 (* 1/2 k))) (* (log (* (* PI 2) n)) (- 1/2 (* 1/2 k))) (* (log (* (* PI 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(* PI 2) n) (log (* (* PI 2) n)) (log (* (* PI 2) n)) (log (* (* PI 2) n)) (* (exp (* n PI)) (exp (* n PI))) (* (* (* (* PI PI) PI) 8) (* (* n n) n)) (* (* (* n n) n) (* (* PI 2) (* (* PI 2) (* PI 2)))) (* (cbrt (* (* PI 2) n)) (cbrt (* (* PI 2) n))) (cbrt (* (* PI 2) n)) (* (* (* PI 2) n) (* (* (* PI 2) n) (* (* PI 2) n))) (sqrt (* (* PI 2) n)) (sqrt (* (* PI 2) n)) (* n 2) (* (cbrt n) (* PI 2)) (* (sqrt n) (* PI 2)) (* (* PI 2) n) (real->posit16 (* (* PI 2) n)) (expm1 (* (* PI 2) n)) (log1p (* (* PI 2) n)) (* (* PI 2) n) (* (* PI 2) n) (log (* (* PI 2) n)) (log (* (* PI 2) n)) (log (* (* PI 2) n)) (* (exp (* n PI)) (exp (* n PI))) (* (* (* (* PI PI) PI) 8) (* (* n n) n)) (* (* (* n n) n) (* (* PI 2) (* (* PI 2) (* PI 2)))) (* (cbrt (* (* PI 2) n)) (cbrt (* (* PI 2) n))) (cbrt (* (* PI 2) n)) (* (* (* PI 2) n) (* (* (* PI 2) n) (* (* PI 2) n))) (sqrt (* (* PI 2) n)) (sqrt (* (* PI 2) n)) (* n 2) (* (cbrt n) (* PI 2)) (* (sqrt n) (* PI 2)) (* (* PI 2) n) (real->posit16 (* (* PI 2) n)) (fma (* 1/4 (log (* PI 2))) (* (* (* k k) (exp (* 1/2 (log (* (* PI 2) n))))) (log n)) (- (fma 1/8 (* (exp (* 1/2 (log (* (* PI 2) n)))) (* (* (log n) k) (* (log n) k))) (fma (* (* (* (log (* PI 2)) (log (* PI 2))) (exp (* 1/2 (log (* (* PI 2) n))))) (* k k)) 1/8 (exp (* 1/2 (log (* (* PI 2) n)))))) (* 1/2 (* k (+ (* (exp (* 1/2 (log (* (* PI 2) n)))) (log n)) (* (log (* PI 2)) (exp (* 1/2 (log (* (* PI 2) n)))))))))) (exp (* (log (* (* PI 2) n)) (- 1/2 (* 1/2 k)))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (fma (* 1/4 (log (* PI 2))) (* (* (* k k) (exp (* 1/2 (log (* (* PI 2) n))))) (log n)) (- (fma 1/8 (* (exp (* 1/2 (log (* (* PI 2) n)))) (* (* (log n) k) (* (log n) k))) (fma (* (* (* (log (* PI 2)) (log (* PI 2))) (exp (* 1/2 (log (* (* PI 2) n))))) (* k k)) 1/8 (exp (* 1/2 (log (* (* PI 2) n)))))) (* 1/2 (* k (+ (* (exp (* 1/2 (log (* (* PI 2) n)))) (log n)) (* (log (* PI 2)) (exp (* 1/2 (log (* (* PI 2) n)))))))))) (exp (* (log (* (* PI 2) n)) (- 1/2 (* 1/2 k)))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* (* PI 2) n) (* (* PI 2) n) (* (* PI 2) n) (* (* PI 2) n) (* (* PI 2) n) (* (* PI 2) n) 29.807 * * * [progress]: adding candidates to table 31.169 * [progress]: [Phase 3 of 3] Extracting. 31.169 * * [regime]: Finding splitpoints for: (# # # # # # # #) 31.170 * * * [regime-changes]: Trying 2 branch expressions: (n k) 31.170 * * * * [regimes]: Trying to branch on n from (# # # # # # # #) 31.225 * * * * [regimes]: Trying to branch on k from (# # # # # # # #) 31.288 * * * [regime]: Found split indices: #